idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
52,801 | Poisson distribution: why does time between events follow an exponential distribution? | Let $X_t$ be the number of arrivals in the Poisson process with rate $\lambda$ between time $0$ and time $t\ge0.$ Then we have
$$
\Pr(X_t=x) = \frac{(\lambda t)^x e^{-\lambda t}}{x!} \text{ for } x=0,1,2,3,\ldots
$$
Let $T$ be the time until the first arrival.
Then the following two events are really both the same even... | Poisson distribution: why does time between events follow an exponential distribution? | Let $X_t$ be the number of arrivals in the Poisson process with rate $\lambda$ between time $0$ and time $t\ge0.$ Then we have
$$
\Pr(X_t=x) = \frac{(\lambda t)^x e^{-\lambda t}}{x!} \text{ for } x=0, | Poisson distribution: why does time between events follow an exponential distribution?
Let $X_t$ be the number of arrivals in the Poisson process with rate $\lambda$ between time $0$ and time $t\ge0.$ Then we have
$$
\Pr(X_t=x) = \frac{(\lambda t)^x e^{-\lambda t}}{x!} \text{ for } x=0,1,2,3,\ldots
$$
Let $T$ be the ti... | Poisson distribution: why does time between events follow an exponential distribution?
Let $X_t$ be the number of arrivals in the Poisson process with rate $\lambda$ between time $0$ and time $t\ge0.$ Then we have
$$
\Pr(X_t=x) = \frac{(\lambda t)^x e^{-\lambda t}}{x!} \text{ for } x=0, |
52,802 | Poisson distribution: why does time between events follow an exponential distribution? | Exponential distribution doesn't imply that time between events grows exponentially. All it tells you is that probability to wait longer between events declines very quickly with waiting time. The probability density is:$$\lambda e^{-\lambda t}$$ where $\lambda$ is Poisson intensity, i.e. average number of events in un... | Poisson distribution: why does time between events follow an exponential distribution? | Exponential distribution doesn't imply that time between events grows exponentially. All it tells you is that probability to wait longer between events declines very quickly with waiting time. The pro | Poisson distribution: why does time between events follow an exponential distribution?
Exponential distribution doesn't imply that time between events grows exponentially. All it tells you is that probability to wait longer between events declines very quickly with waiting time. The probability density is:$$\lambda e^{... | Poisson distribution: why does time between events follow an exponential distribution?
Exponential distribution doesn't imply that time between events grows exponentially. All it tells you is that probability to wait longer between events declines very quickly with waiting time. The pro |
52,803 | Mixed models. Random slopes only, mean and group centering? | This all depends on the nature of your study.
When you fit random intercepts, without random slopes, this assumes that each subject has the same response to the treatment, but each subject has a different baseline value:
When you add random slopes, then you allow each subject to have a different response to the treatm... | Mixed models. Random slopes only, mean and group centering? | This all depends on the nature of your study.
When you fit random intercepts, without random slopes, this assumes that each subject has the same response to the treatment, but each subject has a diffe | Mixed models. Random slopes only, mean and group centering?
This all depends on the nature of your study.
When you fit random intercepts, without random slopes, this assumes that each subject has the same response to the treatment, but each subject has a different baseline value:
When you add random slopes, then you a... | Mixed models. Random slopes only, mean and group centering?
This all depends on the nature of your study.
When you fit random intercepts, without random slopes, this assumes that each subject has the same response to the treatment, but each subject has a diffe |
52,804 | Mixed models. Random slopes only, mean and group centering? | Question is, is a random slopes only model at lvl 3 allowed. Every example I see always has random intercepts first. Is this because it must or because I just got unlucky with examples?
Yes, it is certainly allowed, but as illustrated in the plots in the answer by @Wayne, it is making an assumption about the baseline ... | Mixed models. Random slopes only, mean and group centering? | Question is, is a random slopes only model at lvl 3 allowed. Every example I see always has random intercepts first. Is this because it must or because I just got unlucky with examples?
Yes, it is ce | Mixed models. Random slopes only, mean and group centering?
Question is, is a random slopes only model at lvl 3 allowed. Every example I see always has random intercepts first. Is this because it must or because I just got unlucky with examples?
Yes, it is certainly allowed, but as illustrated in the plots in the answ... | Mixed models. Random slopes only, mean and group centering?
Question is, is a random slopes only model at lvl 3 allowed. Every example I see always has random intercepts first. Is this because it must or because I just got unlucky with examples?
Yes, it is ce |
52,805 | Mixed models. Random slopes only, mean and group centering? | A classic must-read on some aspects is Bill Venables (the Jekyll subset of Ripley/Venables) https://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf.
And as a rare example where fixed zero offsets might be useful: Assume you measure "new-bone growth" after some surgery. By definition newbone is exactly zero at time of surgery... | Mixed models. Random slopes only, mean and group centering? | A classic must-read on some aspects is Bill Venables (the Jekyll subset of Ripley/Venables) https://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf.
And as a rare example where fixed zero offsets might be u | Mixed models. Random slopes only, mean and group centering?
A classic must-read on some aspects is Bill Venables (the Jekyll subset of Ripley/Venables) https://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf.
And as a rare example where fixed zero offsets might be useful: Assume you measure "new-bone growth" after some surge... | Mixed models. Random slopes only, mean and group centering?
A classic must-read on some aspects is Bill Venables (the Jekyll subset of Ripley/Venables) https://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf.
And as a rare example where fixed zero offsets might be u |
52,806 | Importance of the prior | The purpose of a prior is not to reduce uncertainty per se. Rather it is to express what is already known -- and generally agreed upon -- about the parameter or parameters in the model likelihood. Priors can be informative or uniformative. If little is known about a parameter, then an uniformative prior (maximally entr... | Importance of the prior | The purpose of a prior is not to reduce uncertainty per se. Rather it is to express what is already known -- and generally agreed upon -- about the parameter or parameters in the model likelihood. Pri | Importance of the prior
The purpose of a prior is not to reduce uncertainty per se. Rather it is to express what is already known -- and generally agreed upon -- about the parameter or parameters in the model likelihood. Priors can be informative or uniformative. If little is known about a parameter, then an uniformati... | Importance of the prior
The purpose of a prior is not to reduce uncertainty per se. Rather it is to express what is already known -- and generally agreed upon -- about the parameter or parameters in the model likelihood. Pri |
52,807 | Importance of the prior | If priors are supposed to encode "a priori" information of parameters that might be useful during training, then why is it that they are often drawn from probability distributions?
The prior is a distribution or mass function in that the sum of all possible cases must sum to one. That the priors often look like well-... | Importance of the prior | If priors are supposed to encode "a priori" information of parameters that might be useful during training, then why is it that they are often drawn from probability distributions?
The prior is a dis | Importance of the prior
If priors are supposed to encode "a priori" information of parameters that might be useful during training, then why is it that they are often drawn from probability distributions?
The prior is a distribution or mass function in that the sum of all possible cases must sum to one. That the prio... | Importance of the prior
If priors are supposed to encode "a priori" information of parameters that might be useful during training, then why is it that they are often drawn from probability distributions?
The prior is a dis |
52,808 | Variance of sum of dependent random variables | It's quite easy to prove this once you understand the relationship between the covariance and correlation and if you recognize that the variances for both $X_i$ and $X_j$ are identically $\sigma^2$:
\begin{eqnarray*}
V\left[\frac{1}{m}\sum_{i=1}^{m}y_{i}\right] & = & \frac{1}{m^{2}}\left[\sum_{i=1}^{m}V(y_{i})+\sum_{i=... | Variance of sum of dependent random variables | It's quite easy to prove this once you understand the relationship between the covariance and correlation and if you recognize that the variances for both $X_i$ and $X_j$ are identically $\sigma^2$:
\ | Variance of sum of dependent random variables
It's quite easy to prove this once you understand the relationship between the covariance and correlation and if you recognize that the variances for both $X_i$ and $X_j$ are identically $\sigma^2$:
\begin{eqnarray*}
V\left[\frac{1}{m}\sum_{i=1}^{m}y_{i}\right] & = & \frac{... | Variance of sum of dependent random variables
It's quite easy to prove this once you understand the relationship between the covariance and correlation and if you recognize that the variances for both $X_i$ and $X_j$ are identically $\sigma^2$:
\ |
52,809 | Log-normal returns | I suppose you mean $P_t$ and $P_{t-1}$ are i.i.d. Note that we may express
$$ P_t = e^{\mu + \sigma Z_t}, P_{t-1} = e^{\mu + \sigma Z_{t-1}}$$
where $Z_t, Z_{t-1}$ are i.i.d. standard normal. Then
$$ R_t = \frac {P_t - P_{t-1}} {P_{t-1}} = \frac {P_t} {P_{t-1}} -1
= \frac {e^{\mu + \sigma Z_t}} {e^{\mu + \sigma Z_{t-1}... | Log-normal returns | I suppose you mean $P_t$ and $P_{t-1}$ are i.i.d. Note that we may express
$$ P_t = e^{\mu + \sigma Z_t}, P_{t-1} = e^{\mu + \sigma Z_{t-1}}$$
where $Z_t, Z_{t-1}$ are i.i.d. standard normal. Then
$$ | Log-normal returns
I suppose you mean $P_t$ and $P_{t-1}$ are i.i.d. Note that we may express
$$ P_t = e^{\mu + \sigma Z_t}, P_{t-1} = e^{\mu + \sigma Z_{t-1}}$$
where $Z_t, Z_{t-1}$ are i.i.d. standard normal. Then
$$ R_t = \frac {P_t - P_{t-1}} {P_{t-1}} = \frac {P_t} {P_{t-1}} -1
= \frac {e^{\mu + \sigma Z_t}} {e^{\... | Log-normal returns
I suppose you mean $P_t$ and $P_{t-1}$ are i.i.d. Note that we may express
$$ P_t = e^{\mu + \sigma Z_t}, P_{t-1} = e^{\mu + \sigma Z_{t-1}}$$
where $Z_t, Z_{t-1}$ are i.i.d. standard normal. Then
$$ |
52,810 | Log-normal returns | Just some quick thoughts which do not fit into the comment section. If you look at
$$
\log (1+R_t) = \log(P_t) - \log(P_{t-i}) \sim N(0,2\sigma^2)
$$
you find that it is normal distributed (as the difference of two normal distributions).
So $R_t+1$ is lognormally distributed, and $R_t$ is a shifted lognormally distrib... | Log-normal returns | Just some quick thoughts which do not fit into the comment section. If you look at
$$
\log (1+R_t) = \log(P_t) - \log(P_{t-i}) \sim N(0,2\sigma^2)
$$
you find that it is normal distributed (as the dif | Log-normal returns
Just some quick thoughts which do not fit into the comment section. If you look at
$$
\log (1+R_t) = \log(P_t) - \log(P_{t-i}) \sim N(0,2\sigma^2)
$$
you find that it is normal distributed (as the difference of two normal distributions).
So $R_t+1$ is lognormally distributed, and $R_t$ is a shifted ... | Log-normal returns
Just some quick thoughts which do not fit into the comment section. If you look at
$$
\log (1+R_t) = \log(P_t) - \log(P_{t-i}) \sim N(0,2\sigma^2)
$$
you find that it is normal distributed (as the dif |
52,811 | Log-normal returns | Since the returns involve changes in the stock price over consecutive time periods, the answer to your question depends on the joint distribution of the stock price over time. Since you have only specified the marginal distribution of the stock price, you have not given enough information in your question to determine... | Log-normal returns | Since the returns involve changes in the stock price over consecutive time periods, the answer to your question depends on the joint distribution of the stock price over time. Since you have only spe | Log-normal returns
Since the returns involve changes in the stock price over consecutive time periods, the answer to your question depends on the joint distribution of the stock price over time. Since you have only specified the marginal distribution of the stock price, you have not given enough information in your qu... | Log-normal returns
Since the returns involve changes in the stock price over consecutive time periods, the answer to your question depends on the joint distribution of the stock price over time. Since you have only spe |
52,812 | Bayesian inference - iterative updating with Bernoulli distribution | The fact that your first graph merely oscillates between two values suggests to me that you are resetting the prior each time you perform an iteration. So what you are seeing in the graph is a sequence of posteriors, each of which only take one data point into account. That is not the correct method for iterative Bay... | Bayesian inference - iterative updating with Bernoulli distribution | The fact that your first graph merely oscillates between two values suggests to me that you are resetting the prior each time you perform an iteration. So what you are seeing in the graph is a sequen | Bayesian inference - iterative updating with Bernoulli distribution
The fact that your first graph merely oscillates between two values suggests to me that you are resetting the prior each time you perform an iteration. So what you are seeing in the graph is a sequence of posteriors, each of which only take one data p... | Bayesian inference - iterative updating with Bernoulli distribution
The fact that your first graph merely oscillates between two values suggests to me that you are resetting the prior each time you perform an iteration. So what you are seeing in the graph is a sequen |
52,813 | Bayesian inference - iterative updating with Bernoulli distribution | thanks @Ben for insisting that I check my update process. It was broken indeed, I was not updating $P_{posterior}[\theta]$ correctly.
So now I can proclaim that Bayesian inference with Bernoulli works perfectly and I post here the new chart to show it 🙂 | Bayesian inference - iterative updating with Bernoulli distribution | thanks @Ben for insisting that I check my update process. It was broken indeed, I was not updating $P_{posterior}[\theta]$ correctly.
