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 |
|---|---|---|---|---|---|---|
45,501 | Why is the first postulate of the Poisson process that $\lambda dt$ is the probability of exactly one event in $[t,t+dt]$? | In fact, Leibniz' notation for infinitesimal increments can be confusing.
One has to be careful here to keep all terms of the same order: $e^{-\lambda dt}$ must be approximated to first order of $dt$ (not zeroth order, i.e. without any terms in $dt$), i.e. $e^{-\lambda dt}$ is approximately $1 - \lambda dt$ + (plus te... | Why is the first postulate of the Poisson process that $\lambda dt$ is the probability of exactly on | In fact, Leibniz' notation for infinitesimal increments can be confusing.
One has to be careful here to keep all terms of the same order: $e^{-\lambda dt}$ must be approximated to first order of $dt$ | Why is the first postulate of the Poisson process that $\lambda dt$ is the probability of exactly one event in $[t,t+dt]$?
In fact, Leibniz' notation for infinitesimal increments can be confusing.
One has to be careful here to keep all terms of the same order: $e^{-\lambda dt}$ must be approximated to first order of $d... | Why is the first postulate of the Poisson process that $\lambda dt$ is the probability of exactly on
In fact, Leibniz' notation for infinitesimal increments can be confusing.
One has to be careful here to keep all terms of the same order: $e^{-\lambda dt}$ must be approximated to first order of $dt$ |
45,502 | Why is the first postulate of the Poisson process that $\lambda dt$ is the probability of exactly one event in $[t,t+dt]$? | The previous two answer's are I think coming at the problem "backwards" - though they are both correct. They do not start with the postulate and end with the conclusion. If we start from the postulate, then we have:
$$Pr(\text{No event in} [t,t+dt])=1-Pr(\text{1 event in} [t,t+dt])=1-\lambda dt$$
If we define the fun... | Why is the first postulate of the Poisson process that $\lambda dt$ is the probability of exactly on | The previous two answer's are I think coming at the problem "backwards" - though they are both correct. They do not start with the postulate and end with the conclusion. If we start from the postula | Why is the first postulate of the Poisson process that $\lambda dt$ is the probability of exactly one event in $[t,t+dt]$?
The previous two answer's are I think coming at the problem "backwards" - though they are both correct. They do not start with the postulate and end with the conclusion. If we start from the post... | Why is the first postulate of the Poisson process that $\lambda dt$ is the probability of exactly on
The previous two answer's are I think coming at the problem "backwards" - though they are both correct. They do not start with the postulate and end with the conclusion. If we start from the postula |
45,503 | Why is the first postulate of the Poisson process that $\lambda dt$ is the probability of exactly one event in $[t,t+dt]$? | Here's an alternative (but basically equivalent) derivation to @Andre Holzner's:
For a Poisson process $N(t)$ with rate $\lambda$,
$Pr(N(t+\tau) - N(t) = 1) = (\tau\lambda)\exp(-\tau\lambda) = Pr(N(\tau) = 1) $
which has Taylor expansion around $\tau=0$
$\tau\lambda - \tau^2\lambda^2 + O(\tau^3)$
and this is approxima... | Why is the first postulate of the Poisson process that $\lambda dt$ is the probability of exactly on | Here's an alternative (but basically equivalent) derivation to @Andre Holzner's:
For a Poisson process $N(t)$ with rate $\lambda$,
$Pr(N(t+\tau) - N(t) = 1) = (\tau\lambda)\exp(-\tau\lambda) = Pr(N(\ | Why is the first postulate of the Poisson process that $\lambda dt$ is the probability of exactly one event in $[t,t+dt]$?
Here's an alternative (but basically equivalent) derivation to @Andre Holzner's:
For a Poisson process $N(t)$ with rate $\lambda$,
$Pr(N(t+\tau) - N(t) = 1) = (\tau\lambda)\exp(-\tau\lambda) = Pr(... | Why is the first postulate of the Poisson process that $\lambda dt$ is the probability of exactly on
Here's an alternative (but basically equivalent) derivation to @Andre Holzner's:
For a Poisson process $N(t)$ with rate $\lambda$,
$Pr(N(t+\tau) - N(t) = 1) = (\tau\lambda)\exp(-\tau\lambda) = Pr(N(\ |
45,504 | How to simulate data based on a linear mixed model fit object in R? | Note: the simulated data using simulate.lme does not match elements of the original data structure or model fit (eg. variance, effect size...) nor does it creation of data de novo for experimental design testing.
require(nlme)
?nlme::simulate.lme
fit <- lme(distance ~ age + Sex, data = Orthodont, random = ~ 1)
ort... | How to simulate data based on a linear mixed model fit object in R? | Note: the simulated data using simulate.lme does not match elements of the original data structure or model fit (eg. variance, effect size...) nor does it creation of data de novo for experimental des | How to simulate data based on a linear mixed model fit object in R?
