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 |
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11,001 | How do I check if my data fits an exponential distribution? | You can use a qq-plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other.
In R, there is no out-of-the-box qq-plot function for the exponential distribution specifically (at least among the base functions). However, you can use this:
qqexp <- functi... | How do I check if my data fits an exponential distribution? | You can use a qq-plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other.
In R, there is no out-of-the-box qq-plot function for th | How do I check if my data fits an exponential distribution?
You can use a qq-plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other.
In R, there is no out-of-the-box qq-plot function for the exponential distribution specifically (at least among the ... | How do I check if my data fits an exponential distribution?
You can use a qq-plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other.
In R, there is no out-of-the-box qq-plot function for th |
11,002 | Explanation for unequal probabilities of numbers drawn in a lottery | You mentioned that odd-even pattern, so let's investigate that.
Category
Observed
Expected #
Expected
odd
92
110
50%
even
128
110
50%
And test with just these two categories....
Chi squared equals 5.891 with 1 degrees of freedom.
The two-tailed P value equals 0.0152
That would generally be considered sig... | Explanation for unequal probabilities of numbers drawn in a lottery | You mentioned that odd-even pattern, so let's investigate that.
Category
Observed
Expected #
Expected
odd
92
110
50%
even
128
110
50%
And test with just these two categories....
Chi squa | Explanation for unequal probabilities of numbers drawn in a lottery
You mentioned that odd-even pattern, so let's investigate that.
Category
Observed
Expected #
Expected
odd
92
110
50%
even
128
110
50%
And test with just these two categories....
Chi squared equals 5.891 with 1 degrees of freedom.
The two-... | Explanation for unequal probabilities of numbers drawn in a lottery
You mentioned that odd-even pattern, so let's investigate that.
Category
Observed
Expected #
Expected
odd
92
110
50%
even
128
110
50%
And test with just these two categories....
Chi squa |
11,003 | Explanation for unequal probabilities of numbers drawn in a lottery | To determine whether the results seem to indicate some shenanigans were afoot, we can test it!
To begin, we need to specify what our null hypothesis is. I'll take the moment here to stress (as subsequent answers have pointed out in more detail) the importance of forming hypotheses before seeing the data we will use for... | Explanation for unequal probabilities of numbers drawn in a lottery | To determine whether the results seem to indicate some shenanigans were afoot, we can test it!
To begin, we need to specify what our null hypothesis is. I'll take the moment here to stress (as subsequ | Explanation for unequal probabilities of numbers drawn in a lottery
To determine whether the results seem to indicate some shenanigans were afoot, we can test it!
To begin, we need to specify what our null hypothesis is. I'll take the moment here to stress (as subsequent answers have pointed out in more detail) the imp... | Explanation for unequal probabilities of numbers drawn in a lottery
To determine whether the results seem to indicate some shenanigans were afoot, we can test it!
To begin, we need to specify what our null hypothesis is. I'll take the moment here to stress (as subsequ |
11,004 | Explanation for unequal probabilities of numbers drawn in a lottery | Following @doubled's (+1) chi-squared test, a remaining question is whether 220 draws from the machine are enough to
detect an actual small bias. Maybe the odd numbered balls are a bit heavier, lighter,
or less round in such a way that they are slightly more likely to be be drawn.
Maybe the true probability distributio... | Explanation for unequal probabilities of numbers drawn in a lottery | Following @doubled's (+1) chi-squared test, a remaining question is whether 220 draws from the machine are enough to
detect an actual small bias. Maybe the odd numbered balls are a bit heavier, lighte | Explanation for unequal probabilities of numbers drawn in a lottery
Following @doubled's (+1) chi-squared test, a remaining question is whether 220 draws from the machine are enough to
detect an actual small bias. Maybe the odd numbered balls are a bit heavier, lighter,
or less round in such a way that they are slightl... | Explanation for unequal probabilities of numbers drawn in a lottery
Following @doubled's (+1) chi-squared test, a remaining question is whether 220 draws from the machine are enough to
detect an actual small bias. Maybe the odd numbered balls are a bit heavier, lighte |
11,005 | Explanation for unequal probabilities of numbers drawn in a lottery | As an addition to the other answers, let me offer you a visual way to inspect the differences between the expected and observed frequencies: A (hanging) rootogram, invented by John Tukey (see also Kleiber & Zeileis (2016)). In the figure below, the square roots of the expected counts are displayed as red dots. The squa... | Explanation for unequal probabilities of numbers drawn in a lottery | As an addition to the other answers, let me offer you a visual way to inspect the differences between the expected and observed frequencies: A (hanging) rootogram, invented by John Tukey (see also Kle | Explanation for unequal probabilities of numbers drawn in a lottery
As an addition to the other answers, let me offer you a visual way to inspect the differences between the expected and observed frequencies: A (hanging) rootogram, invented by John Tukey (see also Kleiber & Zeileis (2016)). In the figure below, the squ... | Explanation for unequal probabilities of numbers drawn in a lottery
As an addition to the other answers, let me offer you a visual way to inspect the differences between the expected and observed frequencies: A (hanging) rootogram, invented by John Tukey (see also Kle |
11,006 | Explanation for unequal probabilities of numbers drawn in a lottery | I found that there was a correlation of -0.5109730443013045 between the number drawn and its frequency, and a p-value of 0.090274 for that correlation. For a binomial test for a number being odd or even, I got a p-value of 0.00621804354. When I adjusted the odd numbers for the difference in means (that is, added (even ... | Explanation for unequal probabilities of numbers drawn in a lottery | I found that there was a correlation of -0.5109730443013045 between the number drawn and its frequency, and a p-value of 0.090274 for that correlation. For a binomial test for a number being odd or ev | Explanation for unequal probabilities of numbers drawn in a lottery
I found that there was a correlation of -0.5109730443013045 between the number drawn and its frequency, and a p-value of 0.090274 for that correlation. For a binomial test for a number being odd or even, I got a p-value of 0.00621804354. When I adjuste... | Explanation for unequal probabilities of numbers drawn in a lottery
I found that there was a correlation of -0.5109730443013045 between the number drawn and its frequency, and a p-value of 0.090274 for that correlation. For a binomial test for a number being odd or ev |
11,007 | Reason for not shrinking the bias (intercept) term in regression | The Elements of Statistical Learning by Hastie et al. define ridge regression as follows (Section 3.4.1, equation 3.41): $$\hat \beta{}^\mathrm{ridge} = \underset{\beta}{\mathrm{argmin}}\left\{\sum_{i=1}^N(y_i - \beta_0 - \sum_{j=1}^p x_{ij}\beta_j)^2 + \lambda \sum_{j=1}^p \beta_j^2\right\},$$ i.e. explicitly exclude ... | Reason for not shrinking the bias (intercept) term in regression | The Elements of Statistical Learning by Hastie et al. define ridge regression as follows (Section 3.4.1, equation 3.41): $$\hat \beta{}^\mathrm{ridge} = \underset{\beta}{\mathrm{argmin}}\left\{\sum_{i | Reason for not shrinking the bias (intercept) term in regression
The Elements of Statistical Learning by Hastie et al. define ridge regression as follows (Section 3.4.1, equation 3.41): $$\hat \beta{}^\mathrm{ridge} = \underset{\beta}{\mathrm{argmin}}\left\{\sum_{i=1}^N(y_i - \beta_0 - \sum_{j=1}^p x_{ij}\beta_j)^2 + \... | Reason for not shrinking the bias (intercept) term in regression
The Elements of Statistical Learning by Hastie et al. define ridge regression as follows (Section 3.4.1, equation 3.41): $$\hat \beta{}^\mathrm{ridge} = \underset{\beta}{\mathrm{argmin}}\left\{\sum_{i |
11,008 | Reason for not shrinking the bias (intercept) term in regression | Recall the purpose of shrinkage or regularization. It is to prevent the learning algorithm to overfit the training data or equivalently - prevent from picking arbitrarily large parameter values. This is more likely for datasets with more than few training examples in the presence of noise (very interesting discussion a... | Reason for not shrinking the bias (intercept) term in regression | Recall the purpose of shrinkage or regularization. It is to prevent the learning algorithm to overfit the training data or equivalently - prevent from picking arbitrarily large parameter values. This | Reason for not shrinking the bias (intercept) term in regression
Recall the purpose of shrinkage or regularization. It is to prevent the learning algorithm to overfit the training data or equivalently - prevent from picking arbitrarily large parameter values. This is more likely for datasets with more than few training... | Reason for not shrinking the bias (intercept) term in regression
Recall the purpose of shrinkage or regularization. It is to prevent the learning algorithm to overfit the training data or equivalently - prevent from picking arbitrarily large parameter values. This |
11,009 | Reason for not shrinking the bias (intercept) term in regression | The intercept term is absolutely not immune to shrinkage. The general "shrinkage" (i.e. regularization) formulation puts the regularization term in the loss function, e.g.:
$RSS(\beta) = \|y_i - X_i \beta \|^2$
$RegularizedLoss(\beta) = RSS(\beta) - \lambda f(\beta)$
Where $f(\beta)$ is usually related to a lebesgue no... | Reason for not shrinking the bias (intercept) term in regression | The intercept term is absolutely not immune to shrinkage. The general "shrinkage" (i.e. regularization) formulation puts the regularization term in the loss function, e.g.:
$RSS(\beta) = \|y_i - X_i \ | Reason for not shrinking the bias (intercept) term in regression
The intercept term is absolutely not immune to shrinkage. The general "shrinkage" (i.e. regularization) formulation puts the regularization term in the loss function, e.g.:
$RSS(\beta) = \|y_i - X_i \beta \|^2$
$RegularizedLoss(\beta) = RSS(\beta) - \lamb... | Reason for not shrinking the bias (intercept) term in regression
The intercept term is absolutely not immune to shrinkage. The general "shrinkage" (i.e. regularization) formulation puts the regularization term in the loss function, e.g.:
$RSS(\beta) = \|y_i - X_i \ |
11,010 | Reason for not shrinking the bias (intercept) term in regression | I'm not sure the above answer by David Marx is quite right; according to Andrew Ng, by convention the bias/intercept coefficient is typically not regularized in a linear regression, and in any case whether it is regularized or not does not make a significant difference. | Reason for not shrinking the bias (intercept) term in regression | I'm not sure the above answer by David Marx is quite right; according to Andrew Ng, by convention the bias/intercept coefficient is typically not regularized in a linear regression, and in any case wh | Reason for not shrinking the bias (intercept) term in regression
I'm not sure the above answer by David Marx is quite right; according to Andrew Ng, by convention the bias/intercept coefficient is typically not regularized in a linear regression, and in any case whether it is regularized or not does not make a signific... | Reason for not shrinking the bias (intercept) term in regression
I'm not sure the above answer by David Marx is quite right; according to Andrew Ng, by convention the bias/intercept coefficient is typically not regularized in a linear regression, and in any case wh |
11,011 | Reason for not shrinking the bias (intercept) term in regression | I'll give the simplest explanation, then expand.
Suppose you shrink to zero, then your model effectively becomes:
$$y_t=\varepsilon_t$$
Just one problem with this model: $E[\varepsilon_t]=E[y_t]\ne 0$, which violates exogeneity assumption of the linear regression. Hence, the estimated coefficients will not have nice pr... | Reason for not shrinking the bias (intercept) term in regression | I'll give the simplest explanation, then expand.
Suppose you shrink to zero, then your model effectively becomes:
$$y_t=\varepsilon_t$$
Just one problem with this model: $E[\varepsilon_t]=E[y_t]\ne 0$ | Reason for not shrinking the bias (intercept) term in regression
I'll give the simplest explanation, then expand.
Suppose you shrink to zero, then your model effectively becomes:
$$y_t=\varepsilon_t$$
Just one problem with this model: $E[\varepsilon_t]=E[y_t]\ne 0$, which violates exogeneity assumption of the linear re... | Reason for not shrinking the bias (intercept) term in regression
I'll give the simplest explanation, then expand.
Suppose you shrink to zero, then your model effectively becomes:
$$y_t=\varepsilon_t$$
Just one problem with this model: $E[\varepsilon_t]=E[y_t]\ne 0$ |
11,012 | Reason for not shrinking the bias (intercept) term in regression | Suppose one of the predictors $x_i$ happens to have the same nonzero value across all training examples. We would like its coefficient $\beta_i$ to be estimated as zero. To see why, suppose $\beta_i$ is not zero, and $x_i$ takes a different value in some test example. Our prediction will change by some arbitrary amo... | Reason for not shrinking the bias (intercept) term in regression | Suppose one of the predictors $x_i$ happens to have the same nonzero value across all training examples. We would like its coefficient $\beta_i$ to be estimated as zero. To see why, suppose $\beta_i | Reason for not shrinking the bias (intercept) term in regression
Suppose one of the predictors $x_i$ happens to have the same nonzero value across all training examples. We would like its coefficient $\beta_i$ to be estimated as zero. To see why, suppose $\beta_i$ is not zero, and $x_i$ takes a different value in som... | Reason for not shrinking the bias (intercept) term in regression
Suppose one of the predictors $x_i$ happens to have the same nonzero value across all training examples. We would like its coefficient $\beta_i$ to be estimated as zero. To see why, suppose $\beta_i |
11,013 | Can someone help to explain the difference between independent and random? | I'll try to explain it in non-technical terms: A random variable describes an outcome of an experiment; you can not know in advance what the exact outcome will be but you have some information: you know which outcomes are possible and you know, for each outcome, its probability.