So now I can proclaim that Bayesian inference with Bernoulli works | Bayesian inference - iterative updating with Bernoulli distribution
thanks @Ben for insisting that I check my update process. It was broken indeed, I was not updating $P_{posterior}[\theta]$ correctly.
So now I can proclaim that Bayesian inference with Bernoulli works perfectly and I post here the new chart to show it... | Bayesian inference - iterative updating with Bernoulli distribution
thanks @Ben for insisting that I check my update process. It was broken indeed, I was not updating $P_{posterior}[\theta]$ correctly.
So now I can proclaim that Bayesian inference with Bernoulli works |
52,814 | paired T test: how to plot it? | To me, a bivariate plot of the before/after for observations with a 1:1 line works well.
A histogram of the differences conveys the results as well. | paired T test: how to plot it? | To me, a bivariate plot of the before/after for observations with a 1:1 line works well.
A histogram of the differences conveys the results as well. | paired T test: how to plot it?
To me, a bivariate plot of the before/after for observations with a 1:1 line works well.
A histogram of the differences conveys the results as well. | paired T test: how to plot it?
To me, a bivariate plot of the before/after for observations with a 1:1 line works well.
A histogram of the differences conveys the results as well. |
52,815 | paired T test: how to plot it? | Comment: Perhaps the $n = 200$ differences for the one important variable can be summarized as follows:
summary(d)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-28.180 -2.112 4.113 3.589 9.993 29.806
sum(d > 0)
[1] 134
The mean and median are both about 4 > 0; 134 of the 200 observations are larger
than ... | paired T test: how to plot it? | Comment: Perhaps the $n = 200$ differences for the one important variable can be summarized as follows:
summary(d)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-28.180 -2.112 4.113 3.589 9 | paired T test: how to plot it?
Comment: Perhaps the $n = 200$ differences for the one important variable can be summarized as follows:
summary(d)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-28.180 -2.112 4.113 3.589 9.993 29.806
sum(d > 0)
[1] 134
The mean and median are both about 4 > 0; 134 of the 20... | paired T test: how to plot it?
Comment: Perhaps the $n = 200$ differences for the one important variable can be summarized as follows:
summary(d)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-28.180 -2.112 4.113 3.589 9 |
52,816 | paired T test: how to plot it? | Late to the party but I wanted to add a more recent reference from 2017 to this thread for those like me who are looking for inspiration on how to graph paired data. The reference advocates the use of the hybrid parallel line plot for plotting such data.
The reference is as follows:
Graphic Portrayal of Studies With Pa... | paired T test: how to plot it? | Late to the party but I wanted to add a more recent reference from 2017 to this thread for those like me who are looking for inspiration on how to graph paired data. The reference advocates the use of | paired T test: how to plot it?
Late to the party but I wanted to add a more recent reference from 2017 to this thread for those like me who are looking for inspiration on how to graph paired data. The reference advocates the use of the hybrid parallel line plot for plotting such data.
The reference is as follows:
Graph... | paired T test: how to plot it?
Late to the party but I wanted to add a more recent reference from 2017 to this thread for those like me who are looking for inspiration on how to graph paired data. The reference advocates the use of |
52,817 | paired T test: how to plot it? | In addition to the other excellent answer, it could be useful to have a graphical summary. That could be a histogram of the differences, but even more useful could be a scatterplot of means aganst differences: A Tukey mean-difference plot (also called Bland-Altman plot). For discussion and examples see Bland-Altman (... | paired T test: how to plot it? | In addition to the other excellent answer, it could be useful to have a graphical summary. That could be a histogram of the differences, but even more useful could be a scatterplot of means aganst di | paired T test: how to plot it?
In addition to the other excellent answer, it could be useful to have a graphical summary. That could be a histogram of the differences, but even more useful could be a scatterplot of means aganst differences: A Tukey mean-difference plot (also called Bland-Altman plot). For discussion ... | paired T test: how to plot it?
In addition to the other excellent answer, it could be useful to have a graphical summary. That could be a histogram of the differences, but even more useful could be a scatterplot of means aganst di |
52,818 | Wilcoxon signed-rank test null hypothesis statement | This answer has been revised after being accepted, as I did not adequately appreciate Wilcoxon's critique of the sign test to extend the null hypothesis. I address the difference between the revised and previous answer at the end
The Wilcoxon sign rank test has these null and alternative hypotheses (see Snedecor, G. W.... | Wilcoxon signed-rank test null hypothesis statement | This answer has been revised after being accepted, as I did not adequately appreciate Wilcoxon's critique of the sign test to extend the null hypothesis. I address the difference between the revised a | Wilcoxon signed-rank test null hypothesis statement
This answer has been revised after being accepted, as I did not adequately appreciate Wilcoxon's critique of the sign test to extend the null hypothesis. I address the difference between the revised and previous answer at the end
The Wilcoxon sign rank test has these ... | Wilcoxon signed-rank test null hypothesis statement
This answer has been revised after being accepted, as I did not adequately appreciate Wilcoxon's critique of the sign test to extend the null hypothesis. I address the difference between the revised a |
52,819 | Wilcoxon signed-rank test null hypothesis statement | In the general case, the Wilcoxon ranked-sum test (WRS) doesn't address either the mean or the median, so I think I would avoid mentioning either of these when describing the test.
It is easy to think of cases where the median of the differences is 0 but that the WRS rejects the null hypothesis. (One such case is giv... | Wilcoxon signed-rank test null hypothesis statement | In the general case, the Wilcoxon ranked-sum test (WRS) doesn't address either the mean or the median, so I think I would avoid mentioning either of these when describing the test.
It is easy to thi | Wilcoxon signed-rank test null hypothesis statement
In the general case, the Wilcoxon ranked-sum test (WRS) doesn't address either the mean or the median, so I think I would avoid mentioning either of these when describing the test.
It is easy to think of cases where the median of the differences is 0 but that the WR... | Wilcoxon signed-rank test null hypothesis statement
In the general case, the Wilcoxon ranked-sum test (WRS) doesn't address either the mean or the median, so I think I would avoid mentioning either of these when describing the test.
It is easy to thi |
52,820 | Confidence interval for mean of a uniform distribution | A student-$t$ confidence interval is quite robust to deviations from normality. If the data is uniformly distributed, the following simulation shows that the student-$t$ interval is slightly anti-conservative with a true confidence level around 0.947, for a nominal level of 0.95 and a sample size of $n=10$.
> a <- 0
>... | Confidence interval for mean of a uniform distribution | A student-$t$ confidence interval is quite robust to deviations from normality. If the data is uniformly distributed, the following simulation shows that the student-$t$ interval is slightly anti-con | Confidence interval for mean of a uniform distribution
A student-$t$ confidence interval is quite robust to deviations from normality. If the data is uniformly distributed, the following simulation shows that the student-$t$ interval is slightly anti-conservative with a true confidence level around 0.947, for a nomina... | Confidence interval for mean of a uniform distribution
A student-$t$ confidence interval is quite robust to deviations from normality. If the data is uniformly distributed, the following simulation shows that the student-$t$ interval is slightly anti-con |
52,821 | Adding an observation level random term messes up residuals vs fitted plot. Why? | Thanks for updating your post, Charly. I played with some over-dispersed Poisson data to see the impact of adding an observation level effect in the glmer model on the plot of residual versus fitted values. Here is the R code:
# generate data like here: https://rpubs.com/INBOstats/OLRE
set.seed(324)
n.i <- 10
n.j <-... | Adding an observation level random term messes up residuals vs fitted plot. Why? | Thanks for updating your post, Charly. I played with some over-dispersed Poisson data to see the impact of adding an observation level effect in the glmer model on the plot of residual versus fitted v | Adding an observation level random term messes up residuals vs fitted plot. Why?
Thanks for updating your post, Charly. I played with some over-dispersed Poisson data to see the impact of adding an observation level effect in the glmer model on the plot of residual versus fitted values. Here is the R code:
# generate... | Adding an observation level random term messes up residuals vs fitted plot. Why?
Thanks for updating your post, Charly. I played with some over-dispersed Poisson data to see the impact of adding an observation level effect in the glmer model on the plot of residual versus fitted v |
52,822 | Coding as a categorical or continuous variable? | Given these categories as data beyond my control, I would code
1 No
2 Sometimes
3 Yes
4 Don't know
on these grounds:
Sometimes sounds weaker than Yes, which is more emphatic.
Don't know doesn't usually belong in an ordered sequence.
Then some analyses will call for ignoring 4 and some don't. All depends on t... | Coding as a categorical or continuous variable? | Given these categories as data beyond my control, I would code
1 No
2 Sometimes
3 Yes
4 Don't know
on these grounds:
Sometimes sounds weaker than Yes, which is more emphatic.
Don't know doesn | Coding as a categorical or continuous variable?
Given these categories as data beyond my control, I would code
1 No
2 Sometimes
3 Yes
4 Don't know
on these grounds:
Sometimes sounds weaker than Yes, which is more emphatic.
Don't know doesn't usually belong in an ordered sequence.
Then some analyses will call... | Coding as a categorical or continuous variable?
Given these categories as data beyond my control, I would code
1 No
2 Sometimes
3 Yes
4 Don't know
on these grounds:
Sometimes sounds weaker than Yes, which is more emphatic.
Don't know doesn |
52,823 | Coding as a categorical or continuous variable? | (Assuming for simplicity that we're treating "Do not know" as missing:) The three simple approaches are:
Code it as a categorical covariate. If, for instance, you use "No" as the reference level, then you get two coefficients from your regression: a) the log-odds of the outcome (all else being equal, roughly speaking)... | Coding as a categorical or continuous variable? | (Assuming for simplicity that we're treating "Do not know" as missing:) The three simple approaches are:
Code it as a categorical covariate. If, for instance, you use "No" as the reference level, the | Coding as a categorical or continuous variable?
(Assuming for simplicity that we're treating "Do not know" as missing:) The three simple approaches are:
Code it as a categorical covariate. If, for instance, you use "No" as the reference level, then you get two coefficients from your regression: a) the log-odds of the ... | Coding as a categorical or continuous variable?
(Assuming for simplicity that we're treating "Do not know" as missing:) The three simple approaches are:
Code it as a categorical covariate. If, for instance, you use "No" as the reference level, the |
52,824 | hurdle model with non-zero gaussian distribution in R | If you want to model data that essentially follow a normal distribution for the positive values but have a point mass at zero, you could start with a Gaussian model censored at zero. In the econometric literature this is known as the tobit model.
The next step would be to fit a two-part model with (1) a binary hurdle f... | hurdle model with non-zero gaussian distribution in R | If you want to model data that essentially follow a normal distribution for the positive values but have a point mass at zero, you could start with a Gaussian model censored at zero. In the econometri | hurdle model with non-zero gaussian distribution in R
If you want to model data that essentially follow a normal distribution for the positive values but have a point mass at zero, you could start with a Gaussian model censored at zero. In the econometric literature this is known as the tobit model.
The next step would... | hurdle model with non-zero gaussian distribution in R
If you want to model data that essentially follow a normal distribution for the positive values but have a point mass at zero, you could start with a Gaussian model censored at zero. In the econometri |
52,825 | ML: sampling imbalanced dataset leads to selection bias | By sampling we make the algorithm think that the prior probabilities
of the classes are the same. This seems to affect the predictions as
well and therefore the probabilities cannot be interpreted as
probabilities anymore and have to be recalibrated.
You seem mostly correct, the phenomenon is called prior probab... | ML: sampling imbalanced dataset leads to selection bias | By sampling we make the algorithm think that the prior probabilities
of the classes are the same. This seems to affect the predictions as
well and therefore the probabilities cannot be interpreted | ML: sampling imbalanced dataset leads to selection bias
By sampling we make the algorithm think that the prior probabilities
of the classes are the same. This seems to affect the predictions as
well and therefore the probabilities cannot be interpreted as
probabilities anymore and have to be recalibrated.
You se... | ML: sampling imbalanced dataset leads to selection bias
By sampling we make the algorithm think that the prior probabilities
of the classes are the same. This seems to affect the predictions as
well and therefore the probabilities cannot be interpreted |
52,826 | Is excluding cases with missing data fine for a predictive (not explanatory/descriptive) model? | The answer is - it depends.
The issue with missing data and leaving it out of your model completely is that it might affect the representativeness of your sampled data.
The kind of deletion you are referring to in your question is known as listwise deletion. This is where you exclude an observation completely because... | Is excluding cases with missing data fine for a predictive (not explanatory/descriptive) model? | The answer is - it depends.
The issue with missing data and leaving it out of your model completely is that it might affect the representativeness of your sampled data.
The kind of deletion you are | Is excluding cases with missing data fine for a predictive (not explanatory/descriptive) model?
The answer is - it depends.
The issue with missing data and leaving it out of your model completely is that it might affect the representativeness of your sampled data.
The kind of deletion you are referring to in your que... | Is excluding cases with missing data fine for a predictive (not explanatory/descriptive) model?
The answer is - it depends.
The issue with missing data and leaving it out of your model completely is that it might affect the representativeness of your sampled data.