Note: the simulated data using simulate.lme does not match elements of the original data structure or model fit (eg. variance, effect size...) nor does it creation of data de novo for experimental design testing.
require(nlme)
?nlme::simulate.lme
fi... | How to simulate data based on a linear mixed model fit object in R?
Note: the simulated data using simulate.lme does not match elements of the original data structure or model fit (eg. variance, effect size...) nor does it creation of data de novo for experimental des |
45,505 | How to simulate data based on a linear mixed model fit object in R? | Here is one approach that takes all the values from fm2. You could add more arguments to the function to allow you to change values in the simulations.
library(nlme)
fm2 <- lme(distance ~ age + Sex, data = Orthodont, random = ~ 1)
simfun <- function(n) {
# n is the number of subjects, total rows will be 4*n
... | How to simulate data based on a linear mixed model fit object in R? | Here is one approach that takes all the values from fm2. You could add more arguments to the function to allow you to change values in the simulations.
library(nlme)
fm2 <- lme(distance ~ age + Sex, | How to simulate data based on a linear mixed model fit object in R?
Here is one approach that takes all the values from fm2. You could add more arguments to the function to allow you to change values in the simulations.
library(nlme)
fm2 <- lme(distance ~ age + Sex, data = Orthodont, random = ~ 1)
simfun <- functio... | How to simulate data based on a linear mixed model fit object in R?
Here is one approach that takes all the values from fm2. You could add more arguments to the function to allow you to change values in the simulations.
library(nlme)
fm2 <- lme(distance ~ age + Sex, |
45,506 | How to simulate data based on a linear mixed model fit object in R? | I would probably just sample randomly with replacement from the Subjects in your data until I had the right sample size. This is the bootstrap method. It is simpler than identifying the multivariate distribution of the variables and then sampling from it. Also the bootstrap does not make additional assumptions about th... | How to simulate data based on a linear mixed model fit object in R? | I would probably just sample randomly with replacement from the Subjects in your data until I had the right sample size. This is the bootstrap method. It is simpler than identifying the multivariate d | How to simulate data based on a linear mixed model fit object in R?
I would probably just sample randomly with replacement from the Subjects in your data until I had the right sample size. This is the bootstrap method. It is simpler than identifying the multivariate distribution of the variables and then sampling from ... | How to simulate data based on a linear mixed model fit object in R?
I would probably just sample randomly with replacement from the Subjects in your data until I had the right sample size. This is the bootstrap method. It is simpler than identifying the multivariate d |
45,507 | Measure of association for 2x3 contingency table | Linear or monotonic trend tests--$M^2$ association measure, WMW test cited by @GaBorgulya, or the Cochran-Armitage trend test--can also be used, and they are well explained in Agresti (CDA, 2002, §3.4.6, p. 90).
The latter is actually equivalent to a score test for testing $H_0:\; \beta = 0$ in a logistic regression m... | Measure of association for 2x3 contingency table | Linear or monotonic trend tests--$M^2$ association measure, WMW test cited by @GaBorgulya, or the Cochran-Armitage trend test--can also be used, and they are well explained in Agresti (CDA, 2002, §3.4 | Measure of association for 2x3 contingency table
Linear or monotonic trend tests--$M^2$ association measure, WMW test cited by @GaBorgulya, or the Cochran-Armitage trend test--can also be used, and they are well explained in Agresti (CDA, 2002, §3.4.6, p. 90).
The latter is actually equivalent to a score test for test... | Measure of association for 2x3 contingency table
Linear or monotonic trend tests--$M^2$ association measure, WMW test cited by @GaBorgulya, or the Cochran-Armitage trend test--can also be used, and they are well explained in Agresti (CDA, 2002, §3.4 |
45,508 | Measure of association for 2x3 contingency table | On a 2x3 contingency table where the three-level factor is ordered you may use rank correlation (Spearman or Kendall) to assess association between the two variables.
You may also think about the data as an ordered variable observed in two groups. A corresponding significance test could be the Mann-Whitney test (with m... | Measure of association for 2x3 contingency table | On a 2x3 contingency table where the three-level factor is ordered you may use rank correlation (Spearman or Kendall) to assess association between the two variables.
You may also think about the data | Measure of association for 2x3 contingency table
On a 2x3 contingency table where the three-level factor is ordered you may use rank correlation (Spearman or Kendall) to assess association between the two variables.
You may also think about the data as an ordered variable observed in two groups. A corresponding signifi... | Measure of association for 2x3 contingency table
On a 2x3 contingency table where the three-level factor is ordered you may use rank correlation (Spearman or Kendall) to assess association between the two variables.