For example, if you toss a fair coin the... | Can someone help to explain the difference between independent and random? | I'll try to explain it in non-technical terms: A random variable describes an outcome of an experiment; you can not know in advance what the exact outcome will be but you have some information: you kn | Can someone help to explain the difference between independent and random?
I'll try to explain it in non-technical terms: A random variable describes an outcome of an experiment; you can not know in advance what the exact outcome will be but you have some information: you know which outcomes are possible and you know, ... | Can someone help to explain the difference between independent and random?
I'll try to explain it in non-technical terms: A random variable describes an outcome of an experiment; you can not know in advance what the exact outcome will be but you have some information: you kn |
11,014 | Can someone help to explain the difference between independent and random? | Random relates to random variable, and independent relates to probabilistic independence. By independence we mean that observing one variable does not tell us anything about the another, or in more formal terms, if $X$ and $Y$ are two random variables, then we say that they are independent if
$$ p_{X,Y}(x, y) = p_X(x)\... | Can someone help to explain the difference between independent and random? | Random relates to random variable, and independent relates to probabilistic independence. By independence we mean that observing one variable does not tell us anything about the another, or in more fo | Can someone help to explain the difference between independent and random?
Random relates to random variable, and independent relates to probabilistic independence. By independence we mean that observing one variable does not tell us anything about the another, or in more formal terms, if $X$ and $Y$ are two random var... | Can someone help to explain the difference between independent and random?
Random relates to random variable, and independent relates to probabilistic independence. By independence we mean that observing one variable does not tell us anything about the another, or in more fo |
11,015 | Can someone help to explain the difference between independent and random? | The notion of independence is relative, while you can be random by yourself. In your example, you have "two independent random variables", and do not need to talk about several "random sampling".
Suppose you cast a perfect die several times. The outcome $6,5,3,5, 4\ldots$ is a priori random. Knowing the past, you cann... | Can someone help to explain the difference between independent and random? | The notion of independence is relative, while you can be random by yourself. In your example, you have "two independent random variables", and do not need to talk about several "random sampling".
Sup | Can someone help to explain the difference between independent and random?
The notion of independence is relative, while you can be random by yourself. In your example, you have "two independent random variables", and do not need to talk about several "random sampling".
Suppose you cast a perfect die several times. Th... | Can someone help to explain the difference between independent and random?
The notion of independence is relative, while you can be random by yourself. In your example, you have "two independent random variables", and do not need to talk about several "random sampling".
Sup |
11,016 | Can someone help to explain the difference between independent and random? | Variables are used in all fields of mathematics. The definitions for independence and randomness of a variable are applied unilaterally to all forms of mathematics, not just to statistics.
For example, the X and Y axes in 2-dimensional Euclidean geometry represent independent variables, however, their values are not (... | Can someone help to explain the difference between independent and random? | Variables are used in all fields of mathematics. The definitions for independence and randomness of a variable are applied unilaterally to all forms of mathematics, not just to statistics.
For exampl | Can someone help to explain the difference between independent and random?
Variables are used in all fields of mathematics. The definitions for independence and randomness of a variable are applied unilaterally to all forms of mathematics, not just to statistics.
For example, the X and Y axes in 2-dimensional Euclidea... | Can someone help to explain the difference between independent and random?
Variables are used in all fields of mathematics. The definitions for independence and randomness of a variable are applied unilaterally to all forms of mathematics, not just to statistics.
For exampl |
11,017 | Can someone help to explain the difference between independent and random? | When you have a pair of values when the first is randomly generated and the second has any dependence on the first one. e.g. height and weight of a man. There is correlation between them. But they are both random. | Can someone help to explain the difference between independent and random? | When you have a pair of values when the first is randomly generated and the second has any dependence on the first one. e.g. height and weight of a man. There is correlation between them. But they are | Can someone help to explain the difference between independent and random?
When you have a pair of values when the first is randomly generated and the second has any dependence on the first one. e.g. height and weight of a man. There is correlation between them. But they are both random. | Can someone help to explain the difference between independent and random?
When you have a pair of values when the first is randomly generated and the second has any dependence on the first one. e.g. height and weight of a man. There is correlation between them. But they are |
11,018 | Can someone help to explain the difference between independent and random? | The coin example is a great illustration of a random and independent variable, a good good way to think of a random but dependent variable would be the next card drawn from a seven deck shoe of playing cards, the -likelihood- of any specific numerical outcome changes depending on the cards previously dealt, but until o... | Can someone help to explain the difference between independent and random? | The coin example is a great illustration of a random and independent variable, a good good way to think of a random but dependent variable would be the next card drawn from a seven deck shoe of playin | Can someone help to explain the difference between independent and random?
The coin example is a great illustration of a random and independent variable, a good good way to think of a random but dependent variable would be the next card drawn from a seven deck shoe of playing cards, the -likelihood- of any specific num... | Can someone help to explain the difference between independent and random?
The coin example is a great illustration of a random and independent variable, a good good way to think of a random but dependent variable would be the next card drawn from a seven deck shoe of playin |
11,019 | Can someone help to explain the difference between independent and random? | David Bohm in his work Causality and Chance in Modern Physics (London: Routledge, 1957/1984) describes causality, chance, randomness, and independence:
"In nature nothing remains constant. Everything is in a perpetual state of transformation, motion, and change. However, we discover that nothing simply surges up out of... | Can someone help to explain the difference between independent and random? | David Bohm in his work Causality and Chance in Modern Physics (London: Routledge, 1957/1984) describes causality, chance, randomness, and independence:
"In nature nothing remains constant. Everything | Can someone help to explain the difference between independent and random?
David Bohm in his work Causality and Chance in Modern Physics (London: Routledge, 1957/1984) describes causality, chance, randomness, and independence:
"In nature nothing remains constant. Everything is in a perpetual state of transformation, mo... | Can someone help to explain the difference between independent and random?
David Bohm in his work Causality and Chance in Modern Physics (London: Routledge, 1957/1984) describes causality, chance, randomness, and independence:
"In nature nothing remains constant. Everything |
11,020 | Hat matrix and leverages in classical multiple regression | The hat matrix, $\bf H$, is the projection matrix that expresses the values of the observations in the independent variable, $\bf y$, in terms of the linear combinations of the column vectors of the model matrix, $\bf X$, which contains the observations for each of the multiple variables you are regressing on.
Naturall... | Hat matrix and leverages in classical multiple regression | The hat matrix, $\bf H$, is the projection matrix that expresses the values of the observations in the independent variable, $\bf y$, in terms of the linear combinations of the column vectors of the m | Hat matrix and leverages in classical multiple regression
The hat matrix, $\bf H$, is the projection matrix that expresses the values of the observations in the independent variable, $\bf y$, in terms of the linear combinations of the column vectors of the model matrix, $\bf X$, which contains the observations for each... | Hat matrix and leverages in classical multiple regression
The hat matrix, $\bf H$, is the projection matrix that expresses the values of the observations in the independent variable, $\bf y$, in terms of the linear combinations of the column vectors of the m |
11,021 | How to specify a lognormal distribution in the glm family argument in R? | The gamlss package allows you to fit generalized additive models with both lognormal and exponential distributions, and a bunch of others, with some variety in link functions and using, if you wish, semi- or non-parametric models based on penalized splines. It's got some papers published on the algorithms used and doc... | How to specify a lognormal distribution in the glm family argument in R? | The gamlss package allows you to fit generalized additive models with both lognormal and exponential distributions, and a bunch of others, with some variety in link functions and using, if you wish, s | How to specify a lognormal distribution in the glm family argument in R?
The gamlss package allows you to fit generalized additive models with both lognormal and exponential distributions, and a bunch of others, with some variety in link functions and using, if you wish, semi- or non-parametric models based on penalize... | How to specify a lognormal distribution in the glm family argument in R?
The gamlss package allows you to fit generalized additive models with both lognormal and exponential distributions, and a bunch of others, with some variety in link functions and using, if you wish, s |
11,022 | How to specify a lognormal distribution in the glm family argument in R? | Fitting a log-normal GLM has nothing to do with the distribution nor the link option of the glm() function. The term "log-normal" is quite confusing in this sense, but means that the response variable is normally distributed (family=gaussian), and a transformation is applied to this variable the following way:
log.glm ... | How to specify a lognormal distribution in the glm family argument in R? | Fitting a log-normal GLM has nothing to do with the distribution nor the link option of the glm() function. The term "log-normal" is quite confusing in this sense, but means that the response variable | How to specify a lognormal distribution in the glm family argument in R?
Fitting a log-normal GLM has nothing to do with the distribution nor the link option of the glm() function. The term "log-normal" is quite confusing in this sense, but means that the response variable is normally distributed (family=gaussian), and... | How to specify a lognormal distribution in the glm family argument in R?
Fitting a log-normal GLM has nothing to do with the distribution nor the link option of the glm() function. The term "log-normal" is quite confusing in this sense, but means that the response variable |
11,023 | How to specify a lognormal distribution in the glm family argument in R? | Lognormal is not an option because the log-normal distribution is not in the exponential family of distributions. Generalized linear models can only fit distributions from the exponential family.
I'm less clear why exponential is not an option, as the exponential distribution is in the exponential family (as you might ... | How to specify a lognormal distribution in the glm family argument in R? | Lognormal is not an option because the log-normal distribution is not in the exponential family of distributions. Generalized linear models can only fit distributions from the exponential family.
I'm | How to specify a lognormal distribution in the glm family argument in R?
Lognormal is not an option because the log-normal distribution is not in the exponential family of distributions. Generalized linear models can only fit distributions from the exponential family.
I'm less clear why exponential is not an option, as... | How to specify a lognormal distribution in the glm family argument in R?
Lognormal is not an option because the log-normal distribution is not in the exponential family of distributions. Generalized linear models can only fit distributions from the exponential family.
I'm |
11,024 | How to specify a lognormal distribution in the glm family argument in R? | Regarding fitting the exponential model with glm: When using the glm function with family=Gamma one needs to also use the supporting facilities of summary.glm in order to fix the dispersion parameter to 1:
?summary.glm
fit <- glm(formula =..., family = Gamma)
summary(fit,dispersion=1)
And as I was going to point out ... | How to specify a lognormal distribution in the glm family argument in R? | Regarding fitting the exponential model with glm: When using the glm function with family=Gamma one needs to also use the supporting facilities of summary.glm in order to fix the dispersion parameter | How to specify a lognormal distribution in the glm family argument in R?
Regarding fitting the exponential model with glm: When using the glm function with family=Gamma one needs to also use the supporting facilities of summary.glm in order to fix the dispersion parameter to 1:
?summary.glm
fit <- glm(formula =..., fam... | How to specify a lognormal distribution in the glm family argument in R?
Regarding fitting the exponential model with glm: When using the glm function with family=Gamma one needs to also use the supporting facilities of summary.glm in order to fix the dispersion parameter |
11,025 | How to specify a lognormal distribution in the glm family argument in R? | Try using the following command:
log.glm = glm(y ~ x, family=gaussian(link="log"), data=my.dat)
It works here and the AIC seems to be correct. | How to specify a lognormal distribution in the glm family argument in R? | Try using the following command:
log.glm = glm(y ~ x, family=gaussian(link="log"), data=my.dat)
It works here and the AIC seems to be correct. | How to specify a lognormal distribution in the glm family argument in R?
Try using the following command:
log.glm = glm(y ~ x, family=gaussian(link="log"), data=my.dat)
It works here and the AIC seems to be correct. | How to specify a lognormal distribution in the glm family argument in R?
Try using the following command:
log.glm = glm(y ~ x, family=gaussian(link="log"), data=my.dat)
It works here and the AIC seems to be correct. |
11,026 | Can mean plus one standard deviation exceed maximum value? | Certainly the mean plus one sd can exceed the largest observation.
Consider the sample 1, 5, 5, 5 -
it has mean 4 and standard deviation 2, so the mean + sd is 6, one more than the sample maximum. Here's the calculation in R:
> x=c(1,5,5,5)
> mean(x)+sd(x)
[1] 6
It's a common occurrence. It tends to happen when there... | Can mean plus one standard deviation exceed maximum value? | Certainly the mean plus one sd can exceed the largest observation.