The kind of deletion you are |
52,827 | Is excluding cases with missing data fine for a predictive (not explanatory/descriptive) model? | It Depends
Whether excluding cases with missing data is fine or not depends on a few factors. Whatever choice is made requires justification, so there is a bit or work to do with the data. The more ancillary information available to you, the better you can make a choice. Testing the randomness of the missing values is ... | Is excluding cases with missing data fine for a predictive (not explanatory/descriptive) model? | It Depends
Whether excluding cases with missing data is fine or not depends on a few factors. Whatever choice is made requires justification, so there is a bit or work to do with the data. The more an | Is excluding cases with missing data fine for a predictive (not explanatory/descriptive) model?
It Depends
Whether excluding cases with missing data is fine or not depends on a few factors. Whatever choice is made requires justification, so there is a bit or work to do with the data. The more ancillary information avai... | Is excluding cases with missing data fine for a predictive (not explanatory/descriptive) model?
It Depends
Whether excluding cases with missing data is fine or not depends on a few factors. Whatever choice is made requires justification, so there is a bit or work to do with the data. The more an |
52,828 | Is excluding cases with missing data fine for a predictive (not explanatory/descriptive) model? | The answer is "Yes". If you both train and apply your model only on the samples with non-missing $x$, then it is totally OK. Your single heroic assumption here is that the process that makes $x$ be missing is the same for the training and test data, which is quite reasonable.
If you want to train and apply your model o... | Is excluding cases with missing data fine for a predictive (not explanatory/descriptive) model? | The answer is "Yes". If you both train and apply your model only on the samples with non-missing $x$, then it is totally OK. Your single heroic assumption here is that the process that makes $x$ be mi | Is excluding cases with missing data fine for a predictive (not explanatory/descriptive) model?
The answer is "Yes". If you both train and apply your model only on the samples with non-missing $x$, then it is totally OK. Your single heroic assumption here is that the process that makes $x$ be missing is the same for th... | Is excluding cases with missing data fine for a predictive (not explanatory/descriptive) model?
The answer is "Yes". If you both train and apply your model only on the samples with non-missing $x$, then it is totally OK. Your single heroic assumption here is that the process that makes $x$ be mi |
52,829 | Haldane's prior Beta(0,0) - Part 1 | Haldane prior is beta distribution with parameters $\alpha = \beta = 0$. So it is
$$
f(p) = \frac{p^{\alpha-1} (1-p)^{\beta-1}}{B(\alpha, \beta)} = \frac{p^{-1}(1-p)^{-1}}{B(0, 0)}
$$
where $B(0, 0)$ is the normalizing constant that is infinite as described in Wikipedia:
The function $p^{-1}(1-p)^{-1}$ can be viewed a... | Haldane's prior Beta(0,0) - Part 1 | Haldane prior is beta distribution with parameters $\alpha = \beta = 0$. So it is
$$
f(p) = \frac{p^{\alpha-1} (1-p)^{\beta-1}}{B(\alpha, \beta)} = \frac{p^{-1}(1-p)^{-1}}{B(0, 0)}
$$
where $B(0, 0)$ | Haldane's prior Beta(0,0) - Part 1
Haldane prior is beta distribution with parameters $\alpha = \beta = 0$. So it is
$$
f(p) = \frac{p^{\alpha-1} (1-p)^{\beta-1}}{B(\alpha, \beta)} = \frac{p^{-1}(1-p)^{-1}}{B(0, 0)}
$$
where $B(0, 0)$ is the normalizing constant that is infinite as described in Wikipedia:
The function... | Haldane's prior Beta(0,0) - Part 1
Haldane prior is beta distribution with parameters $\alpha = \beta = 0$. So it is
$$
f(p) = \frac{p^{\alpha-1} (1-p)^{\beta-1}}{B(\alpha, \beta)} = \frac{p^{-1}(1-p)^{-1}}{B(0, 0)}
$$
where $B(0, 0)$ |
52,830 | Haldane's prior Beta(0,0) - Part 1 | The second expression is correct as this is an improper distribution, i.e. it doesn't integrate to $1$. Thus it doesn't have a density and you can only specify it up to proportionality. | Haldane's prior Beta(0,0) - Part 1 | The second expression is correct as this is an improper distribution, i.e. it doesn't integrate to $1$. Thus it doesn't have a density and you can only specify it up to proportionality. | Haldane's prior Beta(0,0) - Part 1
The second expression is correct as this is an improper distribution, i.e. it doesn't integrate to $1$. Thus it doesn't have a density and you can only specify it up to proportionality. | Haldane's prior Beta(0,0) - Part 1
The second expression is correct as this is an improper distribution, i.e. it doesn't integrate to $1$. Thus it doesn't have a density and you can only specify it up to proportionality. |
52,831 | normality test on small samples | Elaboration on t.f's answer.
The normality test is a sneaky beast, because conceptually it works the other way round than a "normal" statistical test. Normally, you base your knowledge based on the rejection of the null. Here, the "desired" outcome ("proof" of normality) is the non-rejection. However, failure to reject... | normality test on small samples | Elaboration on t.f's answer.
The normality test is a sneaky beast, because conceptually it works the other way round than a "normal" statistical test. Normally, you base your knowledge based on the re | normality test on small samples
Elaboration on t.f's answer.
The normality test is a sneaky beast, because conceptually it works the other way round than a "normal" statistical test. Normally, you base your knowledge based on the rejection of the null. Here, the "desired" outcome ("proof" of normality) is the non-rejec... | normality test on small samples
Elaboration on t.f's answer.
The normality test is a sneaky beast, because conceptually it works the other way round than a "normal" statistical test. Normally, you base your knowledge based on the re |
52,832 | normality test on small samples | Your conclusion is correct, the normality assumption is required for t-test. However the t-test is fairly robust to violations of it. In any case you can use a non parametric for example the test Mann Whitney when you can guarantee the normality assumption.
You should, with such a small amount of observation the power... | normality test on small samples | Your conclusion is correct, the normality assumption is required for t-test. However the t-test is fairly robust to violations of it. In any case you can use a non parametric for example the test Mann | normality test on small samples
Your conclusion is correct, the normality assumption is required for t-test. However the t-test is fairly robust to violations of it. In any case you can use a non parametric for example the test Mann Whitney when you can guarantee the normality assumption.
You should, with such a small... | normality test on small samples
Your conclusion is correct, the normality assumption is required for t-test. However the t-test is fairly robust to violations of it. In any case you can use a non parametric for example the test Mann |
52,833 | normality test on small samples | No data are ever perfectly normally distributed, so the idea that the data have to be normal for the t-test to be applicable is wrong. If it were so, nobody could ever use the t-test.
For a good range of distributions, the t-test is asymptotically valid for large enough sample size due to the Central Limit Theorem, Sl... | normality test on small samples | No data are ever perfectly normally distributed, so the idea that the data have to be normal for the t-test to be applicable is wrong. If it were so, nobody could ever use the t-test.
For a good rang | normality test on small samples
No data are ever perfectly normally distributed, so the idea that the data have to be normal for the t-test to be applicable is wrong. If it were so, nobody could ever use the t-test.
For a good range of distributions, the t-test is asymptotically valid for large enough sample size due ... | normality test on small samples
No data are ever perfectly normally distributed, so the idea that the data have to be normal for the t-test to be applicable is wrong. If it were so, nobody could ever use the t-test.
For a good rang |
52,834 | normality test on small samples | There's one thing nobody talked about: just look at the given data with common sense.
Group B has 2 zeros, then small values and one 1.125. So - why? Typical result, typo (0.125 as the other ones), ....? This data looks so unstable that I would not trust it to be typical. Just try to imagine how a larger sample of this... | normality test on small samples | There's one thing nobody talked about: just look at the given data with common sense.
Group B has 2 zeros, then small values and one 1.125. So - why? Typical result, typo (0.125 as the other ones), .. | normality test on small samples
There's one thing nobody talked about: just look at the given data with common sense.
Group B has 2 zeros, then small values and one 1.125. So - why? Typical result, typo (0.125 as the other ones), ....? This data looks so unstable that I would not trust it to be typical. Just try to ima... | normality test on small samples
There's one thing nobody talked about: just look at the given data with common sense.
Group B has 2 zeros, then small values and one 1.125. So - why? Typical result, typo (0.125 as the other ones), .. |
52,835 | Unstable logistic regression when data not well separated | The warning about "fitted probabilities numerically 0 or 1" might be useful for diagnosing separability, but these issues are only indirectly related.
Here is a dataset and a binomial GLM fit (in gray) where there is enough overlap among the $x$ values for the two response classes that there is little concern about sep... | Unstable logistic regression when data not well separated | The warning about "fitted probabilities numerically 0 or 1" might be useful for diagnosing separability, but these issues are only indirectly related.
Here is a dataset and a binomial GLM fit (in gray | Unstable logistic regression when data not well separated
The warning about "fitted probabilities numerically 0 or 1" might be useful for diagnosing separability, but these issues are only indirectly related.
Here is a dataset and a binomial GLM fit (in gray) where there is enough overlap among the $x$ values for the t... | Unstable logistic regression when data not well separated
The warning about "fitted probabilities numerically 0 or 1" might be useful for diagnosing separability, but these issues are only indirectly related.
Here is a dataset and a binomial GLM fit (in gray |
52,836 | Unstable logistic regression when data not well separated | Perfect seperation will cause the optimization not converge, not converge will cause the coefficients to be very large, and the very large coefficient will cause "fitted probabilities numerically 0 or 1".
On the reverse side, "fitted probabilities numerically 0 or 1" does not mean the fitting does not converge. It just... | Unstable logistic regression when data not well separated | Perfect seperation will cause the optimization not converge, not converge will cause the coefficients to be very large, and the very large coefficient will cause "fitted probabilities numerically 0 or | Unstable logistic regression when data not well separated
Perfect seperation will cause the optimization not converge, not converge will cause the coefficients to be very large, and the very large coefficient will cause "fitted probabilities numerically 0 or 1".
On the reverse side, "fitted probabilities numerically 0 ... | Unstable logistic regression when data not well separated
Perfect seperation will cause the optimization not converge, not converge will cause the coefficients to be very large, and the very large coefficient will cause "fitted probabilities numerically 0 or |
52,837 | Unstable logistic regression when data not well separated | You are having trouble picturing multidimensional separation. While neither X1 nor X2 separately perfectly predict the Y outcome, together they do. Make use of the coplot to avoid this problem in the future
coplot(y ~ x1 | x2, data=l, panel=panel.smooth)
The same recommendations apply that have been described els... | Unstable logistic regression when data not well separated | You are having trouble picturing multidimensional separation. While neither X1 nor X2 separately perfectly predict the Y outcome, together they do. Make use of the coplot to avoid this problem in the | Unstable logistic regression when data not well separated
You are having trouble picturing multidimensional separation. While neither X1 nor X2 separately perfectly predict the Y outcome, together they do. Make use of the coplot to avoid this problem in the future
coplot(y ~ x1 | x2, data=l, panel=panel.smooth)
T... | Unstable logistic regression when data not well separated
You are having trouble picturing multidimensional separation. While neither X1 nor X2 separately perfectly predict the Y outcome, together they do. Make use of the coplot to avoid this problem in the |
52,838 | AIC with test data, is it possible? | The quantity that AIC / AICc estimates is the expected out-of-sample log-likelihood (see Burnham & Anderson 2004, Sec. 2.2),
$$
\mathbf E_y \mathbf E_x [ \log g(x | \hat \theta (y)) ],
$$
(multiplied with $-2$). This formula means, you obtain maximum likelihood parameter estimates from one sample, $\hat \theta (y)$, th... | AIC with test data, is it possible? | The quantity that AIC / AICc estimates is the expected out-of-sample log-likelihood (see Burnham & Anderson 2004, Sec. 2.2),
$$
\mathbf E_y \mathbf E_x [ \log g(x | \hat \theta (y)) ],
$$
(multiplied | AIC with test data, is it possible?
The quantity that AIC / AICc estimates is the expected out-of-sample log-likelihood (see Burnham & Anderson 2004, Sec. 2.2),
$$
\mathbf E_y \mathbf E_x [ \log g(x | \hat \theta (y)) ],
$$
(multiplied with $-2$). This formula means, you obtain maximum likelihood parameter estimates fr... | AIC with test data, is it possible?