You may also think about the data |
45,509 | Measure of association for 2x3 contingency table | One way to incorporate the ordering of the column factor into your analysis is to use the cumulative frequencies instead of the cell frequencies. So in your table you have:
$$f_{ij}=\frac{n_{ij}}{n_{\bullet\bullet}}\;\;\;\; i=1,2\;\;j=1,2,3$$
where a "$\bullet$" indicates sum over that index. So I suggesting modeling... | Measure of association for 2x3 contingency table | One way to incorporate the ordering of the column factor into your analysis is to use the cumulative frequencies instead of the cell frequencies. So in your table you have:
$$f_{ij}=\frac{n_{ij}}{n_{ | Measure of association for 2x3 contingency table
One way to incorporate the ordering of the column factor into your analysis is to use the cumulative frequencies instead of the cell frequencies. So in your table you have:
$$f_{ij}=\frac{n_{ij}}{n_{\bullet\bullet}}\;\;\;\; i=1,2\;\;j=1,2,3$$
where a "$\bullet$" indicat... | Measure of association for 2x3 contingency table
One way to incorporate the ordering of the column factor into your analysis is to use the cumulative frequencies instead of the cell frequencies. So in your table you have:
$$f_{ij}=\frac{n_{ij}}{n_{ |
45,510 | Measure of association for 2x3 contingency table | You could use the Jonckheere Terpstra test. In SAS, you can get this in PROC FREQ with the /JT option on the tables statement. I didn't see a function for it in R, but there may be one out there. | Measure of association for 2x3 contingency table | You could use the Jonckheere Terpstra test. In SAS, you can get this in PROC FREQ with the /JT option on the tables statement. I didn't see a function for it in R, but there may be one out there. | Measure of association for 2x3 contingency table
You could use the Jonckheere Terpstra test. In SAS, you can get this in PROC FREQ with the /JT option on the tables statement. I didn't see a function for it in R, but there may be one out there. | Measure of association for 2x3 contingency table
You could use the Jonckheere Terpstra test. In SAS, you can get this in PROC FREQ with the /JT option on the tables statement. I didn't see a function for it in R, but there may be one out there. |
45,511 | References for using networks to display correlations? | Do you know the qgraph project (and the related R package)? It aims at providing various displays for psychometric models, especially those relying on correlations. I discovered this approach for displaying correlation measures when I was reading a very nice and revolutionary article on diagnostic medicine by Denny Bor... | References for using networks to display correlations? | Do you know the qgraph project (and the related R package)? It aims at providing various displays for psychometric models, especially those relying on correlations. I discovered this approach for disp | References for using networks to display correlations?
Do you know the qgraph project (and the related R package)? It aims at providing various displays for psychometric models, especially those relying on correlations. I discovered this approach for displaying correlation measures when I was reading a very nice and re... | References for using networks to display correlations?
Do you know the qgraph project (and the related R package)? It aims at providing various displays for psychometric models, especially those relying on correlations. I discovered this approach for disp |
45,512 | References for using networks to display correlations? | Surprisingly, as a search of Google Images indicates, such graphs do not appear to be in common use to study or explain multiple correlations. That's a pity, because I'm sure much of this theory can be reduced to simple operations on graphs.
Nevertheless, this graphical method to display correlations (or their mathema... | References for using networks to display correlations? | Surprisingly, as a search of Google Images indicates, such graphs do not appear to be in common use to study or explain multiple correlations. That's a pity, because I'm sure much of this theory can | References for using networks to display correlations?
Surprisingly, as a search of Google Images indicates, such graphs do not appear to be in common use to study or explain multiple correlations. That's a pity, because I'm sure much of this theory can be reduced to simple operations on graphs.
Nevertheless, this gra... | References for using networks to display correlations?