Consider the sample 1, 5, 5, 5 -
it has mean 4 and standard deviation 2, so the mean + sd is 6, one more than the sample maximum. He | Can mean plus one standard deviation exceed maximum value?
Certainly the mean plus one sd can exceed the largest observation.
Consider the sample 1, 5, 5, 5 -
it has mean 4 and standard deviation 2, so the mean + sd is 6, one more than the sample maximum. Here's the calculation in R:
> x=c(1,5,5,5)
> mean(x)+sd(x)
[1]... | Can mean plus one standard deviation exceed maximum value?
Certainly the mean plus one sd can exceed the largest observation.
Consider the sample 1, 5, 5, 5 -
it has mean 4 and standard deviation 2, so the mean + sd is 6, one more than the sample maximum. He |
11,027 | Can mean plus one standard deviation exceed maximum value? | Per Chebyshev's inequality, less than k -2 points can be more than k standard deviations away. So, for k=1 that means less than 100% of your samples can be more than one standard deviation away.
It's more interesting to look at the low bound. Your professor should be more surprised there are points which are about 2.5... | Can mean plus one standard deviation exceed maximum value? | Per Chebyshev's inequality, less than k -2 points can be more than k standard deviations away. So, for k=1 that means less than 100% of your samples can be more than one standard deviation away.
It's | Can mean plus one standard deviation exceed maximum value?
Per Chebyshev's inequality, less than k -2 points can be more than k standard deviations away. So, for k=1 that means less than 100% of your samples can be more than one standard deviation away.
It's more interesting to look at the low bound. Your professor sh... | Can mean plus one standard deviation exceed maximum value?
Per Chebyshev's inequality, less than k -2 points can be more than k standard deviations away. So, for k=1 that means less than 100% of your samples can be more than one standard deviation away.
It's |
11,028 | Can mean plus one standard deviation exceed maximum value? | In general for the Bernoulli random variable $X$, that takes the value $1$ with probability $0<p<1$ and the value $0$ with probability $1-p$, we have
$$E(X) = p,\;\; SE(X) = \sqrt {p(1-p)}$$
And we want
$$E(X)+ SE(X) > 1 \Rightarrow p +\sqrt {p(1-p)} >1$$
$$\Rightarrow \sqrt {p(1-p)} > (1-p)$$
Square both sides to obta... | Can mean plus one standard deviation exceed maximum value? | In general for the Bernoulli random variable $X$, that takes the value $1$ with probability $0<p<1$ and the value $0$ with probability $1-p$, we have
$$E(X) = p,\;\; SE(X) = \sqrt {p(1-p)}$$
And we wa | Can mean plus one standard deviation exceed maximum value?
In general for the Bernoulli random variable $X$, that takes the value $1$ with probability $0<p<1$ and the value $0$ with probability $1-p$, we have
$$E(X) = p,\;\; SE(X) = \sqrt {p(1-p)}$$
And we want
$$E(X)+ SE(X) > 1 \Rightarrow p +\sqrt {p(1-p)} >1$$
$$\Ri... | Can mean plus one standard deviation exceed maximum value?
In general for the Bernoulli random variable $X$, that takes the value $1$ with probability $0<p<1$ and the value $0$ with probability $1-p$, we have
$$E(X) = p,\;\; SE(X) = \sqrt {p(1-p)}$$
And we wa |
11,029 | Can mean plus one standard deviation exceed maximum value? | The essence of the problem may be that your distribution is not a normal distribution which a standard deviation assumes. Your distribution is likely left skewed, so you need to transform your set into a normal distribution first by picking a suitable transform function, this process is called transformation to normal... | Can mean plus one standard deviation exceed maximum value? | The essence of the problem may be that your distribution is not a normal distribution which a standard deviation assumes. Your distribution is likely left skewed, so you need to transform your set in | Can mean plus one standard deviation exceed maximum value?
The essence of the problem may be that your distribution is not a normal distribution which a standard deviation assumes. Your distribution is likely left skewed, so you need to transform your set into a normal distribution first by picking a suitable transfor... | Can mean plus one standard deviation exceed maximum value?
The essence of the problem may be that your distribution is not a normal distribution which a standard deviation assumes. Your distribution is likely left skewed, so you need to transform your set in |
11,030 | Can mean plus one standard deviation exceed maximum value? | It is quite common that people (including your professor) make this mistake.
People often do calculations assuming that one has a large sample of an ideal normal distribution. At a certain moment they start thinking that alle and everything in life shows a normal distribution. That is not true!
Especially when a distri... | Can mean plus one standard deviation exceed maximum value? | It is quite common that people (including your professor) make this mistake.
People often do calculations assuming that one has a large sample of an ideal normal distribution. At a certain moment they | Can mean plus one standard deviation exceed maximum value?
It is quite common that people (including your professor) make this mistake.
People often do calculations assuming that one has a large sample of an ideal normal distribution. At a certain moment they start thinking that alle and everything in life shows a norm... | Can mean plus one standard deviation exceed maximum value?
It is quite common that people (including your professor) make this mistake.
People often do calculations assuming that one has a large sample of an ideal normal distribution. At a certain moment they |
11,031 | Can mean plus one standard deviation exceed maximum value? | I would like to emphasise with this answer why I think people think of the normal distribution when the subject of standard deviation comes up, like other people have already mentioned in other answers for this question. For a lot of people, indeed the first thing that comes to mind when they think of standard deviatio... | Can mean plus one standard deviation exceed maximum value? | I would like to emphasise with this answer why I think people think of the normal distribution when the subject of standard deviation comes up, like other people have already mentioned in other answer | Can mean plus one standard deviation exceed maximum value?
I would like to emphasise with this answer why I think people think of the normal distribution when the subject of standard deviation comes up, like other people have already mentioned in other answers for this question. For a lot of people, indeed the first th... | Can mean plus one standard deviation exceed maximum value?
I would like to emphasise with this answer why I think people think of the normal distribution when the subject of standard deviation comes up, like other people have already mentioned in other answer |
11,032 | Benefits of using QQ-plots over histograms | The canonical paper here was:
Wilk, M.B. and R. Gnanadesikan. 1968. Probability plotting methods for the analysis of data. Biometrika 55: 1-17
and it still repays close and repeated reading. A lucid treatment with many good examples was given by:
Cleveland, W.S. 1993. Visualizing Data. Summit, NJ: Hobart Press.
and... | Benefits of using QQ-plots over histograms | The canonical paper here was:
Wilk, M.B. and R. Gnanadesikan. 1968. Probability plotting methods for the analysis of data. Biometrika 55: 1-17
and it still repays close and repeated reading. A lucid | Benefits of using QQ-plots over histograms
The canonical paper here was:
Wilk, M.B. and R. Gnanadesikan. 1968. Probability plotting methods for the analysis of data. Biometrika 55: 1-17
and it still repays close and repeated reading. A lucid treatment with many good examples was given by:
Cleveland, W.S. 1993. Visua... | Benefits of using QQ-plots over histograms
The canonical paper here was:
Wilk, M.B. and R. Gnanadesikan. 1968. Probability plotting methods for the analysis of data. Biometrika 55: 1-17
and it still repays close and repeated reading. A lucid |
11,033 | Benefits of using QQ-plots over histograms | See the work of William S. Cleveland.
Visualizing data is probably the best single source, but also see his web page, especially the bibliography and the page for Visualizing Data (including S+ code that is adaptable for use in R).
Cleveland has a lot of reasons why QQ plots are good and why histograms are not so go... | Benefits of using QQ-plots over histograms | See the work of William S. Cleveland.
Visualizing data is probably the best single source, but also see his web page, especially the bibliography and the page for Visualizing Data (including S+ code | Benefits of using QQ-plots over histograms
See the work of William S. Cleveland.
Visualizing data is probably the best single source, but also see his web page, especially the bibliography and the page for Visualizing Data (including S+ code that is adaptable for use in R).
Cleveland has a lot of reasons why QQ plot... | Benefits of using QQ-plots over histograms
See the work of William S. Cleveland.
Visualizing data is probably the best single source, but also see his web page, especially the bibliography and the page for Visualizing Data (including S+ code |
11,034 | Benefits of using QQ-plots over histograms | Once you learn how to use them, Q-Q plots allow you to identify skewness, heavytailedness, general shape, peaks and so on, the same kinds of features people tend to use histograms to try to assess.
Kernel density estimates or log-spline density estimates can avoid some of the issues with histograms that Gala pointed to... | Benefits of using QQ-plots over histograms | Once you learn how to use them, Q-Q plots allow you to identify skewness, heavytailedness, general shape, peaks and so on, the same kinds of features people tend to use histograms to try to assess.
Ke | Benefits of using QQ-plots over histograms
Once you learn how to use them, Q-Q plots allow you to identify skewness, heavytailedness, general shape, peaks and so on, the same kinds of features people tend to use histograms to try to assess.
Kernel density estimates or log-spline density estimates can avoid some of the ... | Benefits of using QQ-plots over histograms
Once you learn how to use them, Q-Q plots allow you to identify skewness, heavytailedness, general shape, peaks and so on, the same kinds of features people tend to use histograms to try to assess.
Ke |
11,035 | Benefits of using QQ-plots over histograms | Since this question has returned to the top... I see many arguments against histograms in favour of qqplots but I'm not entirely convinced. Consider this example:
x <- c(rnorm(10000, mean= 0), rnorm(10000, mean= 3))
par(mfrow= c(1, 2))
hist(x, breaks= 30)
qqnorm(x)
It's obvious from the histogram that there are two p... | Benefits of using QQ-plots over histograms | Since this question has returned to the top... I see many arguments against histograms in favour of qqplots but I'm not entirely convinced. Consider this example:
x <- c(rnorm(10000, mean= 0), rnorm(1 | Benefits of using QQ-plots over histograms
Since this question has returned to the top... I see many arguments against histograms in favour of qqplots but I'm not entirely convinced. Consider this example:
x <- c(rnorm(10000, mean= 0), rnorm(10000, mean= 3))
par(mfrow= c(1, 2))
hist(x, breaks= 30)
qqnorm(x)
It's obvi... | Benefits of using QQ-plots over histograms
Since this question has returned to the top... I see many arguments against histograms in favour of qqplots but I'm not entirely convinced. Consider this example:
x <- c(rnorm(10000, mean= 0), rnorm(1 |
11,036 | Maximum likelihood function for mixed type distribution | I admit to puzzling over this question for quite some time earlier in my career. One way I convinced myself of the answer was to take an extremely practical, applied view of the situation, a view that recognizes no measurement is perfect. Let's see where that might lead.
The point of this exercise is to expose the as... | Maximum likelihood function for mixed type distribution | I admit to puzzling over this question for quite some time earlier in my career. One way I convinced myself of the answer was to take an extremely practical, applied view of the situation, a view tha | Maximum likelihood function for mixed type distribution
I admit to puzzling over this question for quite some time earlier in my career. One way I convinced myself of the answer was to take an extremely practical, applied view of the situation, a view that recognizes no measurement is perfect. Let's see where that mi... | Maximum likelihood function for mixed type distribution
I admit to puzzling over this question for quite some time earlier in my career. One way I convinced myself of the answer was to take an extremely practical, applied view of the situation, a view tha |
11,037 | Maximum likelihood function for mixed type distribution | This question is an extremely important foundational problem in likelihood analysis, and also a very subtle and difficult one, so I'm quite surprised at some of the superficial answers it is receiving in the comments.
In any case, in this answer I am just going to add one small point to whuber's excellent answer (which... | Maximum likelihood function for mixed type distribution | This question is an extremely important foundational problem in likelihood analysis, and also a very subtle and difficult one, so I'm quite surprised at some of the superficial answers it is receiving | Maximum likelihood function for mixed type distribution
This question is an extremely important foundational problem in likelihood analysis, and also a very subtle and difficult one, so I'm quite surprised at some of the superficial answers it is receiving in the comments.
In any case, in this answer I am just going to... | Maximum likelihood function for mixed type distribution
This question is an extremely important foundational problem in likelihood analysis, and also a very subtle and difficult one, so I'm quite surprised at some of the superficial answers it is receiving |
11,038 | Maximum likelihood function for mixed type distribution | The likelihood function $\ell(\theta|\mathbf{x})$ is the density of the data at the observed value $\mathbf{x}$ expressed as a function of $\theta$
$$\ell(\theta|\mathbf{x})=f(\mathbf{x}|\theta)$$
This density is defined for every (acceptable) value of $\theta$ almost everywhere over the support of $\mathbf{x}$, $\math... | Maximum likelihood function for mixed type distribution | The likelihood function $\ell(\theta|\mathbf{x})$ is the density of the data at the observed value $\mathbf{x}$ expressed as a function of $\theta$
$$\ell(\theta|\mathbf{x})=f(\mathbf{x}|\theta)$$
Thi | Maximum likelihood function for mixed type distribution
The likelihood function $\ell(\theta|\mathbf{x})$ is the density of the data at the observed value $\mathbf{x}$ expressed as a function of $\theta$
$$\ell(\theta|\mathbf{x})=f(\mathbf{x}|\theta)$$
This density is defined for every (acceptable) value of $\theta$ al... | Maximum likelihood function for mixed type distribution
The likelihood function $\ell(\theta|\mathbf{x})$ is the density of the data at the observed value $\mathbf{x}$ expressed as a function of $\theta$
$$\ell(\theta|\mathbf{x})=f(\mathbf{x}|\theta)$$
Thi |
11,039 | Maximum likelihood function for mixed type distribution | One example where this occurs, that is, likelihood given by a probability model of mixed continuous/discrete type, is with censored data. For an example see Weighted normal errors regression with censoring .