The quantity that AIC / AICc estimates is the expected out-of-sample log-likelihood (see Burnham & Anderson 2004, Sec. 2.2),
$$
\mathbf E_y \mathbf E_x [ \log g(x | \hat \theta (y)) ],
$$
(multiplied |
52,839 | AIC with test data, is it possible? | a. Is it possible to use AICc with test data
Information criteria shouldn't be necessary if you are evaluating models on a hold-out dataset. You can just choose the model that produces the lowest error (mean squared error, mean absolute error, or whatever metric you prefer) on the test data.
b. Is there some kind of er... | AIC with test data, is it possible? | a. Is it possible to use AICc with test data
Information criteria shouldn't be necessary if you are evaluating models on a hold-out dataset. You can just choose the model that produces the lowest erro | AIC with test data, is it possible?
a. Is it possible to use AICc with test data
Information criteria shouldn't be necessary if you are evaluating models on a hold-out dataset. You can just choose the model that produces the lowest error (mean squared error, mean absolute error, or whatever metric you prefer) on the te... | AIC with test data, is it possible?
a. Is it possible to use AICc with test data
Information criteria shouldn't be necessary if you are evaluating models on a hold-out dataset. You can just choose the model that produces the lowest erro |
52,840 | Gradient descent explodes if learning rate is too large | The learning rate can seen as step size, $\eta$. As such, gradient descent is taking successive steps in the direction of the minimum. If the step size $\eta$ is too large, it can (plausibly) "jump over" the minima we are trying to reach, ie. we overshoot. This can lead to osculations around the minimum or in some case... | Gradient descent explodes if learning rate is too large | The learning rate can seen as step size, $\eta$. As such, gradient descent is taking successive steps in the direction of the minimum. If the step size $\eta$ is too large, it can (plausibly) "jump ov | Gradient descent explodes if learning rate is too large
The learning rate can seen as step size, $\eta$. As such, gradient descent is taking successive steps in the direction of the minimum. If the step size $\eta$ is too large, it can (plausibly) "jump over" the minima we are trying to reach, ie. we overshoot. This ca... | Gradient descent explodes if learning rate is too large
The learning rate can seen as step size, $\eta$. As such, gradient descent is taking successive steps in the direction of the minimum. If the step size $\eta$ is too large, it can (plausibly) "jump ov |
52,841 | Gradient descent explodes if learning rate is too large | There are theoretical results which show that Gradient Descent (GD) is guaranteed to converge, given that we pick the right step size $\eta$ according to the problem at hand.
As far as understand, you want to minimize the least squares cost $f(p) = (1/3)\|y - Xp\|_2^2$, where $p$ is your decision variable and $X$, $y$ ... | Gradient descent explodes if learning rate is too large | There are theoretical results which show that Gradient Descent (GD) is guaranteed to converge, given that we pick the right step size $\eta$ according to the problem at hand.
As far as understand, you | Gradient descent explodes if learning rate is too large
There are theoretical results which show that Gradient Descent (GD) is guaranteed to converge, given that we pick the right step size $\eta$ according to the problem at hand.
As far as understand, you want to minimize the least squares cost $f(p) = (1/3)\|y - Xp\|... | Gradient descent explodes if learning rate is too large
There are theoretical results which show that Gradient Descent (GD) is guaranteed to converge, given that we pick the right step size $\eta$ according to the problem at hand.
As far as understand, you |
52,842 | Kullback–Leibler divergence | I just wonder why he wants to measure the similarity between the
distributions $p(x|\theta)$ and $p(x|\theta_0)$.
You're kind of asking the wrong question. If we're in a setting where we're using MLE, then the idea behind it is that we're estimating the parameters of our model with the parameters that maximize the l... | Kullback–Leibler divergence | I just wonder why he wants to measure the similarity between the
distributions $p(x|\theta)$ and $p(x|\theta_0)$.
You're kind of asking the wrong question. If we're in a setting where we're using M | Kullback–Leibler divergence
I just wonder why he wants to measure the similarity between the
distributions $p(x|\theta)$ and $p(x|\theta_0)$.
You're kind of asking the wrong question. If we're in a setting where we're using MLE, then the idea behind it is that we're estimating the parameters of our model with the pa... | Kullback–Leibler divergence
I just wonder why he wants to measure the similarity between the
distributions $p(x|\theta)$ and $p(x|\theta_0)$.
You're kind of asking the wrong question. If we're in a setting where we're using M |
52,843 | Same results from bayesian and frequentist hypothesis testing? References needed | With flat priors and a large sample size (and many times without both of these things), (a) Bayesian and frequentist point-estimates will be virtually the same, and (b) the credible and confidence intervals will virtually cover the same range, leading to the same "hypothesis test" decision of "reject" or "fail to rejec... | Same results from bayesian and frequentist hypothesis testing? References needed | With flat priors and a large sample size (and many times without both of these things), (a) Bayesian and frequentist point-estimates will be virtually the same, and (b) the credible and confidence int | Same results from bayesian and frequentist hypothesis testing? References needed
With flat priors and a large sample size (and many times without both of these things), (a) Bayesian and frequentist point-estimates will be virtually the same, and (b) the credible and confidence intervals will virtually cover the same ra... | Same results from bayesian and frequentist hypothesis testing? References needed
With flat priors and a large sample size (and many times without both of these things), (a) Bayesian and frequentist point-estimates will be virtually the same, and (b) the credible and confidence int |
52,844 | Same results from bayesian and frequentist hypothesis testing? References needed | This paper of Altham compares Bayesian and non-Bayesian (Fisher's exact) tests for equal proportions between two groups.
It turns out Fisher’s exact test can be understood as taking the prior Beta(1, 0) and Beta(0, 1) which is a surprising because using the uniform prior Beta(1,1) would have been more intuitive. Altha... | Same results from bayesian and frequentist hypothesis testing? References needed | This paper of Altham compares Bayesian and non-Bayesian (Fisher's exact) tests for equal proportions between two groups.
It turns out Fisher’s exact test can be understood as taking the prior Beta(1, | Same results from bayesian and frequentist hypothesis testing? References needed
This paper of Altham compares Bayesian and non-Bayesian (Fisher's exact) tests for equal proportions between two groups.
It turns out Fisher’s exact test can be understood as taking the prior Beta(1, 0) and Beta(0, 1) which is a surprisin... | Same results from bayesian and frequentist hypothesis testing? References needed
This paper of Altham compares Bayesian and non-Bayesian (Fisher's exact) tests for equal proportions between two groups.
It turns out Fisher’s exact test can be understood as taking the prior Beta(1, |
52,845 | Why this formula for 5 year trend? | The formula is the linear regression of the series (whatever the variable is), which I will call $y$, on time ($x$), giving units-of-$y$ per year. This is then divided by average $y$ and the result given as a percentage to get a percentage annual growth relative to the mean $y$ (the estimate of the middle-year value of... | Why this formula for 5 year trend? | The formula is the linear regression of the series (whatever the variable is), which I will call $y$, on time ($x$), giving units-of-$y$ per year. This is then divided by average $y$ and the result gi | Why this formula for 5 year trend?
The formula is the linear regression of the series (whatever the variable is), which I will call $y$, on time ($x$), giving units-of-$y$ per year. This is then divided by average $y$ and the result given as a percentage to get a percentage annual growth relative to the mean $y$ (the e... | Why this formula for 5 year trend?
The formula is the linear regression of the series (whatever the variable is), which I will call $y$, on time ($x$), giving units-of-$y$ per year. This is then divided by average $y$ and the result gi |
52,846 | Removing features with low variance in classification models | If variables represent different physical quantities their scaling can be different. By changing units (e.g. from measuring distance in kilometers to measuring distance in nanometers) you can change the scaling of a variable arbitrarily, so why would you even consider removing low-variance variables?
What does make sen... | Removing features with low variance in classification models | If variables represent different physical quantities their scaling can be different. By changing units (e.g. from measuring distance in kilometers to measuring distance in nanometers) you can change t | Removing features with low variance in classification models
If variables represent different physical quantities their scaling can be different. By changing units (e.g. from measuring distance in kilometers to measuring distance in nanometers) you can change the scaling of a variable arbitrarily, so why would you even... | Removing features with low variance in classification models
If variables represent different physical quantities their scaling can be different. By changing units (e.g. from measuring distance in kilometers to measuring distance in nanometers) you can change t |
52,847 | Removing features with low variance in classification models | It is not always the case that features with low variance are removed. As @appletree stressed, changing the scale of a feature also change its variance ! So it would be dangerous to discard them.
However, if the variance is zero, it means that the feature is constant and will not improve the performance of the model (o... | Removing features with low variance in classification models | It is not always the case that features with low variance are removed. As @appletree stressed, changing the scale of a feature also change its variance ! So it would be dangerous to discard them.
Howe | Removing features with low variance in classification models
It is not always the case that features with low variance are removed. As @appletree stressed, changing the scale of a feature also change its variance ! So it would be dangerous to discard them.
However, if the variance is zero, it means that the feature is ... | Removing features with low variance in classification models
It is not always the case that features with low variance are removed. As @appletree stressed, changing the scale of a feature also change its variance ! So it would be dangerous to discard them.
Howe |
52,848 | Removing features with low variance in classification models | If there is high correlation between 2 features then you would discard one of them. The features that are removed because of low variance have very low variance, that would be near to zero. You should always perform all the tests with existing data before discarding any features. Variables which are all 0's or have nea... | Removing features with low variance in classification models | If there is high correlation between 2 features then you would discard one of them. The features that are removed because of low variance have very low variance, that would be near to zero. You should | Removing features with low variance in classification models
If there is high correlation between 2 features then you would discard one of them. The features that are removed because of low variance have very low variance, that would be near to zero. You should always perform all the tests with existing data before dis... | Removing features with low variance in classification models
If there is high correlation between 2 features then you would discard one of them. The features that are removed because of low variance have very low variance, that would be near to zero. You should |
52,849 | How to divide $n$ students to $m$ groups so that their level is as close as possible? | If you use the k-means algorithm to cluster your students, it will minimize the sum of squares within each group. This algorithm finds groups by penalizing skill variations in each group. The larger the differences in skill relative to the cluster mean, the larger will be the penalty. So, this should suit your needs.
Y... | How to divide $n$ students to $m$ groups so that their level is as close as possible? | If you use the k-means algorithm to cluster your students, it will minimize the sum of squares within each group. This algorithm finds groups by penalizing skill variations in each group. The larger t | How to divide $n$ students to $m$ groups so that their level is as close as possible?
If you use the k-means algorithm to cluster your students, it will minimize the sum of squares within each group. This algorithm finds groups by penalizing skill variations in each group. The larger the differences in skill relative t... | How to divide $n$ students to $m$ groups so that their level is as close as possible?
If you use the k-means algorithm to cluster your students, it will minimize the sum of squares within each group. This algorithm finds groups by penalizing skill variations in each group. The larger t |
52,850 | How to divide $n$ students to $m$ groups so that their level is as close as possible? | The problem of finding the optimal class assignment is equivalent to minimizing the following objective function:
$$ \sum_{i=1}^{10} \sum_{j=1}^{20} \left\| \mathbf x_{ij} - \boldsymbol\mu_i \right\|^2 $$
where:
$$\mathbf x_{ij} = \text{vector of test scores of the } j^{th} \text{ student in the } i^{th} \text{ class}\... | How to divide $n$ students to $m$ groups so that their level is as close as possible? | The problem of finding the optimal class assignment is equivalent to minimizing the following objective function:
$$ \sum_{i=1}^{10} \sum_{j=1}^{20} \left\| \mathbf x_{ij} - \boldsymbol\mu_i \right\|^ | How to divide $n$ students to $m$ groups so that their level is as close as possible?
The problem of finding the optimal class assignment is equivalent to minimizing the following objective function:
$$ \sum_{i=1}^{10} \sum_{j=1}^{20} \left\| \mathbf x_{ij} - \boldsymbol\mu_i \right\|^2 $$
where:
$$\mathbf x_{ij} = \te... | How to divide $n$ students to $m$ groups so that their level is as close as possible?
The problem of finding the optimal class assignment is equivalent to minimizing the following objective function:
$$ \sum_{i=1}^{10} \sum_{j=1}^{20} \left\| \mathbf x_{ij} - \boldsymbol\mu_i \right\|^ |
52,851 | How to divide $n$ students to $m$ groups so that their level is as close as possible? | Do you think that would be an optimal assignment for the class? I would personally split the groups so that I have the top in each category in different groups. The students can leverage their skills and improve in that way.
I could frame the problem as
$\arg\max\limits_{x \in Cat} Score_x \bigcup \arg\min\limits_{x \... | How to divide $n$ students to $m$ groups so that their level is as close as possible? | Do you think that would be an optimal assignment for the class? I would personally split the groups so that I have the top in each category in different groups. The students can leverage their skills | How to divide $n$ students to $m$ groups so that their level is as close as possible?
Do you think that would be an optimal assignment for the class? I would personally split the groups so that I have the top in each category in different groups. The students can leverage their skills and improve in that way.
I could f... | How to divide $n$ students to $m$ groups so that their level is as close as possible?
Do you think that would be an optimal assignment for the class? I would personally split the groups so that I have the top in each category in different groups. The students can leverage their skills |
52,852 | Mathematical function that maps a vector to an ordered version of that vector | There is a fairly standard notation: given a vector $x=(x_1, x_2, \ldots, x_n)$, its order statistics $(x_{[1]}, x_{[2]}, \ldots, x_{[n]})$ are the permutation of $x$ for which $x_{[1]} \le x_{[2]} \le \cdots \le x_{[n]}$. Some people use parentheses instead of square brackets around the indexes, as in $x_{(i)}$ inste... | Mathematical function that maps a vector to an ordered version of that vector | There is a fairly standard notation: given a vector $x=(x_1, x_2, \ldots, x_n)$, its order statistics $(x_{[1]}, x_{[2]}, \ldots, x_{[n]})$ are the permutation of $x$ for which $x_{[1]} \le x_{[2]} \l | Mathematical function that maps a vector to an ordered version of that vector
There is a fairly standard notation: given a vector $x=(x_1, x_2, \ldots, x_n)$, its order statistics $(x_{[1]}, x_{[2]}, \ldots, x_{[n]})$ are the permutation of $x$ for which $x_{[1]} \le x_{[2]} \le \cdots \le x_{[n]}$. Some people use pa... | Mathematical function that maps a vector to an ordered version of that vector
There is a fairly standard notation: given a vector $x=(x_1, x_2, \ldots, x_n)$, its order statistics $(x_{[1]}, x_{[2]}, \ldots, x_{[n]})$ are the permutation of $x$ for which $x_{[1]} \le x_{[2]} \l |
52,853 | How to have a "None of the above" category in a Logistic Regression? | First of all, you are talking about multinomial regression, not logistic regression. Second, neither logistic regression nor multinomial regression are classifiers. Logistic regression and multinomial regression both predict probabilities of belonging to some class. To make a classifier of them you need a decision rule... | How to have a "None of the above" category in a Logistic Regression? | First of all, you are talking about multinomial regression, not logistic regression. Second, neither logistic regression nor multinomial regression are classifiers. Logistic regression and multinomial | How to have a "None of the above" category in a Logistic Regression?