Surprisingly, as a search of Google Images indicates, such graphs do not appear to be in common use to study or explain multiple correlations. That's a pity, because I'm sure much of this theory can |
45,513 | Poisson distribution and statistical significance | There are two points to make:
It is not the specific value of 130 that is unusual, but that it is much larger than 100. If you got more than 130 hits, that would have been even more surprising. So we usually look at the P(X>=130), not just P(X=130). By your logic even 100 hits would be unusual, because dpois(100,100)=... | Poisson distribution and statistical significance | There are two points to make:
It is not the specific value of 130 that is unusual, but that it is much larger than 100. If you got more than 130 hits, that would have been even more surprising. So we | Poisson distribution and statistical significance
There are two points to make:
It is not the specific value of 130 that is unusual, but that it is much larger than 100. If you got more than 130 hits, that would have been even more surprising. So we usually look at the P(X>=130), not just P(X=130). By your logic even ... | Poisson distribution and statistical significance
There are two points to make:
It is not the specific value of 130 that is unusual, but that it is much larger than 100. If you got more than 130 hits, that would have been even more surprising. So we |
45,514 | Poisson distribution and statistical significance | First, note that dpois(130, 100) will give you the probability of exactly 130 hits if you are assuming that the true rate is 100. That probability is indeed very low. However, in the usual hypothesis testing framework, what we calculate is the probability of the observed outcome or an even more extreme outcome. You can... | Poisson distribution and statistical significance | First, note that dpois(130, 100) will give you the probability of exactly 130 hits if you are assuming that the true rate is 100. That probability is indeed very low. However, in the usual hypothesis | Poisson distribution and statistical significance
First, note that dpois(130, 100) will give you the probability of exactly 130 hits if you are assuming that the true rate is 100. That probability is indeed very low. However, in the usual hypothesis testing framework, what we calculate is the probability of the observe... | Poisson distribution and statistical significance
First, note that dpois(130, 100) will give you the probability of exactly 130 hits if you are assuming that the true rate is 100. That probability is indeed very low. However, in the usual hypothesis |
45,515 | Effect of missing data and outliers on least square estimation | I'm not sure about the "missing data", but I can give an answer on "outliers"
This is basically due to the "unbounded" influence that a single observation can have in least squares (or at least in conventional least squares). A very, very simple example of least squares should show this. Suppose you only estimate an ... | Effect of missing data and outliers on least square estimation | I'm not sure about the "missing data", but I can give an answer on "outliers"
This is basically due to the "unbounded" influence that a single observation can have in least squares (or at least in con | Effect of missing data and outliers on least square estimation
I'm not sure about the "missing data", but I can give an answer on "outliers"
This is basically due to the "unbounded" influence that a single observation can have in least squares (or at least in conventional least squares). A very, very simple example of... | Effect of missing data and outliers on least square estimation
I'm not sure about the "missing data", but I can give an answer on "outliers"
This is basically due to the "unbounded" influence that a single observation can have in least squares (or at least in con |
45,516 | Effect of missing data and outliers on least square estimation | If you're using R, try the following example.
library(tcltk)
demo(tkcanvas)
Move the dots around to create all of the outliers you want. The regression will keep up with you. | Effect of missing data and outliers on least square estimation | If you're using R, try the following example.
library(tcltk)
demo(tkcanvas)
Move the dots around to create all of the outliers you want. The regression will keep up with you. | Effect of missing data and outliers on least square estimation
If you're using R, try the following example.
library(tcltk)
demo(tkcanvas)
Move the dots around to create all of the outliers you want. The regression will keep up with you. | Effect of missing data and outliers on least square estimation
If you're using R, try the following example.
library(tcltk)
demo(tkcanvas)
Move the dots around to create all of the outliers you want. The regression will keep up with you. |
45,517 | Effect of missing data and outliers on least square estimation | An graphical example on outliers that requires no software and can be read in 2 minutes is Wikipedia on Anscombe's quartet | Effect of missing data and outliers on least square estimation | An graphical example on outliers that requires no software and can be read in 2 minutes is Wikipedia on Anscombe's quartet | Effect of missing data and outliers on least square estimation
An graphical example on outliers that requires no software and can be read in 2 minutes is Wikipedia on Anscombe's quartet | Effect of missing data and outliers on least square estimation
An graphical example on outliers that requires no software and can be read in 2 minutes is Wikipedia on Anscombe's quartet |
45,518 | If correlation between two variables is affected by a factor, how should I evaluate this correlation? | This might be a case of locally uncorrelated, but globally correlated variables. The variance in each group might be limited because of group homogeneity, therefore there is no evidence for a relationship within each group. But globally, with the full variance, the relationship can be strong. A schematic illustration o... | If correlation between two variables is affected by a factor, how should I evaluate this correlation | This might be a case of locally uncorrelated, but globally correlated variables. The variance in each group might be limited because of group homogeneity, therefore there is no evidence for a relation | If correlation between two variables is affected by a factor, how should I evaluate this correlation?
This might be a case of locally uncorrelated, but globally correlated variables. The variance in each group might be limited because of group homogeneity, therefore there is no evidence for a relationship within each g... | If correlation between two variables is affected by a factor, how should I evaluate this correlation
This might be a case of locally uncorrelated, but globally correlated variables. The variance in each group might be limited because of group homogeneity, therefore there is no evidence for a relation |
45,519 | If correlation between two variables is affected by a factor, how should I evaluate this correlation? | Therefore, it is important to evaluate whether the homogeneity of groups is due to low number of data, or actually these groups are quite homogeneous and different. In the first case, we could ensure the presence of a high correlation even when this has not been observed for each group separately.