In general this can be formulated using measure theory. Then assume a statistical model with a model function... | Maximum likelihood function for mixed type distribution | One example where this occurs, that is, likelihood given by a probability model of mixed continuous/discrete type, is with censored data. For an example see Weighted normal errors regression with cen | Maximum likelihood function for mixed type distribution
One example where this occurs, that is, likelihood given by a probability model of mixed continuous/discrete type, is with censored data. For an example see Weighted normal errors regression with censoring .
In general this can be formulated using measure theor... | Maximum likelihood function for mixed type distribution
One example where this occurs, that is, likelihood given by a probability model of mixed continuous/discrete type, is with censored data. For an example see Weighted normal errors regression with cen |
11,040 | Which optimization algorithm is used in glm function in R? | You will be interested to know that the documentation for glm, accessed via ?glm provides many useful insights: under method we find that iteratively reweighted least squares is the default method for glm.fit, which is the workhorse function for glm. Additionally, the documentation mentions that user-defined functions ... | Which optimization algorithm is used in glm function in R? | You will be interested to know that the documentation for glm, accessed via ?glm provides many useful insights: under method we find that iteratively reweighted least squares is the default method for | Which optimization algorithm is used in glm function in R?
You will be interested to know that the documentation for glm, accessed via ?glm provides many useful insights: under method we find that iteratively reweighted least squares is the default method for glm.fit, which is the workhorse function for glm. Additional... | Which optimization algorithm is used in glm function in R?
You will be interested to know that the documentation for glm, accessed via ?glm provides many useful insights: under method we find that iteratively reweighted least squares is the default method for |
11,041 | Which optimization algorithm is used in glm function in R? | The method used is mentioned in the output itself: it is Fisher Scoring. This is equivalent to Newton-Raphson in most cases. The exception being situations where you are using non-natural parameterizations. Relative risk regression is an example of such a scenario. There, the expected and observed information are diffe... | Which optimization algorithm is used in glm function in R? | The method used is mentioned in the output itself: it is Fisher Scoring. This is equivalent to Newton-Raphson in most cases. The exception being situations where you are using non-natural parameteriza | Which optimization algorithm is used in glm function in R?
The method used is mentioned in the output itself: it is Fisher Scoring. This is equivalent to Newton-Raphson in most cases. The exception being situations where you are using non-natural parameterizations. Relative risk regression is an example of such a scena... | Which optimization algorithm is used in glm function in R?
The method used is mentioned in the output itself: it is Fisher Scoring. This is equivalent to Newton-Raphson in most cases. The exception being situations where you are using non-natural parameteriza |
11,042 | Which optimization algorithm is used in glm function in R? | For the record, a simple pure R implementation of R's glm algorithm, based on Fisher scoring (iteratively reweighted least squares), as explained in the other answer is given by:
glm_irls = function(X, y, weights=rep(1,nrow(X)), family=poisson(log), maxit=25, tol=1e-16) {
if (!is(family, "family")) family = family(... | Which optimization algorithm is used in glm function in R? | For the record, a simple pure R implementation of R's glm algorithm, based on Fisher scoring (iteratively reweighted least squares), as explained in the other answer is given by:
glm_irls = function(X | Which optimization algorithm is used in glm function in R?
For the record, a simple pure R implementation of R's glm algorithm, based on Fisher scoring (iteratively reweighted least squares), as explained in the other answer is given by:
glm_irls = function(X, y, weights=rep(1,nrow(X)), family=poisson(log), maxit=25, t... | Which optimization algorithm is used in glm function in R?
For the record, a simple pure R implementation of R's glm algorithm, based on Fisher scoring (iteratively reweighted least squares), as explained in the other answer is given by:
glm_irls = function(X |
11,043 | Dealing with 0,1 values in a beta regression | According to Smithson & Verkuilen (2006)$^1$, an appropriate transformation is
$$ x' = \frac{x(N-1) + s}{N} $$
"where N is the sample size and s is a constant between 0 and 1. From a Bayesian standpoint, s acts as if we are taking a prior into account. A reasonable choice for s would be .5."
This will squeeze data th... | Dealing with 0,1 values in a beta regression | According to Smithson & Verkuilen (2006)$^1$, an appropriate transformation is
$$ x' = \frac{x(N-1) + s}{N} $$
"where N is the sample size and s is a constant between 0 and 1. From a Bayesian standpo | Dealing with 0,1 values in a beta regression
According to Smithson & Verkuilen (2006)$^1$, an appropriate transformation is
$$ x' = \frac{x(N-1) + s}{N} $$
"where N is the sample size and s is a constant between 0 and 1. From a Bayesian standpoint, s acts as if we are taking a prior into account. A reasonable choice f... | Dealing with 0,1 values in a beta regression
According to Smithson & Verkuilen (2006)$^1$, an appropriate transformation is
$$ x' = \frac{x(N-1) + s}{N} $$
"where N is the sample size and s is a constant between 0 and 1. From a Bayesian standpo |
11,044 | Dealing with 0,1 values in a beta regression | I think the actual "correct" answer to this question is zero-one inflated beta regression. This is designed to handle data that vary continuously on the interval [0,1], and allows many real 0's and 1's to be in the data. This approach fits three separate models in a bayesian context, similar to what @B_Miner proposed.
... | Dealing with 0,1 values in a beta regression | I think the actual "correct" answer to this question is zero-one inflated beta regression. This is designed to handle data that vary continuously on the interval [0,1], and allows many real 0's and 1' | Dealing with 0,1 values in a beta regression
I think the actual "correct" answer to this question is zero-one inflated beta regression. This is designed to handle data that vary continuously on the interval [0,1], and allows many real 0's and 1's to be in the data. This approach fits three separate models in a bayesian... | Dealing with 0,1 values in a beta regression
I think the actual "correct" answer to this question is zero-one inflated beta regression. This is designed to handle data that vary continuously on the interval [0,1], and allows many real 0's and 1' |
11,045 | Dealing with 0,1 values in a beta regression | Dave,
A common approach to this problem is to fit 2 logistic regression models to predict whether a case is 0 or 1. Then, a beta regression is used for those in the range (0,1). | Dealing with 0,1 values in a beta regression | Dave,
A common approach to this problem is to fit 2 logistic regression models to predict whether a case is 0 or 1. Then, a beta regression is used for those in the range (0,1). | Dealing with 0,1 values in a beta regression
Dave,
A common approach to this problem is to fit 2 logistic regression models to predict whether a case is 0 or 1. Then, a beta regression is used for those in the range (0,1). | Dealing with 0,1 values in a beta regression
Dave,
A common approach to this problem is to fit 2 logistic regression models to predict whether a case is 0 or 1. Then, a beta regression is used for those in the range (0,1). |
11,046 | Dealing with 0,1 values in a beta regression | The beta distribution follows from the sufficient statistics $(\log(x), \log(1-x))$. Do those statistics make sense for your data? If you have so many zeros and ones, then it seems doubtful that they do, and you might consider not using a beta distribution at all.
If you were to choose the sufficient statistic $x$ in... | Dealing with 0,1 values in a beta regression | The beta distribution follows from the sufficient statistics $(\log(x), \log(1-x))$. Do those statistics make sense for your data? If you have so many zeros and ones, then it seems doubtful that the | Dealing with 0,1 values in a beta regression
The beta distribution follows from the sufficient statistics $(\log(x), \log(1-x))$. Do those statistics make sense for your data? If you have so many zeros and ones, then it seems doubtful that they do, and you might consider not using a beta distribution at all.
If you w... | Dealing with 0,1 values in a beta regression
The beta distribution follows from the sufficient statistics $(\log(x), \log(1-x))$. Do those statistics make sense for your data? If you have so many zeros and ones, then it seems doubtful that the |
11,047 | Dealing with 0,1 values in a beta regression | My experience with regression modeling, in general, involves also the exercise of judgment and in that regard, it is something of an art, especially when it comes to constructing good forecasting models. My observation is that actually parsimonious models appear to be superior, overfitting a model is not the apparent o... | Dealing with 0,1 values in a beta regression | My experience with regression modeling, in general, involves also the exercise of judgment and in that regard, it is something of an art, especially when it comes to constructing good forecasting mode | Dealing with 0,1 values in a beta regression
My experience with regression modeling, in general, involves also the exercise of judgment and in that regard, it is something of an art, especially when it comes to constructing good forecasting models. My observation is that actually parsimonious models appear to be superi... | Dealing with 0,1 values in a beta regression
My experience with regression modeling, in general, involves also the exercise of judgment and in that regard, it is something of an art, especially when it comes to constructing good forecasting mode |
11,048 | Addressing model uncertainty | There are two cases which arise in dealing with model-selection:
When the true model belongs in the model space.
This is very simple to deal with using BIC. There are results which show that BIC will select the true model with high probability.
However, in practice it is very rare that we know the true model. I must... | Addressing model uncertainty | There are two cases which arise in dealing with model-selection:
When the true model belongs in the model space.
This is very simple to deal with using BIC. There are results which show that BIC will | Addressing model uncertainty
There are two cases which arise in dealing with model-selection:
When the true model belongs in the model space.
This is very simple to deal with using BIC. There are results which show that BIC will select the true model with high probability.
However, in practice it is very rare that w... | Addressing model uncertainty
There are two cases which arise in dealing with model-selection:
When the true model belongs in the model space.
This is very simple to deal with using BIC. There are results which show that BIC will |
11,049 | Addressing model uncertainty | A "true" Bayesian would deal with model uncertainty by marginalising (integrating) over all plausble models. So for example in a linear ridge regression problem you would marginalise over the regression parameters (which would have a Gaussian posterior, so it could be done analytically), but then marginalise over the ... | Addressing model uncertainty | A "true" Bayesian would deal with model uncertainty by marginalising (integrating) over all plausble models. So for example in a linear ridge regression problem you would marginalise over the regress | Addressing model uncertainty
A "true" Bayesian would deal with model uncertainty by marginalising (integrating) over all plausble models. So for example in a linear ridge regression problem you would marginalise over the regression parameters (which would have a Gaussian posterior, so it could be done analytically), b... | Addressing model uncertainty
A "true" Bayesian would deal with model uncertainty by marginalising (integrating) over all plausble models. So for example in a linear ridge regression problem you would marginalise over the regress |
11,050 | Addressing model uncertainty | One of the interesting things I find in the "Model Uncertainty" world is this notion of a "true model". This implicitly means that our "model propositions" are of the form:
$$M_i^{(1)}:\text{The ith model is the true model}$$
From which we calculate the posterior probabilities $P(M_i^{(1)}|DI)$. This procedure seems ... | Addressing model uncertainty | One of the interesting things I find in the "Model Uncertainty" world is this notion of a "true model". This implicitly means that our "model propositions" are of the form:
$$M_i^{(1)}:\text{The ith | Addressing model uncertainty
One of the interesting things I find in the "Model Uncertainty" world is this notion of a "true model". This implicitly means that our "model propositions" are of the form:
$$M_i^{(1)}:\text{The ith model is the true model}$$
From which we calculate the posterior probabilities $P(M_i^{(1)}... | Addressing model uncertainty
One of the interesting things I find in the "Model Uncertainty" world is this notion of a "true model". This implicitly means that our "model propositions" are of the form:
$$M_i^{(1)}:\text{The ith |
11,051 | Addressing model uncertainty | I know people use DIC and Bayes factor, as suncoolsu said. And I was interested when he said "There are results which show that BIC will select the true model with high probability" (references?). But I use the only thing I know, which is posterior predictive check, championed by Andrew Gelman. If you google Andrew Gel... | Addressing model uncertainty | I know people use DIC and Bayes factor, as suncoolsu said. And I was interested when he said "There are results which show that BIC will select the true model with high probability" (references?). But | Addressing model uncertainty
I know people use DIC and Bayes factor, as suncoolsu said. And I was interested when he said "There are results which show that BIC will select the true model with high probability" (references?). But I use the only thing I know, which is posterior predictive check, championed by Andrew Gel... | Addressing model uncertainty
I know people use DIC and Bayes factor, as suncoolsu said. And I was interested when he said "There are results which show that BIC will select the true model with high probability" (references?). But |
11,052 | What could cause big differences in correlation coefficient between Pearson's and Spearman's correlation for a given dataset? | Why the big difference
If your data is normally distributed or uniformly distributed, I would think that Spearman's and Pearson's correlation should be fairly similar.