First of all, you are talking about multinomial regression, not logistic regression. Second, neither logistic regression nor multinomial regression are classifiers. Logistic regression and multinomial regression both predict probabilities of belonging... | How to have a "None of the above" category in a Logistic Regression?
First of all, you are talking about multinomial regression, not logistic regression. Second, neither logistic regression nor multinomial regression are classifiers. Logistic regression and multinomial |
52,854 | How to have a "None of the above" category in a Logistic Regression? | No way, you either have some of the non-class data already and set them into a 6th class and train the model with the 6th class. Or you set some thresholds for scoring the likeliness that a sample falls into each class evaluated by something like hidden markov model, but the accuracy would be worse than machine learnin... | How to have a "None of the above" category in a Logistic Regression? | No way, you either have some of the non-class data already and set them into a 6th class and train the model with the 6th class. Or you set some thresholds for scoring the likeliness that a sample fal | How to have a "None of the above" category in a Logistic Regression?
No way, you either have some of the non-class data already and set them into a 6th class and train the model with the 6th class. Or you set some thresholds for scoring the likeliness that a sample falls into each class evaluated by something like hidd... | How to have a "None of the above" category in a Logistic Regression?
No way, you either have some of the non-class data already and set them into a 6th class and train the model with the 6th class. Or you set some thresholds for scoring the likeliness that a sample fal |
52,855 | $R^2$ Score Vs OOB Score Random Forest | In a cross-sectional data set (no time series or panel data), the OOB estimate of true performance of a random forest is usually very accurate and in my opinion can even replace (cross-)validation. Put differently, you can trust the OOB accuracy in such cases. This is in constrast to the insample (training set) accurac... | $R^2$ Score Vs OOB Score Random Forest | In a cross-sectional data set (no time series or panel data), the OOB estimate of true performance of a random forest is usually very accurate and in my opinion can even replace (cross-)validation. Pu | $R^2$ Score Vs OOB Score Random Forest
In a cross-sectional data set (no time series or panel data), the OOB estimate of true performance of a random forest is usually very accurate and in my opinion can even replace (cross-)validation. Put differently, you can trust the OOB accuracy in such cases. This is in constrast... | $R^2$ Score Vs OOB Score Random Forest
In a cross-sectional data set (no time series or panel data), the OOB estimate of true performance of a random forest is usually very accurate and in my opinion can even replace (cross-)validation. Pu |
52,856 | $R^2$ Score Vs OOB Score Random Forest | How you split your data is fine but it's not right to use your test case for improving your model.
... but this is the highest test accuracy ...
You can't do that. You should look at the cross-validation accuracy, that is your OOB.
It's fine to look at $R^2$, but OOB is generally considered the most unbiased approach... | $R^2$ Score Vs OOB Score Random Forest | How you split your data is fine but it's not right to use your test case for improving your model.
... but this is the highest test accuracy ...
You can't do that. You should look at the cross-valid | $R^2$ Score Vs OOB Score Random Forest
How you split your data is fine but it's not right to use your test case for improving your model.
... but this is the highest test accuracy ...
You can't do that. You should look at the cross-validation accuracy, that is your OOB.
It's fine to look at $R^2$, but OOB is generall... | $R^2$ Score Vs OOB Score Random Forest
How you split your data is fine but it's not right to use your test case for improving your model.
... but this is the highest test accuracy ...
You can't do that. You should look at the cross-valid |
52,857 | Why is $\frac{1}{n}\sum_{i=1}^{n}(y_i-\bar{y})^2=\frac{1}{n^2}\sum_{i<j}(y_i-y_j)^2$ | Recall that, if $\text{var}(X_i)=\sigma^2$ then
$$\mathbb{E}[(X_i-X_j)^2]=\text{var}(X_i-X_j)=2\sigma^2$$
The expansion that helps is
\begin{align*}
\sum_{i<j}(y_i-y_j)^2&=\frac{1}{2}\sum_{i<j}(y_i-y_j)^2+\frac{1}{2}\sum_{i>j}(y_i-y_j)^2\qquad\text{[by symmetry]}\\&=\frac{1}{2}\sum_{i<j}(y_i-y_j)^2+\frac{1}{2}\sum_{i>j... | Why is $\frac{1}{n}\sum_{i=1}^{n}(y_i-\bar{y})^2=\frac{1}{n^2}\sum_{i<j}(y_i-y_j)^2$ | Recall that, if $\text{var}(X_i)=\sigma^2$ then
$$\mathbb{E}[(X_i-X_j)^2]=\text{var}(X_i-X_j)=2\sigma^2$$
The expansion that helps is
\begin{align*}
\sum_{i<j}(y_i-y_j)^2&=\frac{1}{2}\sum_{i<j}(y_i-y_ | Why is $\frac{1}{n}\sum_{i=1}^{n}(y_i-\bar{y})^2=\frac{1}{n^2}\sum_{i<j}(y_i-y_j)^2$
Recall that, if $\text{var}(X_i)=\sigma^2$ then
$$\mathbb{E}[(X_i-X_j)^2]=\text{var}(X_i-X_j)=2\sigma^2$$
The expansion that helps is
\begin{align*}
\sum_{i<j}(y_i-y_j)^2&=\frac{1}{2}\sum_{i<j}(y_i-y_j)^2+\frac{1}{2}\sum_{i>j}(y_i-y_j)... | Why is $\frac{1}{n}\sum_{i=1}^{n}(y_i-\bar{y})^2=\frac{1}{n^2}\sum_{i<j}(y_i-y_j)^2$
Recall that, if $\text{var}(X_i)=\sigma^2$ then
$$\mathbb{E}[(X_i-X_j)^2]=\text{var}(X_i-X_j)=2\sigma^2$$
The expansion that helps is
\begin{align*}
\sum_{i<j}(y_i-y_j)^2&=\frac{1}{2}\sum_{i<j}(y_i-y_ |
52,858 | What is the difference between sample space and random variable? | From statistical inference by Casella and Berger,
Definition 1.1.1 The set, $S$, of all possible outcomes of a particular experiment is called the sample space for the experiment.
So sample space can be thought of as all possible observations one could make from a particular experiment. A sample space for a coin tos... | What is the difference between sample space and random variable? | From statistical inference by Casella and Berger,
Definition 1.1.1 The set, $S$, of all possible outcomes of a particular experiment is called the sample space for the experiment.
So sample space c | What is the difference between sample space and random variable?
From statistical inference by Casella and Berger,
Definition 1.1.1 The set, $S$, of all possible outcomes of a particular experiment is called the sample space for the experiment.
So sample space can be thought of as all possible observations one could... | What is the difference between sample space and random variable?
From statistical inference by Casella and Berger,
Definition 1.1.1 The set, $S$, of all possible outcomes of a particular experiment is called the sample space for the experiment.
So sample space c |
52,859 | What is the difference between sample space and random variable? | A sample space is the SET of values a random variable can take.
You can think of random variable as an unopened box. This unopened box contains each member of the sample space with some probability.
In your example of a dice roll, the sample space is {1,2,3,4,5,6}. The random variable that represents a roll of the di... | What is the difference between sample space and random variable? | A sample space is the SET of values a random variable can take.
You can think of random variable as an unopened box. This unopened box contains each member of the sample space with some probability. | What is the difference between sample space and random variable?
A sample space is the SET of values a random variable can take.
You can think of random variable as an unopened box. This unopened box contains each member of the sample space with some probability.
In your example of a dice roll, the sample space is {1... | What is the difference between sample space and random variable?
A sample space is the SET of values a random variable can take.
You can think of random variable as an unopened box. This unopened box contains each member of the sample space with some probability. |
52,860 | What is the difference between sample space and random variable? | Amazonian's answer is wrong. The sample space IS NOT the set of values a random variable can take. The sample space is the domain upon which a random variable is defined. The example Amazonian gave is one example of a random variable whose values happen to be the elements in the sample space.
A random variable is a fun... | What is the difference between sample space and random variable? | Amazonian's answer is wrong. The sample space IS NOT the set of values a random variable can take. The sample space is the domain upon which a random variable is defined. The example Amazonian gave is | What is the difference between sample space and random variable?
Amazonian's answer is wrong. The sample space IS NOT the set of values a random variable can take. The sample space is the domain upon which a random variable is defined. The example Amazonian gave is one example of a random variable whose values happen t... | What is the difference between sample space and random variable?
Amazonian's answer is wrong. The sample space IS NOT the set of values a random variable can take. The sample space is the domain upon which a random variable is defined. The example Amazonian gave is |
52,861 | What is the difference between sample space and random variable? | When the sample space consists
exclusively of real numbers (as in your examples),
there is no difference between the sample space and the random variable.
The difference arises in other situations, because
the sample space may be a set of arbitrary elements, e.g. $\{\color{red} {\text{red}}, \color{green... | What is the difference between sample space and random variable? | When the sample space consists
exclusively of real numbers (as in your examples),
there is no difference between the sample space and the random variable.
The difference arises in other situations, | What is the difference between sample space and random variable?
When the sample space consists
exclusively of real numbers (as in your examples),
there is no difference between the sample space and the random variable.
The difference arises in other situations, because
the sample space may be a set of a... | What is the difference between sample space and random variable?
When the sample space consists
exclusively of real numbers (as in your examples),
there is no difference between the sample space and the random variable.
The difference arises in other situations, |
52,862 | What is the difference between sample space and random variable? | I believe the confusion comes from the choice of examples used. For sake of clarity lets use instead the example of the throw of 2 dices. Then, in that case the sample space would be: {(1,1),(1,2),(2,1),(1,3),(3,1),...,(5,6),(6,5),(6,6)}.
A random variable is just a function having this set as domain and the Reals as c... | What is the difference between sample space and random variable? | I believe the confusion comes from the choice of examples used. For sake of clarity lets use instead the example of the throw of 2 dices. Then, in that case the sample space would be: {(1,1),(1,2),(2, | What is the difference between sample space and random variable?
I believe the confusion comes from the choice of examples used. For sake of clarity lets use instead the example of the throw of 2 dices. Then, in that case the sample space would be: {(1,1),(1,2),(2,1),(1,3),(3,1),...,(5,6),(6,5),(6,6)}.
A random variabl... | What is the difference between sample space and random variable?
I believe the confusion comes from the choice of examples used. For sake of clarity lets use instead the example of the throw of 2 dices. Then, in that case the sample space would be: {(1,1),(1,2),(2, |
52,863 | What is the difference between sample space and random variable? | For flipping a coin:
The sample space is {head, tail},
the random variable is {0, 1}.
For rolling a die:
The sample space is {1, 2, 3, 4, 5, 6},
the random variable is {1, 2, 3, 4, 5, 6}, too,
because the sample space already is the set of numbers only.
In other words, the sample space is the set of arbitrary eleme... | What is the difference between sample space and random variable? | For flipping a coin:
The sample space is {head, tail},
the random variable is {0, 1}.
For rolling a die:
The sample space is {1, 2, 3, 4, 5, 6},
the random variable is {1, 2, 3, 4, 5, 6}, too,
beca | What is the difference between sample space and random variable?
For flipping a coin:
The sample space is {head, tail},
the random variable is {0, 1}.
For rolling a die:
The sample space is {1, 2, 3, 4, 5, 6},
the random variable is {1, 2, 3, 4, 5, 6}, too,
because the sample space already is the set of numbers only... | What is the difference between sample space and random variable?
For flipping a coin:
The sample space is {head, tail},
the random variable is {0, 1}.
For rolling a die:
The sample space is {1, 2, 3, 4, 5, 6},
the random variable is {1, 2, 3, 4, 5, 6}, too,
beca |
52,864 | Why are the ROC curves not smooth? | I know the question is two years old and the technical answer was given in the comments, but a more elaborate answer might help others still struggling with the concepts.
OP's ROC curve wrong because he used the predicted values of his models instead of the probabilities.
What does this mean?
When a model is trained ... | Why are the ROC curves not smooth? | I know the question is two years old and the technical answer was given in the comments, but a more elaborate answer might help others still struggling with the concepts.
OP's ROC curve wrong because | Why are the ROC curves not smooth?
I know the question is two years old and the technical answer was given in the comments, but a more elaborate answer might help others still struggling with the concepts.
OP's ROC curve wrong because he used the predicted values of his models instead of the probabilities.
What does ... | Why are the ROC curves not smooth?
I know the question is two years old and the technical answer was given in the comments, but a more elaborate answer might help others still struggling with the concepts.
OP's ROC curve wrong because |
52,865 | Why is $R^2$ the proportion of total variance of the data explained by the model? | There is an error in your equations, $RSS = \sum(Y_i - \hat{Y}_i)^2$
Maybe it would help not looking at so many equations to understand.