But what would happen... | If correlation between two variables is affected by a factor, how should I evaluate this correlation | Therefore, it is important to evaluate whether the homogeneity of groups is due to low number of data, or actually these groups are quite homogeneous and different. In the first case, we could ensure | If correlation between two variables is affected by a factor, how should I evaluate this correlation?
Therefore, it is important to evaluate whether the homogeneity of groups is due to low number of data, or actually these groups are quite homogeneous and different. In the first case, we could ensure the presence of a ... | If correlation between two variables is affected by a factor, how should I evaluate this correlation
Therefore, it is important to evaluate whether the homogeneity of groups is due to low number of data, or actually these groups are quite homogeneous and different. In the first case, we could ensure |
45,520 | Quantile-Quantile Plot with Unknown Distribution? | There are a variety of different possibilities. For example, a chi-square distribution with degrees of freedom in the range of 30-40 would give rise to such a qq-plot. In R:
x <- rchisq(10000, df=35)
qqnorm(x)
qqline(x)
looks like this:
A mixture of two normals with different means doesn't apply though.
x <- c(rnorm(... | Quantile-Quantile Plot with Unknown Distribution? | There are a variety of different possibilities. For example, a chi-square distribution with degrees of freedom in the range of 30-40 would give rise to such a qq-plot. In R:
x <- rchisq(10000, df=35)
| Quantile-Quantile Plot with Unknown Distribution?
There are a variety of different possibilities. For example, a chi-square distribution with degrees of freedom in the range of 30-40 would give rise to such a qq-plot. In R:
x <- rchisq(10000, df=35)
qqnorm(x)
qqline(x)
looks like this:
A mixture of two normals with d... | Quantile-Quantile Plot with Unknown Distribution?
There are a variety of different possibilities. For example, a chi-square distribution with degrees of freedom in the range of 30-40 would give rise to such a qq-plot. In R:
x <- rchisq(10000, df=35)
|
45,521 | Quantile-Quantile Plot with Unknown Distribution? | Your dataset clearly is not normal. (With this much data, any goodness of fit test will tell you that.) But you can read much more than that from the normal probability plot:
The generally smooth curvature does not hint at a mixture structure.
The upper tail is too stretched out (values too high compared to the refe... | Quantile-Quantile Plot with Unknown Distribution? | Your dataset clearly is not normal. (With this much data, any goodness of fit test will tell you that.) But you can read much more than that from the normal probability plot:
The generally smooth c | Quantile-Quantile Plot with Unknown Distribution?
Your dataset clearly is not normal. (With this much data, any goodness of fit test will tell you that.) But you can read much more than that from the normal probability plot:
The generally smooth curvature does not hint at a mixture structure.
The upper tail is too s... | Quantile-Quantile Plot with Unknown Distribution?
Your dataset clearly is not normal. (With this much data, any goodness of fit test will tell you that.) But you can read much more than that from the normal probability plot:
The generally smooth c |
45,522 | Quantile-Quantile Plot with Unknown Distribution? | You may want to take a look at the Anderson-Darling test for normality which empirically tests whether or not your data comes from a given distribution. @chl recommends looking at the scipy toolkit, specifically anderson() in morestats.py for an implementation. | Quantile-Quantile Plot with Unknown Distribution? | You may want to take a look at the Anderson-Darling test for normality which empirically tests whether or not your data comes from a given distribution. @chl recommends looking at the scipy toolkit, | Quantile-Quantile Plot with Unknown Distribution?
You may want to take a look at the Anderson-Darling test for normality which empirically tests whether or not your data comes from a given distribution. @chl recommends looking at the scipy toolkit, specifically anderson() in morestats.py for an implementation. | Quantile-Quantile Plot with Unknown Distribution?