If they are giving very different results as in your case (.65 versus .30), my guess is that you have skewed data or outliers, and that outliers are le... | What could cause big differences in correlation coefficient between Pearson's and Spearman's correla | Why the big difference
If your data is normally distributed or uniformly distributed, I would think that Spearman's and Pearson's correlation should be fairly similar.
If they are giving very differe | What could cause big differences in correlation coefficient between Pearson's and Spearman's correlation for a given dataset?
Why the big difference
If your data is normally distributed or uniformly distributed, I would think that Spearman's and Pearson's correlation should be fairly similar.
If they are giving very d... | What could cause big differences in correlation coefficient between Pearson's and Spearman's correla
Why the big difference
If your data is normally distributed or uniformly distributed, I would think that Spearman's and Pearson's correlation should be fairly similar.
If they are giving very differe |
11,053 | Why is skip-gram better for infrequent words than CBOW? | Here is my oversimplified and rather naive understanding of the difference:
As we know, CBOW is learning to predict the word by the context. Or maximize the probability of the target word by looking at the context. And this happens to be a problem for rare words. For example, given the context yesterday was really [...... | Why is skip-gram better for infrequent words than CBOW? | Here is my oversimplified and rather naive understanding of the difference:
As we know, CBOW is learning to predict the word by the context. Or maximize the probability of the target word by looking a | Why is skip-gram better for infrequent words than CBOW?
Here is my oversimplified and rather naive understanding of the difference:
As we know, CBOW is learning to predict the word by the context. Or maximize the probability of the target word by looking at the context. And this happens to be a problem for rare words. ... | Why is skip-gram better for infrequent words than CBOW?
Here is my oversimplified and rather naive understanding of the difference:
As we know, CBOW is learning to predict the word by the context. Or maximize the probability of the target word by looking a |
11,054 | Why is skip-gram better for infrequent words than CBOW? | In CBOW the vectors from the context words are averaged before predicting the center word. In skip-gram there is no averaging of embedding vectors. It seems like the model can learn better representations for the rare words when their vectors are not averaged with the other context words in the process of making the pr... | Why is skip-gram better for infrequent words than CBOW? | In CBOW the vectors from the context words are averaged before predicting the center word. In skip-gram there is no averaging of embedding vectors. It seems like the model can learn better representat | Why is skip-gram better for infrequent words than CBOW?
In CBOW the vectors from the context words are averaged before predicting the center word. In skip-gram there is no averaging of embedding vectors. It seems like the model can learn better representations for the rare words when their vectors are not averaged with... | Why is skip-gram better for infrequent words than CBOW?
In CBOW the vectors from the context words are averaged before predicting the center word. In skip-gram there is no averaging of embedding vectors. It seems like the model can learn better representat |
11,055 | Why is skip-gram better for infrequent words than CBOW? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
I have just come across a paper that shows the opposit... | Why is skip-gram better for infrequent words than CBOW? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Why is skip-gram better for infrequent words than CBOW?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | Why is skip-gram better for infrequent words than CBOW?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
11,056 | Goodness of fit and which model to choose linear regression or Poisson | Most important is the logic behind the model. Your variable "number of patents per year" is a count variable, so Poisson regression is indicated. That is a GLM (generalized linear model) with (usually) log link function, while the usual linear regression is a Gaussian GLM with identity link. Here, it is truly the log ... | Goodness of fit and which model to choose linear regression or Poisson | Most important is the logic behind the model. Your variable "number of patents per year" is a count variable, so Poisson regression is indicated. That is a GLM (generalized linear model) with (usually | Goodness of fit and which model to choose linear regression or Poisson
Most important is the logic behind the model. Your variable "number of patents per year" is a count variable, so Poisson regression is indicated. That is a GLM (generalized linear model) with (usually) log link function, while the usual linear regre... | Goodness of fit and which model to choose linear regression or Poisson
Most important is the logic behind the model. Your variable "number of patents per year" is a count variable, so Poisson regression is indicated. That is a GLM (generalized linear model) with (usually |
11,057 | Always Report Robust (White) Standard Errors? | Using robust standard errors has become common practice in economics. Robust standard errors are typically larger than non-robust (standard?) standard errors, so the practice can be viewed as an effort to be conservative.
In large samples (e.g., if you are working with Census data with millions of observations or data... | Always Report Robust (White) Standard Errors? | Using robust standard errors has become common practice in economics. Robust standard errors are typically larger than non-robust (standard?) standard errors, so the practice can be viewed as an effor | Always Report Robust (White) Standard Errors?
Using robust standard errors has become common practice in economics. Robust standard errors are typically larger than non-robust (standard?) standard errors, so the practice can be viewed as an effort to be conservative.
In large samples (e.g., if you are working with Cen... | Always Report Robust (White) Standard Errors?
Using robust standard errors has become common practice in economics. Robust standard errors are typically larger than non-robust (standard?) standard errors, so the practice can be viewed as an effor |
11,058 | Always Report Robust (White) Standard Errors? | Robust standard errors provide unbiased standard errors estimates under heteroscedasticity. There exists several statistical text books that provide a large and lengthy discussion on robust standard errors. The following site provides a somewhat comprehensive summary on robust standard errors:
https://economictheoryblo... | Always Report Robust (White) Standard Errors? | Robust standard errors provide unbiased standard errors estimates under heteroscedasticity. There exists several statistical text books that provide a large and lengthy discussion on robust standard e | Always Report Robust (White) Standard Errors?
Robust standard errors provide unbiased standard errors estimates under heteroscedasticity. There exists several statistical text books that provide a large and lengthy discussion on robust standard errors. The following site provides a somewhat comprehensive summary on rob... | Always Report Robust (White) Standard Errors?
Robust standard errors provide unbiased standard errors estimates under heteroscedasticity. There exists several statistical text books that provide a large and lengthy discussion on robust standard e |
11,059 | Always Report Robust (White) Standard Errors? | In Introductory Econometrics (Woolridge, 2009 edition page 268) this question is addressed. Woolridge says that when using robust standard errors, the t-statistics obtained only have distributions which are similar to the exact t-distributions if the sample size is large. If the sample size is small, the t-stats obtai... | Always Report Robust (White) Standard Errors? | In Introductory Econometrics (Woolridge, 2009 edition page 268) this question is addressed. Woolridge says that when using robust standard errors, the t-statistics obtained only have distributions wh | Always Report Robust (White) Standard Errors?
In Introductory Econometrics (Woolridge, 2009 edition page 268) this question is addressed. Woolridge says that when using robust standard errors, the t-statistics obtained only have distributions which are similar to the exact t-distributions if the sample size is large. ... | Always Report Robust (White) Standard Errors?
In Introductory Econometrics (Woolridge, 2009 edition page 268) this question is addressed. Woolridge says that when using robust standard errors, the t-statistics obtained only have distributions wh |
11,060 | Always Report Robust (White) Standard Errors? | There are a lot of reasons to avoid using robust standard errors. Technically what happens is, that the variances get weighted by weights that you can not prove in reality. Thus robustness is just a cosmetic tool. In general you should thin about changing the model.
There are a lot of implications to deal with heterog... | Always Report Robust (White) Standard Errors? | There are a lot of reasons to avoid using robust standard errors. Technically what happens is, that the variances get weighted by weights that you can not prove in reality. Thus robustness is just a c | Always Report Robust (White) Standard Errors?
There are a lot of reasons to avoid using robust standard errors. Technically what happens is, that the variances get weighted by weights that you can not prove in reality. Thus robustness is just a cosmetic tool. In general you should thin about changing the model.
There ... | Always Report Robust (White) Standard Errors?
There are a lot of reasons to avoid using robust standard errors. Technically what happens is, that the variances get weighted by weights that you can not prove in reality. Thus robustness is just a c |
11,061 | Always Report Robust (White) Standard Errors? | I thought that the White Standard Error and the Standard Error computed in the "normal" way (eg, Hessian and/or OPG in the case of maximum likelihood) were asymptotically equivalent in the case of homoskedasticity?
Only if there is heteroskedasticity will the "normal" standard error be inappropriate, which means that ... | Always Report Robust (White) Standard Errors? | I thought that the White Standard Error and the Standard Error computed in the "normal" way (eg, Hessian and/or OPG in the case of maximum likelihood) were asymptotically equivalent in the case of hom | Always Report Robust (White) Standard Errors?
I thought that the White Standard Error and the Standard Error computed in the "normal" way (eg, Hessian and/or OPG in the case of maximum likelihood) were asymptotically equivalent in the case of homoskedasticity?
Only if there is heteroskedasticity will the "normal" stan... | Always Report Robust (White) Standard Errors?
I thought that the White Standard Error and the Standard Error computed in the "normal" way (eg, Hessian and/or OPG in the case of maximum likelihood) were asymptotically equivalent in the case of hom |
11,062 | Always Report Robust (White) Standard Errors? | I have a textbook entitled Introduction to Econometrics, 3rd ed. by Stock and Watson that reads, "if the errors are heteroskedastic, then the t-statistic computed using the homoskedasticity-only standard error does not have a standard normal distribution, even in large samples." I believe you cannot do proper inference... | Always Report Robust (White) Standard Errors? | I have a textbook entitled Introduction to Econometrics, 3rd ed. by Stock and Watson that reads, "if the errors are heteroskedastic, then the t-statistic computed using the homoskedasticity-only stand | Always Report Robust (White) Standard Errors?
I have a textbook entitled Introduction to Econometrics, 3rd ed. by Stock and Watson that reads, "if the errors are heteroskedastic, then the t-statistic computed using the homoskedasticity-only standard error does not have a standard normal distribution, even in large samp... | Always Report Robust (White) Standard Errors?