RSS is the sum of the residual variance, basically the sum of all the variance that the model can't explain.
Therefore
$\frac{RSS}{\sum{(Y_i - \bar{Y})^2}}$ is $\frac{unexplained \ v... | Why is $R^2$ the proportion of total variance of the data explained by the model? | There is an error in your equations, $RSS = \sum(Y_i - \hat{Y}_i)^2$
Maybe it would help not looking at so many equations to understand.
RSS is the sum of the residual variance, basically the sum of | Why is $R^2$ the proportion of total variance of the data explained by the model?
There is an error in your equations, $RSS = \sum(Y_i - \hat{Y}_i)^2$
Maybe it would help not looking at so many equations to understand.
RSS is the sum of the residual variance, basically the sum of all the variance that the model can't ... | Why is $R^2$ the proportion of total variance of the data explained by the model?
There is an error in your equations, $RSS = \sum(Y_i - \hat{Y}_i)^2$
Maybe it would help not looking at so many equations to understand.
RSS is the sum of the residual variance, basically the sum of |
52,866 | Why is $R^2$ the proportion of total variance of the data explained by the model? | We have $TSS = \sum_i (Y_i - \bar{Y})^2,\ RSS = \sum_i(Y_i - \hat{Y}_i)^2,\ ESS = \sum_i(\hat{Y}_i - \bar{Y})^2$
$TSS$ - total variance, $RSS$ - residual variance, $ESS$ - regression variance
From ANOVA identity we know that
$$TSS = RSS + ESS$$
So we have $R^2 = 1 - \frac{RSS}{TSS} = \frac{ESS}{TSS}$. From last equat... | Why is $R^2$ the proportion of total variance of the data explained by the model? | We have $TSS = \sum_i (Y_i - \bar{Y})^2,\ RSS = \sum_i(Y_i - \hat{Y}_i)^2,\ ESS = \sum_i(\hat{Y}_i - \bar{Y})^2$
$TSS$ - total variance, $RSS$ - residual variance, $ESS$ - regression variance
From A | Why is $R^2$ the proportion of total variance of the data explained by the model?
We have $TSS = \sum_i (Y_i - \bar{Y})^2,\ RSS = \sum_i(Y_i - \hat{Y}_i)^2,\ ESS = \sum_i(\hat{Y}_i - \bar{Y})^2$
$TSS$ - total variance, $RSS$ - residual variance, $ESS$ - regression variance
From ANOVA identity we know that
$$TSS = RSS... | Why is $R^2$ the proportion of total variance of the data explained by the model?
We have $TSS = \sum_i (Y_i - \bar{Y})^2,\ RSS = \sum_i(Y_i - \hat{Y}_i)^2,\ ESS = \sum_i(\hat{Y}_i - \bar{Y})^2$
$TSS$ - total variance, $RSS$ - residual variance, $ESS$ - regression variance
From A |
52,867 | $X,Y,Z$ are IID ${\rm Poisson}(\lambda)$. Find the correlation between $X$ and $X+Y+Z$ | If $X,Y$ and $Z$ are independent, then their covariance is 0. So is their correlation.
For the sums look at
$$
cov(X,X+Y+Z) = Cov(X,X) + Cov(X,Y) + Cov(X,Z)
$$
the latter 2 are zero (due to independence) and the first one is $Cov(X,X) = Var(X) = \lambda$.
For the variance we get
$$
VAR(X+Y+Z) = VAR(X) + VAR(Y) + VAR(Z... | $X,Y,Z$ are IID ${\rm Poisson}(\lambda)$. Find the correlation between $X$ and $X+Y+Z$ | If $X,Y$ and $Z$ are independent, then their covariance is 0. So is their correlation.
For the sums look at
$$
cov(X,X+Y+Z) = Cov(X,X) + Cov(X,Y) + Cov(X,Z)
$$
the latter 2 are zero (due to independe | $X,Y,Z$ are IID ${\rm Poisson}(\lambda)$. Find the correlation between $X$ and $X+Y+Z$
If $X,Y$ and $Z$ are independent, then their covariance is 0. So is their correlation.
For the sums look at
$$
cov(X,X+Y+Z) = Cov(X,X) + Cov(X,Y) + Cov(X,Z)
$$
the latter 2 are zero (due to independence) and the first one is $Cov(X,... | $X,Y,Z$ are IID ${\rm Poisson}(\lambda)$. Find the correlation between $X$ and $X+Y+Z$
If $X,Y$ and $Z$ are independent, then their covariance is 0. So is their correlation.
For the sums look at
$$
cov(X,X+Y+Z) = Cov(X,X) + Cov(X,Y) + Cov(X,Z)
$$
the latter 2 are zero (due to independe |
52,868 | Distribution given sum | It can be instructional and satisfying to work this out using basic statistical knowledge, rather than just doing the integrals. It turns out that no calculations are needed!
Here's the circle of ideas:
The $X_i$ can be thought of as waiting times between random events.
When the waiting times have independent identi... | Distribution given sum | It can be instructional and satisfying to work this out using basic statistical knowledge, rather than just doing the integrals. It turns out that no calculations are needed!
Here's the circle of ide | Distribution given sum
It can be instructional and satisfying to work this out using basic statistical knowledge, rather than just doing the integrals. It turns out that no calculations are needed!
Here's the circle of ideas:
The $X_i$ can be thought of as waiting times between random events.
When the waiting times ... | Distribution given sum
It can be instructional and satisfying to work this out using basic statistical knowledge, rather than just doing the integrals. It turns out that no calculations are needed!
Here's the circle of ide |
52,869 | Distribution given sum | This might be the most "text book" answer on $f_{X_1|Y}(x_1|y)$.
Let $Z = X_2 + ... + X_n$. Then $Y = Z + X_1$.
First the joint distribution of $(Z, X_1)$ which is $f_{Z,X_1}(z,x_1) = \dfrac{\lambda^{n-1}}{\Gamma(n-1)}\,z^{n-2}\,e^{-z\lambda}\,\lambda \times e^{-x_1 \lambda}$ for $z \ge 0, x_1 \ge 0$.
Next we get the ... | Distribution given sum | This might be the most "text book" answer on $f_{X_1|Y}(x_1|y)$.
Let $Z = X_2 + ... + X_n$. Then $Y = Z + X_1$.
First the joint distribution of $(Z, X_1)$ which is $f_{Z,X_1}(z,x_1) = \dfrac{\lambda^ | Distribution given sum
This might be the most "text book" answer on $f_{X_1|Y}(x_1|y)$.
Let $Z = X_2 + ... + X_n$. Then $Y = Z + X_1$.
First the joint distribution of $(Z, X_1)$ which is $f_{Z,X_1}(z,x_1) = \dfrac{\lambda^{n-1}}{\Gamma(n-1)}\,z^{n-2}\,e^{-z\lambda}\,\lambda \times e^{-x_1 \lambda}$ for $z \ge 0, x_1 \... | Distribution given sum
This might be the most "text book" answer on $f_{X_1|Y}(x_1|y)$.
Let $Z = X_2 + ... + X_n$. Then $Y = Z + X_1$.
First the joint distribution of $(Z, X_1)$ which is $f_{Z,X_1}(z,x_1) = \dfrac{\lambda^ |
52,870 | What's the difference between prior and marginal probabilities? | $P(S=s)$ and $P(R=r)$ both are marginal probabilities from the following table
$$
\begin{array}{c|cc|c}
& R=0 & R=1 \\
\hline
S=0 & 0.20 & 0.08 & 0.28 \\
S=1 & 0.70 & 0.02 & 0.72 \\
\hline
& 0.90 & 0.10 &
\end{array}
$$
Given such table, you can calculate conditional probabiliti... | What's the difference between prior and marginal probabilities? | $P(S=s)$ and $P(R=r)$ both are marginal probabilities from the following table
$$
\begin{array}{c|cc|c}
& R=0 & R=1 \\
\hline
S=0 & 0.20 & 0.08 & 0.28 \\
S=1 & 0.70 & 0.02 & 0.7 | What's the difference between prior and marginal probabilities?
$P(S=s)$ and $P(R=r)$ both are marginal probabilities from the following table
$$
\begin{array}{c|cc|c}
& R=0 & R=1 \\
\hline
S=0 & 0.20 & 0.08 & 0.28 \\
S=1 & 0.70 & 0.02 & 0.72 \\
\hline
& 0.90 & 0.10 &
\end{array... | What's the difference between prior and marginal probabilities?
$P(S=s)$ and $P(R=r)$ both are marginal probabilities from the following table
$$
\begin{array}{c|cc|c}
& R=0 & R=1 \\
\hline
S=0 & 0.20 & 0.08 & 0.28 \\
S=1 & 0.70 & 0.02 & 0.7 |
52,871 | What's the difference between prior and marginal probabilities? | If you think of a table with columns as possible parameter values and with rows as possible data values (see image below), then the lower marginal distribution is the prior distribution on the parameter. The observed data indicate which row of the table is the row we actually live in, so to speak, hence we conditionali... | What's the difference between prior and marginal probabilities? | If you think of a table with columns as possible parameter values and with rows as possible data values (see image below), then the lower marginal distribution is the prior distribution on the paramet | What's the difference between prior and marginal probabilities?
If you think of a table with columns as possible parameter values and with rows as possible data values (see image below), then the lower marginal distribution is the prior distribution on the parameter. The observed data indicate which row of the table is... | What's the difference between prior and marginal probabilities?
If you think of a table with columns as possible parameter values and with rows as possible data values (see image below), then the lower marginal distribution is the prior distribution on the paramet |
52,872 | Repeated measures ANOVA in R: Error(Subject) vs. Error(Subject/Day) | Depending on the contrasts you are using, the R command
aov(Temperature~Day+Error(Subject))
fits a model like
$$y_{ij} = \mu + \beta_j + b_i + \epsilon_{ij},$$
where $y_{ij}$ is the response value for the $i$th individual at the $j$th period (day), $\mu$ is global mean, $\beta_j$ is the effect of $j$th day, $b_i\sim ... | Repeated measures ANOVA in R: Error(Subject) vs. Error(Subject/Day) | Depending on the contrasts you are using, the R command
aov(Temperature~Day+Error(Subject))
fits a model like
$$y_{ij} = \mu + \beta_j + b_i + \epsilon_{ij},$$
where $y_{ij}$ is the response value f | Repeated measures ANOVA in R: Error(Subject) vs. Error(Subject/Day)
Depending on the contrasts you are using, the R command
aov(Temperature~Day+Error(Subject))
fits a model like
$$y_{ij} = \mu + \beta_j + b_i + \epsilon_{ij},$$
where $y_{ij}$ is the response value for the $i$th individual at the $j$th period (day), $... | Repeated measures ANOVA in R: Error(Subject) vs. Error(Subject/Day)
Depending on the contrasts you are using, the R command
aov(Temperature~Day+Error(Subject))
fits a model like
$$y_{ij} = \mu + \beta_j + b_i + \epsilon_{ij},$$
where $y_{ij}$ is the response value f |
52,873 | What is this math symbol used in a backpropagation tutorial: $\circ$ | The symbol $\circ$ is often used to denote element-wise multiplication (a.k.a. Hadamard product, Schur product, entrywise product, component-wise multiplication); $\odot$ and $*$ are common alternatives. | What is this math symbol used in a backpropagation tutorial: $\circ$ | The symbol $\circ$ is often used to denote element-wise multiplication (a.k.a. Hadamard product, Schur product, entrywise product, component-wise multiplication); $\odot$ and $*$ are common alternativ | What is this math symbol used in a backpropagation tutorial: $\circ$
The symbol $\circ$ is often used to denote element-wise multiplication (a.k.a. Hadamard product, Schur product, entrywise product, component-wise multiplication); $\odot$ and $*$ are common alternatives. | What is this math symbol used in a backpropagation tutorial: $\circ$
The symbol $\circ$ is often used to denote element-wise multiplication (a.k.a. Hadamard product, Schur product, entrywise product, component-wise multiplication); $\odot$ and $*$ are common alternativ |
52,874 | Calculating standard deviation after log transformation | Several approaches:
(i) you can estimate mean and standard deviation on both the original and the log scale as needed, in the usual fashion. However, they may not necessarily be the most efficient way on the untransformed data (nor will the two sets of estimates necessarily be very consistent with each other)
(ii) via ... | Calculating standard deviation after log transformation | Several approaches:
(i) you can estimate mean and standard deviation on both the original and the log scale as needed, in the usual fashion. However, they may not necessarily be the most efficient way | Calculating standard deviation after log transformation
Several approaches:
(i) you can estimate mean and standard deviation on both the original and the log scale as needed, in the usual fashion. However, they may not necessarily be the most efficient way on the untransformed data (nor will the two sets of estimates n... | Calculating standard deviation after log transformation
Several approaches:
(i) you can estimate mean and standard deviation on both the original and the log scale as needed, in the usual fashion. However, they may not necessarily be the most efficient way |
52,875 | Interaction between a predictor and its quadratic form? | The interaction term between x and $x^2$ is $x^3$ . So you are just creating a cubic polynomial regression rather than a quadratic polynomial regression. In general one can create degree n polynomial regressions. Will adding the cubic term, or any other degree term, increase the predictive power of the model ? That is ... | Interaction between a predictor and its quadratic form? | The interaction term between x and $x^2$ is $x^3$ . So you are just creating a cubic polynomial regression rather than a quadratic polynomial regression. In general one can create degree n polynomial | Interaction between a predictor and its quadratic form?