You may want to take a look at the Anderson-Darling test for normality which empirically tests whether or not your data comes from a given distribution. @chl recommends looking at the scipy toolkit, |
45,523 | Method to reliably determine abnormal statistical values | Your use of the stddev indicates you look at every variable seperately. If you look at them together, you might have more chance. An outlier in one dimension can be coincidence, an outlier in more dimensions is more surely an anomaly. I don't know much about games, but I reckon that you could use find extra variables l... | Method to reliably determine abnormal statistical values | Your use of the stddev indicates you look at every variable seperately. If you look at them together, you might have more chance. An outlier in one dimension can be coincidence, an outlier in more dim | Method to reliably determine abnormal statistical values
Your use of the stddev indicates you look at every variable seperately. If you look at them together, you might have more chance. An outlier in one dimension can be coincidence, an outlier in more dimensions is more surely an anomaly. I don't know much about game... | Method to reliably determine abnormal statistical values
Your use of the stddev indicates you look at every variable seperately. If you look at them together, you might have more chance. An outlier in one dimension can be coincidence, an outlier in more dim |
45,524 | Method to reliably determine abnormal statistical values | I will repost the answer I gave on math.stackexchange:
Your question needs some more information:
How is their score generated (what kind of game is it)? What should your non-cheating data look like? How do people cheat? How will their score be different (in a statistical sense) when they are not cheating? Do you know ... | Method to reliably determine abnormal statistical values | I will repost the answer I gave on math.stackexchange:
Your question needs some more information:
How is their score generated (what kind of game is it)? What should your non-cheating data look like? | Method to reliably determine abnormal statistical values
I will repost the answer I gave on math.stackexchange:
Your question needs some more information:
How is their score generated (what kind of game is it)? What should your non-cheating data look like? How do people cheat? How will their score be different (in a st... | Method to reliably determine abnormal statistical values
I will repost the answer I gave on math.stackexchange:
Your question needs some more information:
How is their score generated (what kind of game is it)? What should your non-cheating data look like? |
45,525 | Repeatability and measurement error from and between observers | What you describe is a reliability study where each subject is going to be assessed by the same three raters on two occasions. Analysis can be done separately on the two outcomes (length and weight, though I assume they will be highly correlated and you're not interested in how this correlation is reflected in raters' ... | Repeatability and measurement error from and between observers | What you describe is a reliability study where each subject is going to be assessed by the same three raters on two occasions. Analysis can be done separately on the two outcomes (length and weight, t | Repeatability and measurement error from and between observers
What you describe is a reliability study where each subject is going to be assessed by the same three raters on two occasions. Analysis can be done separately on the two outcomes (length and weight, though I assume they will be highly correlated and you're ... | Repeatability and measurement error from and between observers
What you describe is a reliability study where each subject is going to be assessed by the same three raters on two occasions. Analysis can be done separately on the two outcomes (length and weight, t |
45,526 | Repeatability and measurement error from and between observers | You need to repeat the same process separately for length and weight, as these are completely separate outcomes with different units and methods of measurement.
I'd start, as so often, by plotting some exploratory graphs. In this case a set of Bland–Altman (diffference vs. average) plots, one for each observer. If the ... | Repeatability and measurement error from and between observers | You need to repeat the same process separately for length and weight, as these are completely separate outcomes with different units and methods of measurement.
I'd start, as so often, by plotting som | Repeatability and measurement error from and between observers
You need to repeat the same process separately for length and weight, as these are completely separate outcomes with different units and methods of measurement.
I'd start, as so often, by plotting some exploratory graphs. In this case a set of Bland–Altman ... | Repeatability and measurement error from and between observers
You need to repeat the same process separately for length and weight, as these are completely separate outcomes with different units and methods of measurement.
I'd start, as so often, by plotting som |
45,527 | Data visualisation- summarise 190 means and response rates | I find a heatmap to be one of the most effective ways of summarizing large amounts of multi-dimensional data in a confined space. The LearnR blog has a nice example of creating one in ggplot2. | Data visualisation- summarise 190 means and response rates | I find a heatmap to be one of the most effective ways of summarizing large amounts of multi-dimensional data in a confined space. The LearnR blog has a nice example of creating one in ggplot2. | Data visualisation- summarise 190 means and response rates
I find a heatmap to be one of the most effective ways of summarizing large amounts of multi-dimensional data in a confined space. The LearnR blog has a nice example of creating one in ggplot2. | Data visualisation- summarise 190 means and response rates
I find a heatmap to be one of the most effective ways of summarizing large amounts of multi-dimensional data in a confined space. The LearnR blog has a nice example of creating one in ggplot2. |
45,528 | Data visualisation- summarise 190 means and response rates | To give you a few more things to look at:
Principal components - look at some previous answers about PC. In particular, this answer may be helpful.
Cluster analysis. This page gives quite a nice overall in R.
I would recommend trying as many things as possible and see what comes out. Once you have your data in R in a... | Data visualisation- summarise 190 means and response rates | To give you a few more things to look at:
Principal components - look at some previous answers about PC. In particular, this answer may be helpful.
Cluster analysis. This page gives quite a nice over | Data visualisation- summarise 190 means and response rates
To give you a few more things to look at:
Principal components - look at some previous answers about PC. In particular, this answer may be helpful.
Cluster analysis. This page gives quite a nice overall in R.
I would recommend trying as many things as possibl... | Data visualisation- summarise 190 means and response rates
To give you a few more things to look at:
Principal components - look at some previous answers about PC. In particular, this answer may be helpful.