I have a textbook entitled Introduction to Econometrics, 3rd ed. by Stock and Watson that reads, "if the errors are heteroskedastic, then the t-statistic computed using the homoskedasticity-only stand |
11,063 | Bayesian updating with new data | The basic idea of Bayesian updating is that given some data $X$ and prior over parameter of interest $\theta$, where the relation between data and parameter is described using likelihood function, you use Bayes theorem to obtain posterior
$$ p(\theta \mid X) \propto p(X \mid \theta) \, p(\theta) $$
This can be done seq... | Bayesian updating with new data | The basic idea of Bayesian updating is that given some data $X$ and prior over parameter of interest $\theta$, where the relation between data and parameter is described using likelihood function, you | Bayesian updating with new data
The basic idea of Bayesian updating is that given some data $X$ and prior over parameter of interest $\theta$, where the relation between data and parameter is described using likelihood function, you use Bayes theorem to obtain posterior
$$ p(\theta \mid X) \propto p(X \mid \theta) \, p... | Bayesian updating with new data
The basic idea of Bayesian updating is that given some data $X$ and prior over parameter of interest $\theta$, where the relation between data and parameter is described using likelihood function, you |
11,064 | Bayesian updating with new data | If you have a prior $P(\theta)$ and a likelihood function $P(x \mid \theta)$ you can calculate the posterior with:
$$ P(\theta \mid x) = \frac{\sum_\theta P(x \mid \theta) P(\theta)}{P(x)} $$
Since $P(x)$ is just a normalization constant to make probabilities sum to one, you could write:
$$P(\theta \mid x) \sim \sum_\... | Bayesian updating with new data | If you have a prior $P(\theta)$ and a likelihood function $P(x \mid \theta)$ you can calculate the posterior with:
$$ P(\theta \mid x) = \frac{\sum_\theta P(x \mid \theta) P(\theta)}{P(x)} $$
Since $ | Bayesian updating with new data
If you have a prior $P(\theta)$ and a likelihood function $P(x \mid \theta)$ you can calculate the posterior with:
$$ P(\theta \mid x) = \frac{\sum_\theta P(x \mid \theta) P(\theta)}{P(x)} $$
Since $P(x)$ is just a normalization constant to make probabilities sum to one, you could write... | Bayesian updating with new data
If you have a prior $P(\theta)$ and a likelihood function $P(x \mid \theta)$ you can calculate the posterior with:
$$ P(\theta \mid x) = \frac{\sum_\theta P(x \mid \theta) P(\theta)}{P(x)} $$
Since $ |
11,065 | Bayesian updating with new data | This is the central computation issue for Bayesian data analysis. It really depends on the data and distributions involved. For simple cases where everything can be expressed in closed form (e.g., with conjugate priors), you can use Bayes's theorem directly. The most popular family of techniques for more complex cases ... | Bayesian updating with new data | This is the central computation issue for Bayesian data analysis. It really depends on the data and distributions involved. For simple cases where everything can be expressed in closed form (e.g., wit | Bayesian updating with new data
This is the central computation issue for Bayesian data analysis. It really depends on the data and distributions involved. For simple cases where everything can be expressed in closed form (e.g., with conjugate priors), you can use Bayes's theorem directly. The most popular family of te... | Bayesian updating with new data
This is the central computation issue for Bayesian data analysis. It really depends on the data and distributions involved. For simple cases where everything can be expressed in closed form (e.g., wit |
11,066 | VAR forecasting methodology | I think you got it pretty right, but when building a VAR model, I usually make sure I follow these steps:
1. Select the variables
This is the most important part of building your model. If you want to forecast the price of an asset, you need to include variables that are related with the mechanism of price formation. T... | VAR forecasting methodology | I think you got it pretty right, but when building a VAR model, I usually make sure I follow these steps:
1. Select the variables
This is the most important part of building your model. If you want to | VAR forecasting methodology
I think you got it pretty right, but when building a VAR model, I usually make sure I follow these steps:
1. Select the variables
This is the most important part of building your model. If you want to forecast the price of an asset, you need to include variables that are related with the mec... | VAR forecasting methodology
I think you got it pretty right, but when building a VAR model, I usually make sure I follow these steps:
1. Select the variables
This is the most important part of building your model. If you want to |
11,067 | VAR forecasting methodology | I thought I would add to Regis A Ely very nice answer. His answer is not wrong, but using a VAR to forecast is different than using a VAR to do other VAR type things (i.e. IRF, FEVD, Historical Decomp. etc...). Consequently, some of the steps outlined by Regis A Ely will negatively effect your forecast in some cases.... | VAR forecasting methodology | I thought I would add to Regis A Ely very nice answer. His answer is not wrong, but using a VAR to forecast is different than using a VAR to do other VAR type things (i.e. IRF, FEVD, Historical Decom | VAR forecasting methodology
I thought I would add to Regis A Ely very nice answer. His answer is not wrong, but using a VAR to forecast is different than using a VAR to do other VAR type things (i.e. IRF, FEVD, Historical Decomp. etc...). Consequently, some of the steps outlined by Regis A Ely will negatively effect ... | VAR forecasting methodology
I thought I would add to Regis A Ely very nice answer. His answer is not wrong, but using a VAR to forecast is different than using a VAR to do other VAR type things (i.e. IRF, FEVD, Historical Decom |
11,068 | How to interpret parameters in GLM with family=Gamma | The log-linked gamma GLM specification is identical to exponential regression:
$$E[y \vert x,z] = \exp \left( \alpha + \beta \cdot x +\gamma \cdot z \right)=\hat y$$
This means that $E[y \vert x=0,z=0]=\exp(\alpha)$. That's not a very meaningful value (unless you centered your variables to be be mean zero beforehand).... | How to interpret parameters in GLM with family=Gamma | The log-linked gamma GLM specification is identical to exponential regression:
$$E[y \vert x,z] = \exp \left( \alpha + \beta \cdot x +\gamma \cdot z \right)=\hat y$$
This means that $E[y \vert x=0,z= | How to interpret parameters in GLM with family=Gamma
The log-linked gamma GLM specification is identical to exponential regression:
$$E[y \vert x,z] = \exp \left( \alpha + \beta \cdot x +\gamma \cdot z \right)=\hat y$$
This means that $E[y \vert x=0,z=0]=\exp(\alpha)$. That's not a very meaningful value (unless you ce... | How to interpret parameters in GLM with family=Gamma
The log-linked gamma GLM specification is identical to exponential regression:
$$E[y \vert x,z] = \exp \left( \alpha + \beta \cdot x +\gamma \cdot z \right)=\hat y$$
This means that $E[y \vert x=0,z= |
11,069 | How to interpret parameters in GLM with family=Gamma | First I would look at the residuals to see how well the model fits. If it's OK, I would try using other link functions unless I had reason to believe it really came from a gamma distribution. If the gamma still looked convincing, I would conclude that the statistically significant terms are the intercept, height, educa... | How to interpret parameters in GLM with family=Gamma | First I would look at the residuals to see how well the model fits. If it's OK, I would try using other link functions unless I had reason to believe it really came from a gamma distribution. If the g | How to interpret parameters in GLM with family=Gamma
First I would look at the residuals to see how well the model fits. If it's OK, I would try using other link functions unless I had reason to believe it really came from a gamma distribution. If the gamma still looked convincing, I would conclude that the statistical... | How to interpret parameters in GLM with family=Gamma
First I would look at the residuals to see how well the model fits. If it's OK, I would try using other link functions unless I had reason to believe it really came from a gamma distribution. If the g |
11,070 | Does differential geometry have anything to do with statistics? | Two canonical books on the subject, with reviews, then two other references:
Differential Geometry and Statistics, M.K. Murray, J.W. Rice
Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions there has been interest among statisticians in the application ... | Does differential geometry have anything to do with statistics? | Two canonical books on the subject, with reviews, then two other references:
Differential Geometry and Statistics, M.K. Murray, J.W. Rice
Ever since the introduction by Rao in 1945 of the Fisher inf | Does differential geometry have anything to do with statistics?
Two canonical books on the subject, with reviews, then two other references:
Differential Geometry and Statistics, M.K. Murray, J.W. Rice
Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions... | Does differential geometry have anything to do with statistics?
Two canonical books on the subject, with reviews, then two other references:
Differential Geometry and Statistics, M.K. Murray, J.W. Rice
Ever since the introduction by Rao in 1945 of the Fisher inf |
11,071 | Does differential geometry have anything to do with statistics? | Riemannian geometry is used in the study of random fields (a generalization of stochastic processes), where the process doesn't have to be stationary. The reference I'm studying is given below with two reviews. There are applications in oceanography, astrophysics and brain imaging.
Random Fields and Geometry, Adler, R.... | Does differential geometry have anything to do with statistics? | Riemannian geometry is used in the study of random fields (a generalization of stochastic processes), where the process doesn't have to be stationary. The reference I'm studying is given below with tw | Does differential geometry have anything to do with statistics?
Riemannian geometry is used in the study of random fields (a generalization of stochastic processes), where the process doesn't have to be stationary. The reference I'm studying is given below with two reviews. There are applications in oceanography, astro... | Does differential geometry have anything to do with statistics?
Riemannian geometry is used in the study of random fields (a generalization of stochastic processes), where the process doesn't have to be stationary. The reference I'm studying is given below with tw |
11,072 | Does differential geometry have anything to do with statistics? | One area of statistics/applied mathematics where differential geometry is used in an essential way (together with a lot of other areas of mathematics!) is pattern theory. You could have a look at the book by Ulf Grenander: https://www.amazon.com/Pattern-Theory-Representation-Inference-European/dp/0199297061/ref=asap_b... | Does differential geometry have anything to do with statistics? | One area of statistics/applied mathematics where differential geometry is used in an essential way (together with a lot of other areas of mathematics!) is pattern theory. You could have a look at the | Does differential geometry have anything to do with statistics?
One area of statistics/applied mathematics where differential geometry is used in an essential way (together with a lot of other areas of mathematics!) is pattern theory. You could have a look at the book by Ulf Grenander: https://www.amazon.com/Pattern-T... | Does differential geometry have anything to do with statistics?
One area of statistics/applied mathematics where differential geometry is used in an essential way (together with a lot of other areas of mathematics!) is pattern theory. You could have a look at the |
11,073 | Choosing between $z$-test and $t$-test | @AdamO is right, you simply always use the $t$-test if you don't know the population standard deviation a-priori. You don't have to worry about when to switch to the $z$-test, because the $t$-distribution 'switches' for you. More specifically, the $t$-distribution converges to the normal, thus it is the correct distr... | Choosing between $z$-test and $t$-test | @AdamO is right, you simply always use the $t$-test if you don't know the population standard deviation a-priori. You don't have to worry about when to switch to the $z$-test, because the $t$-distrib | Choosing between $z$-test and $t$-test
@AdamO is right, you simply always use the $t$-test if you don't know the population standard deviation a-priori. You don't have to worry about when to switch to the $z$-test, because the $t$-distribution 'switches' for you. More specifically, the $t$-distribution converges to t... | Choosing between $z$-test and $t$-test
@AdamO is right, you simply always use the $t$-test if you don't know the population standard deviation a-priori. You don't have to worry about when to switch to the $z$-test, because the $t$-distrib |
11,074 | Choosing between $z$-test and $t$-test | There's nothing to discuss on the matter. Use a $t$-test always for a nonparametric test of differences in means, unless a more sophisticated resampling tool—e.g. permutation or bootstrap—is called for (useful in very small samples with large departures from normality).
If the degrees of freedom actually matter, then t... | Choosing between $z$-test and $t$-test | There's nothing to discuss on the matter. Use a $t$-test always for a nonparametric test of differences in means, unless a more sophisticated resampling tool—e.g. permutation or bootstrap—is called fo | Choosing between $z$-test and $t$-test
There's nothing to discuss on the matter. Use a $t$-test always for a nonparametric test of differences in means, unless a more sophisticated resampling tool—e.g. permutation or bootstrap—is called for (useful in very small samples with large departures from normality).
If the deg... | Choosing between $z$-test and $t$-test
There's nothing to discuss on the matter. Use a $t$-test always for a nonparametric test of differences in means, unless a more sophisticated resampling tool—e.g. permutation or bootstrap—is called fo |
11,075 | t-test on highly skewed data | Neither the t-test nor the permutation test have much power to identify a difference in means between two such extraordinarily skewed distributions. Thus they both give anodyne p-values indicating no significance at all. The issue is not that they seem to agree; it is that because they have a hard time detecting any ... | t-test on highly skewed data | Neither the t-test nor the permutation test have much power to identify a difference in means between two such extraordinarily skewed distributions. Thus they both give anodyne p-values indicating no | t-test on highly skewed data
Neither the t-test nor the permutation test have much power to identify a difference in means between two such extraordinarily skewed distributions. Thus they both give anodyne p-values indicating no significance at all. The issue is not that they seem to agree; it is that because they ha... | t-test on highly skewed data
Neither the t-test nor the permutation test have much power to identify a difference in means between two such extraordinarily skewed distributions. Thus they both give anodyne p-values indicating no |
11,076 | t-test on highly skewed data | When n is large (like 300, even far less than 3000), the t-test is essentially the same as the z-test. That is, the t-test becomes nothing more than an application of the central limit theorem, which says that the MEAN for each of your two groups is almost exactly normally distributed (even if the observations underly... | t-test on highly skewed data | When n is large (like 300, even far less than 3000), the t-test is essentially the same as the z-test. That is, the t-test becomes nothing more than an application of the central limit theorem, which | t-test on highly skewed data
When n is large (like 300, even far less than 3000), the t-test is essentially the same as the z-test. That is, the t-test becomes nothing more than an application of the central limit theorem, which says that the MEAN for each of your two groups is almost exactly normally distributed (eve... | t-test on highly skewed data
When n is large (like 300, even far less than 3000), the t-test is essentially the same as the z-test. That is, the t-test becomes nothing more than an application of the central limit theorem, which |
11,077 | t-test on highly skewed data | I know this answer is way late. However, I am getting a PhD in health services research, so I work with healthcare data a lot, including cost data.
I don't know what data the OP had. If it were cross-sectional data, then chances are it was justifiably IID. Independence means that each unit, so each person, is independe... | t-test on highly skewed data | I know this answer is way late. However, I am getting a PhD in health services research, so I work with healthcare data a lot, including cost data.
I don't know what data the OP had. If it were cross- | t-test on highly skewed data
I know this answer is way late. However, I am getting a PhD in health services research, so I work with healthcare data a lot, including cost data.
I don't know what data the OP had. If it were cross-sectional data, then chances are it was justifiably IID. Independence means that each unit,... | t-test on highly skewed data
I know this answer is way late. However, I am getting a PhD in health services research, so I work with healthcare data a lot, including cost data.
I don't know what data the OP had. If it were cross- |
11,078 | Does non-zero correlation imply dependence? | Yes, because
$$\text{Corr}(X,Y)\ne0 \Rightarrow \text{Cov}(X,Y)\ne0$$
$$\Rightarrow E(XY) - E(X)E(Y) \ne 0 $$
$$\Rightarrow \int \int xyf_{X,Y}(x,y)dxdy -\int xf_X(x) dx\int yf_Y(y)dy \ne 0$$
$$\Rightarrow \int \int xyf_{X,Y}(x,y)dxdy -\int \int xyf_X(x) f_Y(y)dxdy \ne 0$$
$$\Rightarrow \int \int xy \big[f_{X,Y}(x,y) ... | Does non-zero correlation imply dependence? | Yes, because
$$\text{Corr}(X,Y)\ne0 \Rightarrow \text{Cov}(X,Y)\ne0$$
$$\Rightarrow E(XY) - E(X)E(Y) \ne 0 $$
$$\Rightarrow \int \int xyf_{X,Y}(x,y)dxdy -\int xf_X(x) dx\int yf_Y(y)dy \ne 0$$
$$\Right | Does non-zero correlation imply dependence?