The interaction term between x and $x^2$ is $x^3$ . So you are just creating a cubic polynomial regression rather than a quadratic polynomial regression. In general one can create degree n polynomial regressions. Will adding the cubic term, or any other degree ter... | Interaction between a predictor and its quadratic form?
The interaction term between x and $x^2$ is $x^3$ . So you are just creating a cubic polynomial regression rather than a quadratic polynomial regression. In general one can create degree n polynomial |
52,876 | What is the machine learning technique used by IBM Watson? | Here is a great article by Robert L. Blum: http://www.bobblum.com/ESSAYS/COMPSCI/Watson.html
Among other things it contains useful pointers:
The best high level article on Watson was written by Ferrucci's IBM team (mirror: http://www.aaai.org/ojs/index.php/aimagazine/article/view/2303), and appeared in AI Magazine in ... | What is the machine learning technique used by IBM Watson? | Here is a great article by Robert L. Blum: http://www.bobblum.com/ESSAYS/COMPSCI/Watson.html
Among other things it contains useful pointers:
The best high level article on Watson was written by Ferru | What is the machine learning technique used by IBM Watson?
Here is a great article by Robert L. Blum: http://www.bobblum.com/ESSAYS/COMPSCI/Watson.html
Among other things it contains useful pointers:
The best high level article on Watson was written by Ferrucci's IBM team (mirror: http://www.aaai.org/ojs/index.php/aim... | What is the machine learning technique used by IBM Watson?
Here is a great article by Robert L. Blum: http://www.bobblum.com/ESSAYS/COMPSCI/Watson.html
Among other things it contains useful pointers:
The best high level article on Watson was written by Ferru |
52,877 | What is the machine learning technique used by IBM Watson? | In this Quora question, an IBM researcher answers that the statistical modeling done by Watson is mostly logistic regression, although this is built into a very complex hierarchy. They also state that the statistical modeling is not necessarily the most challenging part of Watson.
I have also independently heard the s... | What is the machine learning technique used by IBM Watson? | In this Quora question, an IBM researcher answers that the statistical modeling done by Watson is mostly logistic regression, although this is built into a very complex hierarchy. They also state that | What is the machine learning technique used by IBM Watson?
In this Quora question, an IBM researcher answers that the statistical modeling done by Watson is mostly logistic regression, although this is built into a very complex hierarchy. They also state that the statistical modeling is not necessarily the most challen... | What is the machine learning technique used by IBM Watson?
In this Quora question, an IBM researcher answers that the statistical modeling done by Watson is mostly logistic regression, although this is built into a very complex hierarchy. They also state that |
52,878 | Chi-squared test: Investigating fruit flies attraction to different colours | You shouldn't be using a 'one-way' or 'goodness-of-fit' chi-squared test here six times over. You should be using a chi-squared test of independence on a two-way contingency table. In addition, as @DJohnson notes below, you need to use the actual counts observed, not average counts (I'm not sure I understand how you ... | Chi-squared test: Investigating fruit flies attraction to different colours | You shouldn't be using a 'one-way' or 'goodness-of-fit' chi-squared test here six times over. You should be using a chi-squared test of independence on a two-way contingency table. In addition, as @ | Chi-squared test: Investigating fruit flies attraction to different colours
You shouldn't be using a 'one-way' or 'goodness-of-fit' chi-squared test here six times over. You should be using a chi-squared test of independence on a two-way contingency table. In addition, as @DJohnson notes below, you need to use the ac... | Chi-squared test: Investigating fruit flies attraction to different colours
You shouldn't be using a 'one-way' or 'goodness-of-fit' chi-squared test here six times over. You should be using a chi-squared test of independence on a two-way contingency table. In addition, as @ |
52,879 | Chi-squared test: Investigating fruit flies attraction to different colours | Gung's test is a test of independence in the two-way classification table. Additional tests are possible, as described in Wicken's book Multiway Contingency Tables Analysis for the Social Sciences, one of the last, great treatments of this topic before the advent of tensor models. As Wickens notes:
There are three dif... | Chi-squared test: Investigating fruit flies attraction to different colours | Gung's test is a test of independence in the two-way classification table. Additional tests are possible, as described in Wicken's book Multiway Contingency Tables Analysis for the Social Sciences, on | Chi-squared test: Investigating fruit flies attraction to different colours
Gung's test is a test of independence in the two-way classification table. Additional tests are possible, as described in Wicken's book Multiway Contingency Tables Analysis for the Social Sciences, one of the last, great treatments of this topi... | Chi-squared test: Investigating fruit flies attraction to different colours
Gung's test is a test of independence in the two-way classification table. Additional tests are possible, as described in Wicken's book Multiway Contingency Tables Analysis for the Social Sciences, on |
52,880 | ReLUs and Gradient Descent for Deep Neural Nets | In practice, it's unlikely that one hidden unit has an input of precisely 0, so it doesn't matter much whether you take 0 or 1 for gradient in that situation. E.g. Theano considers that the gradient at 0 is 0. Tensorflow's playground does the same:
public static RELU: ActivationFunction = {
output: x => Math.max(0,... | ReLUs and Gradient Descent for Deep Neural Nets | In practice, it's unlikely that one hidden unit has an input of precisely 0, so it doesn't matter much whether you take 0 or 1 for gradient in that situation. E.g. Theano considers that the gradient a | ReLUs and Gradient Descent for Deep Neural Nets
In practice, it's unlikely that one hidden unit has an input of precisely 0, so it doesn't matter much whether you take 0 or 1 for gradient in that situation. E.g. Theano considers that the gradient at 0 is 0. Tensorflow's playground does the same:
public static RELU: Act... | ReLUs and Gradient Descent for Deep Neural Nets
In practice, it's unlikely that one hidden unit has an input of precisely 0, so it doesn't matter much whether you take 0 or 1 for gradient in that situation. E.g. Theano considers that the gradient a |
52,881 | How do I interpret these results from a paired t-test? | No, we don't "accept $H_o$", instead we fail to reject the null hypothesis. So we are not "rejecting the null", implying that we don't have enough evidence to assume that the difference in means is different from zero.
The confidence interval includes the value zero, and gives us the ranges of values within which the m... | How do I interpret these results from a paired t-test? | No, we don't "accept $H_o$", instead we fail to reject the null hypothesis. So we are not "rejecting the null", implying that we don't have enough evidence to assume that the difference in means is di | How do I interpret these results from a paired t-test?
No, we don't "accept $H_o$", instead we fail to reject the null hypothesis. So we are not "rejecting the null", implying that we don't have enough evidence to assume that the difference in means is different from zero.
The confidence interval includes the value zer... | How do I interpret these results from a paired t-test?
No, we don't "accept $H_o$", instead we fail to reject the null hypothesis. So we are not "rejecting the null", implying that we don't have enough evidence to assume that the difference in means is di |
52,882 | How do I interpret these results from a paired t-test? | The alternative hypothesis that you proposed is one-sided but you have used a two-sided t-test. Had you set alt="greater" in the t-test to get the one-sided result you would have had p-value = 0.082.
Do not dichotomise the result into significant and not significant on the basis of comparison of your observed p-value a... | How do I interpret these results from a paired t-test? | The alternative hypothesis that you proposed is one-sided but you have used a two-sided t-test. Had you set alt="greater" in the t-test to get the one-sided result you would have had p-value = 0.082.
| How do I interpret these results from a paired t-test?
The alternative hypothesis that you proposed is one-sided but you have used a two-sided t-test. Had you set alt="greater" in the t-test to get the one-sided result you would have had p-value = 0.082.
Do not dichotomise the result into significant and not significan... | How do I interpret these results from a paired t-test?
The alternative hypothesis that you proposed is one-sided but you have used a two-sided t-test. Had you set alt="greater" in the t-test to get the one-sided result you would have had p-value = 0.082.
|
52,883 | Zero conditional mean assumption (how can in not hold?) | In a more technical parlance, I believe your asking, is the strict exogeneity assumption ever violated. Where the strict exogeneity assumption is...
$$E(\epsilon|X)=0$$
In practice this happens all the time. As a matter of fact the majority of the field of econometrics is focused on the failure of this assumption. W... | Zero conditional mean assumption (how can in not hold?) | In a more technical parlance, I believe your asking, is the strict exogeneity assumption ever violated. Where the strict exogeneity assumption is...
$$E(\epsilon|X)=0$$
In practice this happens all t | Zero conditional mean assumption (how can in not hold?)
In a more technical parlance, I believe your asking, is the strict exogeneity assumption ever violated. Where the strict exogeneity assumption is...
$$E(\epsilon|X)=0$$
In practice this happens all the time. As a matter of fact the majority of the field of econo... | Zero conditional mean assumption (how can in not hold?)
In a more technical parlance, I believe your asking, is the strict exogeneity assumption ever violated. Where the strict exogeneity assumption is...
$$E(\epsilon|X)=0$$
In practice this happens all t |
52,884 | Zero conditional mean assumption (how can in not hold?) | In American football, the total score is given by:
Total football score = 6 * (Touchdowns) + 1 * (ExtraPoints) + 2 * (TwoPointConversions) + 2 * (safeties) + 3 * field goals.
But if you ran the regression:
TotalFootBallScore = b1 * touchdowns + b2 * fieldgoals + e
You wouldn't estimate a value of 6 for b1. Regress the ... | Zero conditional mean assumption (how can in not hold?) | In American football, the total score is given by:
Total football score = 6 * (Touchdowns) + 1 * (ExtraPoints) + 2 * (TwoPointConversions) + 2 * (safeties) + 3 * field goals.
But if you ran the regres | Zero conditional mean assumption (how can in not hold?)
In American football, the total score is given by:
Total football score = 6 * (Touchdowns) + 1 * (ExtraPoints) + 2 * (TwoPointConversions) + 2 * (safeties) + 3 * field goals.
But if you ran the regression:
TotalFootBallScore = b1 * touchdowns + b2 * fieldgoals + e... | Zero conditional mean assumption (how can in not hold?)
In American football, the total score is given by:
Total football score = 6 * (Touchdowns) + 1 * (ExtraPoints) + 2 * (TwoPointConversions) + 2 * (safeties) + 3 * field goals.
But if you ran the regres |
52,885 | Alternatives to multilevel model with log transformed outcome | This is a great use case for the inverse hyperbolic sine transformation [1], [2]:
$$
\log\left( y + \sqrt{y^2 + 1} \right)
$$
Except for very small values of y, the inverse sine is approximately equal to log(2yi) or log(2)+log(yi), and so it can be interpreted in exactly the same way as a standard logarithmic dependen... | Alternatives to multilevel model with log transformed outcome | This is a great use case for the inverse hyperbolic sine transformation [1], [2]:
$$
\log\left( y + \sqrt{y^2 + 1} \right)
$$
Except for very small values of y, the inverse sine is approximately equa | Alternatives to multilevel model with log transformed outcome
This is a great use case for the inverse hyperbolic sine transformation [1], [2]:
$$
\log\left( y + \sqrt{y^2 + 1} \right)
$$
Except for very small values of y, the inverse sine is approximately equal to log(2yi) or log(2)+log(yi), and so it can be interpre... | Alternatives to multilevel model with log transformed outcome
This is a great use case for the inverse hyperbolic sine transformation [1], [2]:
$$
\log\left( y + \sqrt{y^2 + 1} \right)
$$
Except for very small values of y, the inverse sine is approximately equa |
52,886 | Alternatives to multilevel model with log transformed outcome | It is not uncommon to offset a variable by a constant prior to taking its log when it cannot be log-transformed directly (for example because some observations are 0 and would map to $-\infty$).
For example, you could offset all of the observations for the variable by 1 and therefore have a log-transformed variable th... | Alternatives to multilevel model with log transformed outcome | It is not uncommon to offset a variable by a constant prior to taking its log when it cannot be log-transformed directly (for example because some observations are 0 and would map to $-\infty$).
For | Alternatives to multilevel model with log transformed outcome
It is not uncommon to offset a variable by a constant prior to taking its log when it cannot be log-transformed directly (for example because some observations are 0 and would map to $-\infty$).
For example, you could offset all of the observations for the ... | Alternatives to multilevel model with log transformed outcome
It is not uncommon to offset a variable by a constant prior to taking its log when it cannot be log-transformed directly (for example because some observations are 0 and would map to $-\infty$).
For |
52,887 | Unit root tests ambiguous - is time series stationary? | I am not surprised by these results. I got them very often. The KPSS test for some reason is very sensitive, if not overly so, as it rejects the vast majority of variables as stationary. In other words, it diagnoses almost everything as non-stationary. Because of that, I have stopped using the KPSS test for station... | Unit root tests ambiguous - is time series stationary? | I am not surprised by these results. I got them very often. The KPSS test for some reason is very sensitive, if not overly so, as it rejects the vast majority of variables as stationary. In other w | Unit root tests ambiguous - is time series stationary?
I am not surprised by these results. I got them very often. The KPSS test for some reason is very sensitive, if not overly so, as it rejects the vast majority of variables as stationary. In other words, it diagnoses almost everything as non-stationary. Because ... | Unit root tests ambiguous - is time series stationary?