Cluster analysis. This page gives quite a nice over |
45,529 | Data visualisation- summarise 190 means and response rates | I would suggest you check out either box-plots (if you have an intro text to R, box plots always seem to be one of the first plots they use), or you can plot the means of each group on the Y axis and use the X-axis to represent each of your 190 work areas (and then maybe put error bars representing a confidence interva... | Data visualisation- summarise 190 means and response rates | I would suggest you check out either box-plots (if you have an intro text to R, box plots always seem to be one of the first plots they use), or you can plot the means of each group on the Y axis and | Data visualisation- summarise 190 means and response rates
I would suggest you check out either box-plots (if you have an intro text to R, box plots always seem to be one of the first plots they use), or you can plot the means of each group on the Y axis and use the X-axis to represent each of your 190 work areas (and ... | Data visualisation- summarise 190 means and response rates
I would suggest you check out either box-plots (if you have an intro text to R, box plots always seem to be one of the first plots they use), or you can plot the means of each group on the Y axis and |
45,530 | Series expansion of a density function | You can also use Edgeworth series, if your random variable has a finite mean and variance, which expands the CDF of your random variable in terms of the Gaussian CDF. At first glance it's not quite as tidy conceptually as using a mixture model, but the derivation is quite pretty and it gives you a closed form with ver... | Series expansion of a density function | You can also use Edgeworth series, if your random variable has a finite mean and variance, which expands the CDF of your random variable in terms of the Gaussian CDF. At first glance it's not quite a | Series expansion of a density function
You can also use Edgeworth series, if your random variable has a finite mean and variance, which expands the CDF of your random variable in terms of the Gaussian CDF. At first glance it's not quite as tidy conceptually as using a mixture model, but the derivation is quite pretty ... | Series expansion of a density function
You can also use Edgeworth series, if your random variable has a finite mean and variance, which expands the CDF of your random variable in terms of the Gaussian CDF. At first glance it's not quite a |
45,531 | Series expansion of a density function | Histogram density estimator is estimating the density with a sum of piecewise functions (density of a uniform).
KDE is using a sum of smooth function (gaussian is an example) (as long as they are positive they can be transformed into a density by normalization)
The use of "mixture" in statistic is about convex combin... | Series expansion of a density function | Histogram density estimator is estimating the density with a sum of piecewise functions (density of a uniform).
KDE is using a sum of smooth function (gaussian is an example) (as long as they are pos | Series expansion of a density function
Histogram density estimator is estimating the density with a sum of piecewise functions (density of a uniform).
KDE is using a sum of smooth function (gaussian is an example) (as long as they are positive they can be transformed into a density by normalization)
The use of "mixtu... | Series expansion of a density function
Histogram density estimator is estimating the density with a sum of piecewise functions (density of a uniform).
KDE is using a sum of smooth function (gaussian is an example) (as long as they are pos |
45,532 | Series expansion of a density function | You can do this with mixture modeling. There are a number of R packages on CRAN for doing this. Search for "mixture" at http://cran.r-project.org/web/packages/ | Series expansion of a density function | You can do this with mixture modeling. There are a number of R packages on CRAN for doing this. Search for "mixture" at http://cran.r-project.org/web/packages/ | Series expansion of a density function
You can do this with mixture modeling. There are a number of R packages on CRAN for doing this. Search for "mixture" at http://cran.r-project.org/web/packages/ | Series expansion of a density function
You can do this with mixture modeling. There are a number of R packages on CRAN for doing this. Search for "mixture" at http://cran.r-project.org/web/packages/ |
45,533 | Suggested R packages for frontier estimation or segmentation of hyperspectral images | I am afraid there is no; during my little adventure with such data we have just converted it to a data frame form, added some extra attributes made from neighborhoods of pixels and used standard methods. Still, packages ripa and hyperSpec might be useful.