Yes, because
$$\text{Corr}(X,Y)\ne0 \Rightarrow \text{Cov}(X,Y)\ne0$$
$$\Rightarrow E(XY) - E(X)E(Y) \ne 0 $$
$$\Rightarrow \int \int xyf_{X,Y}(x,y)dxdy -\int xf_X(x) dx\int yf_Y(y)dy \ne 0$$
$$\Rightarrow \int \int xyf_{X,Y}(x,y)dxdy -\int \int xyf_X(x) f_Y(y)dxdy \ne 0$$
$$... | Does non-zero correlation imply dependence?
Yes, because
$$\text{Corr}(X,Y)\ne0 \Rightarrow \text{Cov}(X,Y)\ne0$$
$$\Rightarrow E(XY) - E(X)E(Y) \ne 0 $$
$$\Rightarrow \int \int xyf_{X,Y}(x,y)dxdy -\int xf_X(x) dx\int yf_Y(y)dy \ne 0$$
$$\Right |
11,079 | Does non-zero correlation imply dependence? | Let $X$ and $Y$ denote random variables such that $E[X^2]$ and $E[Y^2]$
are finite. Then, $E[XY]$, $E[X]$ and $E[Y]$ all are finite.
Restricting our attention to such random variables, let
$A$ denote the statement that $X$ and $Y$ are independent random variables
and $B$ the statement that $X$ and $Y$ are uncorrelate... | Does non-zero correlation imply dependence? | Let $X$ and $Y$ denote random variables such that $E[X^2]$ and $E[Y^2]$
are finite. Then, $E[XY]$, $E[X]$ and $E[Y]$ all are finite.
Restricting our attention to such random variables, let
$A$ denot | Does non-zero correlation imply dependence?
Let $X$ and $Y$ denote random variables such that $E[X^2]$ and $E[Y^2]$
are finite. Then, $E[XY]$, $E[X]$ and $E[Y]$ all are finite.
Restricting our attention to such random variables, let
$A$ denote the statement that $X$ and $Y$ are independent random variables
and $B$ th... | Does non-zero correlation imply dependence?
Let $X$ and $Y$ denote random variables such that $E[X^2]$ and $E[Y^2]$
are finite. Then, $E[XY]$, $E[X]$ and $E[Y]$ all are finite.
Restricting our attention to such random variables, let
$A$ denot |
11,080 | Does non-zero correlation imply dependence? | Here a purely logical proof. If $A\rightarrow B$ then necessarily $\neg B \rightarrow \neg A$, as the two are equivalent. Thus if $\neg B$ then $\neg A$. Now replace $A$ with independence and $B$ with correlation.
Think about a statement "if volcano erupts there are going to be damages". Now think about a case where th... | Does non-zero correlation imply dependence? | Here a purely logical proof. If $A\rightarrow B$ then necessarily $\neg B \rightarrow \neg A$, as the two are equivalent. Thus if $\neg B$ then $\neg A$. Now replace $A$ with independence and $B$ with | Does non-zero correlation imply dependence?
Here a purely logical proof. If $A\rightarrow B$ then necessarily $\neg B \rightarrow \neg A$, as the two are equivalent. Thus if $\neg B$ then $\neg A$. Now replace $A$ with independence and $B$ with correlation.
Think about a statement "if volcano erupts there are going to ... | Does non-zero correlation imply dependence?
Here a purely logical proof. If $A\rightarrow B$ then necessarily $\neg B \rightarrow \neg A$, as the two are equivalent. Thus if $\neg B$ then $\neg A$. Now replace $A$ with independence and $B$ with |
11,081 | Interpreting spline results | You can reverse-engineer the spline formulae without having to go into the R code. It suffices to know that
A spline is a piecewise polynomial function.
Polynomials of degree $d$ are determined by their values at $d+1$ points.
The coefficients of a polynomial can be obtained via linear regression.
Thus, you only hav... | Interpreting spline results | You can reverse-engineer the spline formulae without having to go into the R code. It suffices to know that
A spline is a piecewise polynomial function.
Polynomials of degree $d$ are determined by t | Interpreting spline results
You can reverse-engineer the spline formulae without having to go into the R code. It suffices to know that
A spline is a piecewise polynomial function.
Polynomials of degree $d$ are determined by their values at $d+1$ points.
The coefficients of a polynomial can be obtained via linear reg... | Interpreting spline results
You can reverse-engineer the spline formulae without having to go into the R code. It suffices to know that
A spline is a piecewise polynomial function.
Polynomials of degree $d$ are determined by t |
11,082 | Interpreting spline results | You may find it easier to use the truncated power basis for cubic regression splines, using the R rms package. Once you fit the model you can retrieve the algebraic representation of the fitted spline function using the Function or latex functions in rms. | Interpreting spline results | You may find it easier to use the truncated power basis for cubic regression splines, using the R rms package. Once you fit the model you can retrieve the algebraic representation of the fitted splin | Interpreting spline results
You may find it easier to use the truncated power basis for cubic regression splines, using the R rms package. Once you fit the model you can retrieve the algebraic representation of the fitted spline function using the Function or latex functions in rms. | Interpreting spline results
You may find it easier to use the truncated power basis for cubic regression splines, using the R rms package. Once you fit the model you can retrieve the algebraic representation of the fitted splin |
11,083 | Interpreting spline results | You already did the following:
> rm(list=ls())
> set.seed(1066)
> x<- 1:1000
> y<- rep(0,1000)
> y[1:500]<- pmax(x[1:500]+(runif(500)-.5)*67*500/pmax(x[1:500],100),0.01)
> y[501:1000]<-500+x[501:1000]^1.05*(runif(500)-.5)/7.5
> df<-as.data.frame(cbind(x,y))
> library(splines)
> spline1 <- glm(y~ns(x,knots=c(500)),data... | Interpreting spline results | You already did the following:
> rm(list=ls())
> set.seed(1066)
> x<- 1:1000
> y<- rep(0,1000)
> y[1:500]<- pmax(x[1:500]+(runif(500)-.5)*67*500/pmax(x[1:500],100),0.01)
> y[501:1000]<-500+x[501:1000 | Interpreting spline results
You already did the following:
> rm(list=ls())
> set.seed(1066)
> x<- 1:1000
> y<- rep(0,1000)
> y[1:500]<- pmax(x[1:500]+(runif(500)-.5)*67*500/pmax(x[1:500],100),0.01)
> y[501:1000]<-500+x[501:1000]^1.05*(runif(500)-.5)/7.5
> df<-as.data.frame(cbind(x,y))
> library(splines)
> spline1 <- g... | Interpreting spline results
You already did the following:
> rm(list=ls())
> set.seed(1066)
> x<- 1:1000
> y<- rep(0,1000)
> y[1:500]<- pmax(x[1:500]+(runif(500)-.5)*67*500/pmax(x[1:500],100),0.01)
> y[501:1000]<-500+x[501:1000 |
11,084 | How would you explain Moment Generating Function(MGF) in layman's terms? | Let's assume that an equation-free intuition is not possible, and still insist on boiling down the math to the very essentials to get an idea of what's going on: we are trying to obtain the statistical raw moments, which, after the obligatory reference to physics, we define as the expected value of a power of a random ... | How would you explain Moment Generating Function(MGF) in layman's terms? | Let's assume that an equation-free intuition is not possible, and still insist on boiling down the math to the very essentials to get an idea of what's going on: we are trying to obtain the statistica | How would you explain Moment Generating Function(MGF) in layman's terms?
Let's assume that an equation-free intuition is not possible, and still insist on boiling down the math to the very essentials to get an idea of what's going on: we are trying to obtain the statistical raw moments, which, after the obligatory refe... | How would you explain Moment Generating Function(MGF) in layman's terms?
Let's assume that an equation-free intuition is not possible, and still insist on boiling down the math to the very essentials to get an idea of what's going on: we are trying to obtain the statistica |
11,085 | How would you explain Moment Generating Function(MGF) in layman's terms? | In the most layman terms it's a way to encode all characteristics of the probability distribution into one short phrase. For instance, if I know that MGF of the distribution is $$M(t)=e^{t\mu+1/2\sigma^2t^2}$$
I can find out the mean of this distribution by taking first term of Taylor expansion:
$$\left. \frac d {dt}M(... | How would you explain Moment Generating Function(MGF) in layman's terms? | In the most layman terms it's a way to encode all characteristics of the probability distribution into one short phrase. For instance, if I know that MGF of the distribution is $$M(t)=e^{t\mu+1/2\sigm | How would you explain Moment Generating Function(MGF) in layman's terms?
In the most layman terms it's a way to encode all characteristics of the probability distribution into one short phrase. For instance, if I know that MGF of the distribution is $$M(t)=e^{t\mu+1/2\sigma^2t^2}$$
I can find out the mean of this distr... | How would you explain Moment Generating Function(MGF) in layman's terms?
In the most layman terms it's a way to encode all characteristics of the probability distribution into one short phrase. For instance, if I know that MGF of the distribution is $$M(t)=e^{t\mu+1/2\sigm |
11,086 | Weibull Distribution v/s Gamma Distribution | Both the gamma and Weibull distributions can be seen as generalisations of the exponential distribution. If we look at the exponential distribution as describing the waiting time of a Poisson process (the time we have to wait until an event happens, if that event is equally likely to occur in any time interval), then t... | Weibull Distribution v/s Gamma Distribution | Both the gamma and Weibull distributions can be seen as generalisations of the exponential distribution. If we look at the exponential distribution as describing the waiting time of a Poisson process | Weibull Distribution v/s Gamma Distribution
Both the gamma and Weibull distributions can be seen as generalisations of the exponential distribution. If we look at the exponential distribution as describing the waiting time of a Poisson process (the time we have to wait until an event happens, if that event is equally l... | Weibull Distribution v/s Gamma Distribution
Both the gamma and Weibull distributions can be seen as generalisations of the exponential distribution. If we look at the exponential distribution as describing the waiting time of a Poisson process |
11,087 | What's the most pain-free way to fit logistic growth curves in R? | See the nls() function. It has a self starting logistic curve model function via SSlogis(). E.g. from the ?nls help page
DNase1 <- subset(DNase, Run == 1)
## using a selfStart model
fm1DNase1 <- nls(density ~ SSlogis(log(conc), Asym, xmid, scal),
DNase1)
I suggest you read the help pages for ... | What's the most pain-free way to fit logistic growth curves in R? | See the nls() function. It has a self starting logistic curve model function via SSlogis(). E.g. from the ?nls help page
DNase1 <- subset(DNase, Run == 1)
## using a selfStart model
fm1DNase1 < | What's the most pain-free way to fit logistic growth curves in R?
See the nls() function. It has a self starting logistic curve model function via SSlogis(). E.g. from the ?nls help page
DNase1 <- subset(DNase, Run == 1)
## using a selfStart model
fm1DNase1 <- nls(density ~ SSlogis(log(conc), Asym, xmid, scal), ... | What's the most pain-free way to fit logistic growth curves in R?
See the nls() function. It has a self starting logistic curve model function via SSlogis(). E.g. from the ?nls help page
DNase1 <- subset(DNase, Run == 1)
## using a selfStart model
fm1DNase1 < |
11,088 | What's the most pain-free way to fit logistic growth curves in R? | I had the same question a little while ago. This is what I found:
Fox and Weisberg wrote a great supplemental article using the nls function (both with and without the self-starting option mentioned by Gavin). It can be found here.
From that article, I ended up writing a function for my class to use when fitting a logi... | What's the most pain-free way to fit logistic growth curves in R? | I had the same question a little while ago. This is what I found:
Fox and Weisberg wrote a great supplemental article using the nls function (both with and without the self-starting option mentioned b | What's the most pain-free way to fit logistic growth curves in R?
I had the same question a little while ago. This is what I found:
Fox and Weisberg wrote a great supplemental article using the nls function (both with and without the self-starting option mentioned by Gavin). It can be found here.
From that article, I e... | What's the most pain-free way to fit logistic growth curves in R?
I had the same question a little while ago. This is what I found:
Fox and Weisberg wrote a great supplemental article using the nls function (both with and without the self-starting option mentioned b |
11,089 | What is Connectionist Temporal Classification (CTC)? | You have a dataset containing:
images I1, I2, ...
ground truth texts T1, T2, ... for the images I1, I2, ...
So your dataset could look something like that:
A Neural Network (NN) outputs a score for each possible horizontal position (often called time-step t in the literature) of the image.