I am not surprised by these results. I got them very often. The KPSS test for some reason is very sensitive, if not overly so, as it rejects the vast majority of variables as stationary. In other w |
52,888 | Unit root tests ambiguous - is time series stationary? | ADF and PP tests address a specific form of nonstationarity, i.e. unit-root nonstationarity. Apparently, you reject that form. However, unit-root nonstationarity it is not the only possible form of nostationarity. Hence, you do not conclude that the data is stationary (you only conclude that there is not enough evidenc... | Unit root tests ambiguous - is time series stationary? | ADF and PP tests address a specific form of nonstationarity, i.e. unit-root nonstationarity. Apparently, you reject that form. However, unit-root nonstationarity it is not the only possible form of no | Unit root tests ambiguous - is time series stationary?
ADF and PP tests address a specific form of nonstationarity, i.e. unit-root nonstationarity. Apparently, you reject that form. However, unit-root nonstationarity it is not the only possible form of nostationarity. Hence, you do not conclude that the data is station... | Unit root tests ambiguous - is time series stationary?
ADF and PP tests address a specific form of nonstationarity, i.e. unit-root nonstationarity. Apparently, you reject that form. However, unit-root nonstationarity it is not the only possible form of no |
52,889 | Unit root tests ambiguous - is time series stationary? | There are six different unit root test available in Eviews:
The Augmented Dickey-Fuller (ADF) Test
Dickey-Fuller Test with GLS Detrending (DFGLS)
The Phillips-Perron (PP) Test
The Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) Test
Elliot, Rothenberg, and Stock Point Optimal (ERS) Test
Ng and Perron (NP) Te... | Unit root tests ambiguous - is time series stationary? | There are six different unit root test available in Eviews:
The Augmented Dickey-Fuller (ADF) Test
Dickey-Fuller Test with GLS Detrending (DFGLS)
The Phillips-Perron (PP) Test
The Kwiatkowski, P | Unit root tests ambiguous - is time series stationary?
There are six different unit root test available in Eviews:
The Augmented Dickey-Fuller (ADF) Test
Dickey-Fuller Test with GLS Detrending (DFGLS)
The Phillips-Perron (PP) Test
The Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) Test
Elliot, Rothenberg, an... | Unit root tests ambiguous - is time series stationary?
There are six different unit root test available in Eviews:
The Augmented Dickey-Fuller (ADF) Test
Dickey-Fuller Test with GLS Detrending (DFGLS)
The Phillips-Perron (PP) Test
The Kwiatkowski, P |
52,890 | What is the difference between Machine Learning and Deep Learning? | Starting with the first page of Goolge Scholar, one finds some promising abstracts.
I. Arel,D. C. Rose, T. P. Karnowski Deep Machine Learning - A New Frontier in Artificial Intelligence Research
This article provides an overview of the mainstream deep learning approaches and research directions proposed over the past ... | What is the difference between Machine Learning and Deep Learning? | Starting with the first page of Goolge Scholar, one finds some promising abstracts.
I. Arel,D. C. Rose, T. P. Karnowski Deep Machine Learning - A New Frontier in Artificial Intelligence Research
This | What is the difference between Machine Learning and Deep Learning?
Starting with the first page of Goolge Scholar, one finds some promising abstracts.
I. Arel,D. C. Rose, T. P. Karnowski Deep Machine Learning - A New Frontier in Artificial Intelligence Research
This article provides an overview of the mainstream deep ... | What is the difference between Machine Learning and Deep Learning?
Starting with the first page of Goolge Scholar, one finds some promising abstracts.
I. Arel,D. C. Rose, T. P. Karnowski Deep Machine Learning - A New Frontier in Artificial Intelligence Research
This |
52,891 | What is the difference between Machine Learning and Deep Learning? | What is Machine Learning?
Machine Learning is a way in which scientists build algorithms that can learn.
Choose any Task T, such as driving a car.
Then your algorithm can display a certain level of performance P.
If this improves with experience E, then the algorithm is said to have...
learned!
So what is Deep Learni... | What is the difference between Machine Learning and Deep Learning? | What is Machine Learning?
Machine Learning is a way in which scientists build algorithms that can learn.
Choose any Task T, such as driving a car.
Then your algorithm can display a certain level of p | What is the difference between Machine Learning and Deep Learning?
What is Machine Learning?
Machine Learning is a way in which scientists build algorithms that can learn.
Choose any Task T, such as driving a car.
Then your algorithm can display a certain level of performance P.
If this improves with experience E, the... | What is the difference between Machine Learning and Deep Learning?
What is Machine Learning?
Machine Learning is a way in which scientists build algorithms that can learn.
Choose any Task T, such as driving a car.
Then your algorithm can display a certain level of p |
52,892 | What is the difference between Machine Learning and Deep Learning? | Google "machine learning" and you will find a lot of definitions. What is deep learning might be just slightly harder to put a finger on. Everyone will agree that neural nets is a method that is part of machine learning. However 'traditional' neural nets tended to work very poorly ('overtrain') on nets with a large ... | What is the difference between Machine Learning and Deep Learning? | Google "machine learning" and you will find a lot of definitions. What is deep learning might be just slightly harder to put a finger on. Everyone will agree that neural nets is a method that is par | What is the difference between Machine Learning and Deep Learning?
Google "machine learning" and you will find a lot of definitions. What is deep learning might be just slightly harder to put a finger on. Everyone will agree that neural nets is a method that is part of machine learning. However 'traditional' neural ... | What is the difference between Machine Learning and Deep Learning?
Google "machine learning" and you will find a lot of definitions. What is deep learning might be just slightly harder to put a finger on. Everyone will agree that neural nets is a method that is par |
52,893 | What is the difference between Machine Learning and Deep Learning? | Artificial Intelligence is the greater area, a field of knowledge. Machine Learning is a sub-field that consists of, for example, several techniques such as supervised and unsupervised methods. In supervised learning, one famous approach is called artificial neural networks. An artificial neural network with a certain ... | What is the difference between Machine Learning and Deep Learning? | Artificial Intelligence is the greater area, a field of knowledge. Machine Learning is a sub-field that consists of, for example, several techniques such as supervised and unsupervised methods. In sup | What is the difference between Machine Learning and Deep Learning?
Artificial Intelligence is the greater area, a field of knowledge. Machine Learning is a sub-field that consists of, for example, several techniques such as supervised and unsupervised methods. In supervised learning, one famous approach is called artif... | What is the difference between Machine Learning and Deep Learning?
Artificial Intelligence is the greater area, a field of knowledge. Machine Learning is a sub-field that consists of, for example, several techniques such as supervised and unsupervised methods. In sup |
52,894 | predict seasonality and trend combined, better approach? | There are several methods and models for this kind of analysis, for example: exponential smoothing, ARIMA time series models or structural time series models. The topic is too broad to be covered here. Below, I give some examples in R just for illustration. For further details, you may start for example looking at this... | predict seasonality and trend combined, better approach? | There are several methods and models for this kind of analysis, for example: exponential smoothing, ARIMA time series models or structural time series models. The topic is too broad to be covered here | predict seasonality and trend combined, better approach?
There are several methods and models for this kind of analysis, for example: exponential smoothing, ARIMA time series models or structural time series models. The topic is too broad to be covered here. Below, I give some examples in R just for illustration. For f... | predict seasonality and trend combined, better approach?
There are several methods and models for this kind of analysis, for example: exponential smoothing, ARIMA time series models or structural time series models. The topic is too broad to be covered here |
52,895 | predict seasonality and trend combined, better approach? | If your data are simple, and you are just toying around, the decomposition into seasonal and overall trend should already be pretty good. But if you want to dig deeper, there is a more formal approach: Using Kernels to define the relations between your points.
The best exemple I have seen of this kind of task is on the... | predict seasonality and trend combined, better approach? | If your data are simple, and you are just toying around, the decomposition into seasonal and overall trend should already be pretty good. But if you want to dig deeper, there is a more formal approach | predict seasonality and trend combined, better approach?
If your data are simple, and you are just toying around, the decomposition into seasonal and overall trend should already be pretty good. But if you want to dig deeper, there is a more formal approach: Using Kernels to define the relations between your points.
Th... | predict seasonality and trend combined, better approach?
If your data are simple, and you are just toying around, the decomposition into seasonal and overall trend should already be pretty good. But if you want to dig deeper, there is a more formal approach |
52,896 | Variation or variance | Variation is a general term which express the dispersion. Variation is not precisely defined, it talks only about the quality of some process which produces imprecise results and express the imprecision. Variance is a measure for variation, which is defined as the second central moment. There are many measures of varia... | Variation or variance | Variation is a general term which express the dispersion. Variation is not precisely defined, it talks only about the quality of some process which produces imprecise results and express the imprecisi | Variation or variance
Variation is a general term which express the dispersion. Variation is not precisely defined, it talks only about the quality of some process which produces imprecise results and express the imprecision. Variance is a measure for variation, which is defined as the second central moment. There are ... | Variation or variance
Variation is a general term which express the dispersion. Variation is not precisely defined, it talks only about the quality of some process which produces imprecise results and express the imprecisi |
52,897 | Comparing two or more treatments with inverse probablity of treatment weighting | You can use twang with more than 2 treatment levels -- I use it all the time to obtain propensity scores for multiple (i.e. >2) treatments and it's one of my all time favorite R packages because there is no need to guess the functional relationships between your treatments and covariates. Since twang uses gradient boo... | Comparing two or more treatments with inverse probablity of treatment weighting | You can use twang with more than 2 treatment levels -- I use it all the time to obtain propensity scores for multiple (i.e. >2) treatments and it's one of my all time favorite R packages because there | Comparing two or more treatments with inverse probablity of treatment weighting
You can use twang with more than 2 treatment levels -- I use it all the time to obtain propensity scores for multiple (i.e. >2) treatments and it's one of my all time favorite R packages because there is no need to guess the functional rela... | Comparing two or more treatments with inverse probablity of treatment weighting
You can use twang with more than 2 treatment levels -- I use it all the time to obtain propensity scores for multiple (i.e. >2) treatments and it's one of my all time favorite R packages because there |
52,898 | Comparing two or more treatments with inverse probablity of treatment weighting | Imbens (2000) and Imbens and Wooldridge (2009) outline a method of adjusting for treatment choice based on pre-treatment characteristics in situations where treatment takes on more than two values. This approach is termed generalized propensity scores. The first step is to predict treatment category using multinomial l... | Comparing two or more treatments with inverse probablity of treatment weighting | Imbens (2000) and Imbens and Wooldridge (2009) outline a method of adjusting for treatment choice based on pre-treatment characteristics in situations where treatment takes on more than two values. Th | Comparing two or more treatments with inverse probablity of treatment weighting
Imbens (2000) and Imbens and Wooldridge (2009) outline a method of adjusting for treatment choice based on pre-treatment characteristics in situations where treatment takes on more than two values. This approach is termed generalized propen... | Comparing two or more treatments with inverse probablity of treatment weighting
Imbens (2000) and Imbens and Wooldridge (2009) outline a method of adjusting for treatment choice based on pre-treatment characteristics in situations where treatment takes on more than two values. Th |
52,899 | Expected Value of Gamma Distribution | I would go about it the lazy way: by starting with a definition and looking hard at what ensues, in order to see whether somebody has already shown me the answer. In what follows no calculations are needed at all, and only the very simplest rules (of exponents and integrals) are required to follow the algebra.
Let's ... | Expected Value of Gamma Distribution | I would go about it the lazy way: by starting with a definition and looking hard at what ensues, in order to see whether somebody has already shown me the answer. In what follows no calculations are | Expected Value of Gamma Distribution
I would go about it the lazy way: by starting with a definition and looking hard at what ensues, in order to see whether somebody has already shown me the answer. In what follows no calculations are needed at all, and only the very simplest rules (of exponents and integrals) are re... | Expected Value of Gamma Distribution
I would go about it the lazy way: by starting with a definition and looking hard at what ensues, in order to see whether somebody has already shown me the answer. In what follows no calculations are |
52,900 | Expected Value of Gamma Distribution | Assuming you're concerning random variable of Gamma distribution with shape $\alpha > 0$ and rate $\beta > 0$ parameters, that is $X \sim Gamma(\alpha,\beta)$, you can find $\mathbb{E}[\frac{1}{X^2}]$ in the following manner:
For any random variable X of continuous distribution (like Gamma) for which $f$ denotes its pr... | Expected Value of Gamma Distribution | Assuming you're concerning random variable of Gamma distribution with shape $\alpha > 0$ and rate $\beta > 0$ parameters, that is $X \sim Gamma(\alpha,\beta)$, you can find $\mathbb{E}[\frac{1}{X^2}]$ | Expected Value of Gamma Distribution
Assuming you're concerning random variable of Gamma distribution with shape $\alpha > 0$ and rate $\beta > 0$ parameters, that is $X \sim Gamma(\alpha,\beta)$, you can find $\mathbb{E}[\frac{1}{X^2}]$ in the following manner:
For any random variable X of continuous distribution (lik... | Expected Value of Gamma Distribution
Assuming you're concerning random variable of Gamma distribution with shape $\alpha > 0$ and rate $\beta > 0$ parameters, that is $X \sim Gamma(\alpha,\beta)$, you can find $\mathbb{E}[\frac{1}{X^2}]$ |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.