This looks something like ... | What is Connectionist Temporal Classification (CTC)? | You have a dataset containing:
images I1, I2, ...
ground truth texts T1, T2, ... for the images I1, I2, ...
So your dataset could look something like that:
A Neural Network (NN) outputs a score for | What is Connectionist Temporal Classification (CTC)?
You have a dataset containing:
images I1, I2, ...
ground truth texts T1, T2, ... for the images I1, I2, ...
So your dataset could look something like that:
A Neural Network (NN) outputs a score for each possible horizontal position (often called time-step t in the... | What is Connectionist Temporal Classification (CTC)?
You have a dataset containing:
images I1, I2, ...
ground truth texts T1, T2, ... for the images I1, I2, ...
So your dataset could look something like that:
A Neural Network (NN) outputs a score for |
11,090 | Analyse ACF and PACF plots | Looking at your ACF and PACF is useful in the full context of your analysis as well. Your Ljung-Box Q-statistic; p-value; confidence interval, ACF and PACF should be viewed together. For instance the Q test here:
acf, ci, Q, pvalue = tsa.acf(res1.resid,
nlags=4, confint=95, qstat=True,
unbiased=True)
Here - our... | Analyse ACF and PACF plots | Looking at your ACF and PACF is useful in the full context of your analysis as well. Your Ljung-Box Q-statistic; p-value; confidence interval, ACF and PACF should be viewed together. For instance the | Analyse ACF and PACF plots
Looking at your ACF and PACF is useful in the full context of your analysis as well. Your Ljung-Box Q-statistic; p-value; confidence interval, ACF and PACF should be viewed together. For instance the Q test here:
acf, ci, Q, pvalue = tsa.acf(res1.resid,
nlags=4, confint=95, qstat=True,
... | Analyse ACF and PACF plots
Looking at your ACF and PACF is useful in the full context of your analysis as well. Your Ljung-Box Q-statistic; p-value; confidence interval, ACF and PACF should be viewed together. For instance the |
11,091 | Analyse ACF and PACF plots | The sole reliance on the ACF and PACF using tools suggested in the mid 60's is sometimes but seldomly correct except for simulated data. Model Identification tools like AIC/BIC almost never correctly identify a useful model but rather show what happens when you don't read the small print regarding the assumptions. I wo... | Analyse ACF and PACF plots | The sole reliance on the ACF and PACF using tools suggested in the mid 60's is sometimes but seldomly correct except for simulated data. Model Identification tools like AIC/BIC almost never correctly | Analyse ACF and PACF plots
The sole reliance on the ACF and PACF using tools suggested in the mid 60's is sometimes but seldomly correct except for simulated data. Model Identification tools like AIC/BIC almost never correctly identify a useful model but rather show what happens when you don't read the small print rega... | Analyse ACF and PACF plots
The sole reliance on the ACF and PACF using tools suggested in the mid 60's is sometimes but seldomly correct except for simulated data. Model Identification tools like AIC/BIC almost never correctly |
11,092 | Analyse ACF and PACF plots | It looks to me like you're counting the spikes at lag 0.
Your PACF shows one reasonably large spike at lag 1, suggesting AR(1). This will of course induce a geometric-like decrease in the ACF (which, broadly speaking, you see). You seem to be trying to fit the same dependence twice - both as AR and MA.
I'd have just ... | Analyse ACF and PACF plots | It looks to me like you're counting the spikes at lag 0.
Your PACF shows one reasonably large spike at lag 1, suggesting AR(1). This will of course induce a geometric-like decrease in the ACF (which, | Analyse ACF and PACF plots
It looks to me like you're counting the spikes at lag 0.
Your PACF shows one reasonably large spike at lag 1, suggesting AR(1). This will of course induce a geometric-like decrease in the ACF (which, broadly speaking, you see). You seem to be trying to fit the same dependence twice - both as... | Analyse ACF and PACF plots
It looks to me like you're counting the spikes at lag 0.
Your PACF shows one reasonably large spike at lag 1, suggesting AR(1). This will of course induce a geometric-like decrease in the ACF (which, |
11,093 | How do you see a Markov chain is irreducible? | Here are three examples (taken from Greenberg, Introduction to Bayesian Econometrics, if I remember correctly) for transition matrices, the first two for the reducible case, the last for the irreducible one.
\begin{eqnarray*}
P_1 &=& \left(
\begin{array}{cccc}
0.5 & 0.5 & 0 & 0 \\
0.9 & 0.1 & 0 & 0 \\
0 & 0 & 0.2 & 0.8... | How do you see a Markov chain is irreducible? | Here are three examples (taken from Greenberg, Introduction to Bayesian Econometrics, if I remember correctly) for transition matrices, the first two for the reducible case, the last for the irreducib | How do you see a Markov chain is irreducible?
Here are three examples (taken from Greenberg, Introduction to Bayesian Econometrics, if I remember correctly) for transition matrices, the first two for the reducible case, the last for the irreducible one.
\begin{eqnarray*}
P_1 &=& \left(
\begin{array}{cccc}
0.5 & 0.5 & 0... | How do you see a Markov chain is irreducible?
Here are three examples (taken from Greenberg, Introduction to Bayesian Econometrics, if I remember correctly) for transition matrices, the first two for the reducible case, the last for the irreducib |
11,094 | How do you see a Markov chain is irreducible? | The state $j$ is said to be accessible from a state $i$ (usually denoted by $i \to j$) if there exists some $n\geq 0$ such that:
$$p^n_{ij}=\mathbb P(X_n=j\mid X_0=i) > 0$$
That is, one can get from the state $i$ to the state $j$ in $n$ steps with probability $p^n_{ij}$.
If both $i\to j$ and $j\to i$ hold true then th... | How do you see a Markov chain is irreducible? | The state $j$ is said to be accessible from a state $i$ (usually denoted by $i \to j$) if there exists some $n\geq 0$ such that:
$$p^n_{ij}=\mathbb P(X_n=j\mid X_0=i) > 0$$
That is, one can get from | How do you see a Markov chain is irreducible?
The state $j$ is said to be accessible from a state $i$ (usually denoted by $i \to j$) if there exists some $n\geq 0$ such that:
$$p^n_{ij}=\mathbb P(X_n=j\mid X_0=i) > 0$$
That is, one can get from the state $i$ to the state $j$ in $n$ steps with probability $p^n_{ij}$.
I... | How do you see a Markov chain is irreducible?
The state $j$ is said to be accessible from a state $i$ (usually denoted by $i \to j$) if there exists some $n\geq 0$ such that:
$$p^n_{ij}=\mathbb P(X_n=j\mid X_0=i) > 0$$
That is, one can get from |
11,095 | How do you see a Markov chain is irreducible? | Some of the existing answers seem to be incorrect to me.
As cited in Stochastic Processes by J. Medhi (page 79, edition 4), a Markov chain is irreducible if it does not contain any proper 'closed' subset other than the state space.
So if in your transition probability matrix, there is a subset of states such that y... | How do you see a Markov chain is irreducible? | Some of the existing answers seem to be incorrect to me.
As cited in Stochastic Processes by J. Medhi (page 79, edition 4), a Markov chain is irreducible if it does not contain any proper 'closed' s | How do you see a Markov chain is irreducible?
Some of the existing answers seem to be incorrect to me.
As cited in Stochastic Processes by J. Medhi (page 79, edition 4), a Markov chain is irreducible if it does not contain any proper 'closed' subset other than the state space.
So if in your transition probability m... | How do you see a Markov chain is irreducible?
Some of the existing answers seem to be incorrect to me.
As cited in Stochastic Processes by J. Medhi (page 79, edition 4), a Markov chain is irreducible if it does not contain any proper 'closed' s |
11,096 | How do you see a Markov chain is irreducible? | Let $i$ and $j$ be two distinct states of a Markov Chain. If there is some positive probability for the process to go from state $i$ to state $j$, whatever be the number of steps(say 1, 2, 3$\cdots$), then we say that state $j$ is accessible from state $i$.
Notationally, we express this as $i\rightarrow j$. In terms ... | How do you see a Markov chain is irreducible? | Let $i$ and $j$ be two distinct states of a Markov Chain. If there is some positive probability for the process to go from state $i$ to state $j$, whatever be the number of steps(say 1, 2, 3$\cdots$) | How do you see a Markov chain is irreducible?
Let $i$ and $j$ be two distinct states of a Markov Chain. If there is some positive probability for the process to go from state $i$ to state $j$, whatever be the number of steps(say 1, 2, 3$\cdots$), then we say that state $j$ is accessible from state $i$.
Notationally, ... | How do you see a Markov chain is irreducible?
Let $i$ and $j$ be two distinct states of a Markov Chain. If there is some positive probability for the process to go from state $i$ to state $j$, whatever be the number of steps(say 1, 2, 3$\cdots$) |
11,097 | How do you see a Markov chain is irreducible? | First a word of warning : never look at a matrix unless you have a serious reason to do so : the only one I can think of is checking for mistakenly typed digits, or reading in a textbook.
If $P$ is your transition matrix, compute $\exp(P)$. If all entries are nonzero, then the matrix is irreducible. Otherwise, it's red... | How do you see a Markov chain is irreducible? | First a word of warning : never look at a matrix unless you have a serious reason to do so : the only one I can think of is checking for mistakenly typed digits, or reading in a textbook.
If $P$ is yo | How do you see a Markov chain is irreducible?
First a word of warning : never look at a matrix unless you have a serious reason to do so : the only one I can think of is checking for mistakenly typed digits, or reading in a textbook.
If $P$ is your transition matrix, compute $\exp(P)$. If all entries are nonzero, then ... | How do you see a Markov chain is irreducible?
First a word of warning : never look at a matrix unless you have a serious reason to do so : the only one I can think of is checking for mistakenly typed digits, or reading in a textbook.
If $P$ is yo |
11,098 | What does "fiducial" mean (in the context of statistics)? | The fiducial argument is to interpret likelihood as a probability.
Edit: not exactly, see the answer of @Sextus for more details.
Even if likelihood measures the plausibility of an event, it does not satisfy the axioms of probability measures (in particular there is no guarantee that it sums to 1), which is one of the ... | What does "fiducial" mean (in the context of statistics)? | The fiducial argument is to interpret likelihood as a probability.
Edit: not exactly, see the answer of @Sextus for more details.
Even if likelihood measures the plausibility of an event, it does not | What does "fiducial" mean (in the context of statistics)?
The fiducial argument is to interpret likelihood as a probability.
Edit: not exactly, see the answer of @Sextus for more details.
Even if likelihood measures the plausibility of an event, it does not satisfy the axioms of probability measures (in particular ther... | What does "fiducial" mean (in the context of statistics)?
The fiducial argument is to interpret likelihood as a probability.
Edit: not exactly, see the answer of @Sextus for more details.
Even if likelihood measures the plausibility of an event, it does not |
11,099 | What does "fiducial" mean (in the context of statistics)? | Several well-known statisticians try to rekindle an interest in Fisher's fiducial argument. Bradley Efron: (I cannot copy even small quotes from google books), the topic is also treated in Bradley Efron 2. He says something to the effect of (not a direct quote): Fiducial inference, sometimes considered Fisher's lar... | What does "fiducial" mean (in the context of statistics)? | Several well-known statisticians try to rekindle an interest in Fisher's fiducial argument. Bradley Efron: (I cannot copy even small quotes from google books), the topic is also treated in Bradley | What does "fiducial" mean (in the context of statistics)?
Several well-known statisticians try to rekindle an interest in Fisher's fiducial argument. Bradley Efron: (I cannot copy even small quotes from google books), the topic is also treated in Bradley Efron 2. He says something to the effect of (not a direct quo... | What does "fiducial" mean (in the context of statistics)?
Several well-known statisticians try to rekindle an interest in Fisher's fiducial argument. Bradley Efron: (I cannot copy even small quotes from google books), the topic is also treated in Bradley |
11,100 | What does "fiducial" mean (in the context of statistics)? | In the answer from gui11aume it is stated that
The fiducial argument is to interpret likelihood as a probability.
However, there is a subtle difference between the fiducial distribution and the likelihood function. If $F(\hat\theta; \theta)$ is the cumulative distribution function of some parameter estimate $\hat\the... | What does "fiducial" mean (in the context of statistics)? | In the answer from gui11aume it is stated that
The fiducial argument is to interpret likelihood as a probability.
However, there is a subtle difference between the fiducial distribution and the like | What does "fiducial" mean (in the context of statistics)?
In the answer from gui11aume it is stated that
The fiducial argument is to interpret likelihood as a probability.
However, there is a subtle difference between the fiducial distribution and the likelihood function. If $F(\hat\theta; \theta)$ is the cumulative ... | What does "fiducial" mean (in the context of statistics)?
In the answer from gui11aume it is stated that
The fiducial argument is to interpret likelihood as a probability.
However, there is a subtle difference between the fiducial distribution and the like |
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