For other software, I've got an impression that most of sensible... | Suggested R packages for frontier estimation or segmentation of hyperspectral images | I am afraid there is no; during my little adventure with such data we have just converted it to a data frame form, added some extra attributes made from neighborhoods of pixels and used standard metho | Suggested R packages for frontier estimation or segmentation of hyperspectral images
I am afraid there is no; during my little adventure with such data we have just converted it to a data frame form, added some extra attributes made from neighborhoods of pixels and used standard methods. Still, packages ripa and hyperS... | Suggested R packages for frontier estimation or segmentation of hyperspectral images
I am afraid there is no; during my little adventure with such data we have just converted it to a data frame form, added some extra attributes made from neighborhoods of pixels and used standard metho |
45,534 | Suggested R packages for frontier estimation or segmentation of hyperspectral images | Not an R package, but D. A. Landgrebe from Purdue (author of Signal theory methods in multispectral remote sensing) has sponsored the MultiSpec freeware. Its a rather clunky GUI but gets the job done for most of the common hyperspectral algorithms. | Suggested R packages for frontier estimation or segmentation of hyperspectral images | Not an R package, but D. A. Landgrebe from Purdue (author of Signal theory methods in multispectral remote sensing) has sponsored the MultiSpec freeware. Its a rather clunky GUI but gets the job done | Suggested R packages for frontier estimation or segmentation of hyperspectral images
Not an R package, but D. A. Landgrebe from Purdue (author of Signal theory methods in multispectral remote sensing) has sponsored the MultiSpec freeware. Its a rather clunky GUI but gets the job done for most of the common hyperspectr... | Suggested R packages for frontier estimation or segmentation of hyperspectral images
Not an R package, but D. A. Landgrebe from Purdue (author of Signal theory methods in multispectral remote sensing) has sponsored the MultiSpec freeware. Its a rather clunky GUI but gets the job done |
45,535 | Suggested R packages for frontier estimation or segmentation of hyperspectral images | The best place to look for free/open source capabilities of this nature is GRASS GIS. The image processing manual is here. Because this is constantly undergoing development, it would be worthwhile posting an inquiry on one of the GRASS user lists (found through links on the home page here. | Suggested R packages for frontier estimation or segmentation of hyperspectral images | The best place to look for free/open source capabilities of this nature is GRASS GIS. The image processing manual is here. Because this is constantly undergoing development, it would be worthwhile p | Suggested R packages for frontier estimation or segmentation of hyperspectral images
The best place to look for free/open source capabilities of this nature is GRASS GIS. The image processing manual is here. Because this is constantly undergoing development, it would be worthwhile posting an inquiry on one of the GRA... | Suggested R packages for frontier estimation or segmentation of hyperspectral images
The best place to look for free/open source capabilities of this nature is GRASS GIS. The image processing manual is here. Because this is constantly undergoing development, it would be worthwhile p |
45,536 | Suggested R packages for frontier estimation or segmentation of hyperspectral images | This is a very late response, so this may no longer be of interest, but I am working on putting together an R library with various hyperspectral image processing capabilities. At the moment my focus has been on endmember detection and unmixing. If this is still something which is of interest please let me know. My hope... | Suggested R packages for frontier estimation or segmentation of hyperspectral images | This is a very late response, so this may no longer be of interest, but I am working on putting together an R library with various hyperspectral image processing capabilities. At the moment my focus h | Suggested R packages for frontier estimation or segmentation of hyperspectral images
This is a very late response, so this may no longer be of interest, but I am working on putting together an R library with various hyperspectral image processing capabilities. At the moment my focus has been on endmember detection and ... | Suggested R packages for frontier estimation or segmentation of hyperspectral images
This is a very late response, so this may no longer be of interest, but I am working on putting together an R library with various hyperspectral image processing capabilities. At the moment my focus h |
45,537 | Survival analysis with only censored event times? | It's not that you don't have events, it's just that you don't have exact times for the events. You do, however, have a lower and an upper limit to the time to each event. That's what's called "interval censored" data in general. In your situation, there's only 1 observation time per individual, so you have "current sta... | Survival analysis with only censored event times? | It's not that you don't have events, it's just that you don't have exact times for the events. You do, however, have a lower and an upper limit to the time to each event. That's what's called "interva | Survival analysis with only censored event times?
It's not that you don't have events, it's just that you don't have exact times for the events. You do, however, have a lower and an upper limit to the time to each event. That's what's called "interval censored" data in general. In your situation, there's only 1 observa... | Survival analysis with only censored event times?
It's not that you don't have events, it's just that you don't have exact times for the events. You do, however, have a lower and an upper limit to the time to each event. That's what's called "interva |
45,538 | Survival analysis with only censored event times? | This is a case of right censoring and (if there had been events) interval censoring. I.e. when a fish is event free when dissected, the event time is right censored (assuming all fish would eventually have the event). If you upon dissection a fish has the event, the event is interval censored to lie between time 0 and ... | Survival analysis with only censored event times? | This is a case of right censoring and (if there had been events) interval censoring. I.e. when a fish is event free when dissected, the event time is right censored (assuming all fish would eventually | Survival analysis with only censored event times?
This is a case of right censoring and (if there had been events) interval censoring. I.e. when a fish is event free when dissected, the event time is right censored (assuming all fish would eventually have the event). If you upon dissection a fish has the event, the eve... | Survival analysis with only censored event times?
This is a case of right censoring and (if there had been events) interval censoring. I.e. when a fish is event free when dissected, the event time is right censored (assuming all fish would eventually |
45,539 | Survival analysis with only censored event times? | Since the observation times are non-random, logistic regression can be used to estimate the event rate per each 24h interval. You can even just use proportions tests to estimate CIs, unless there are stratification features you want to implement, like species, weight, etc.
For fish sacrificed at time 1, denote the prob... | Survival analysis with only censored event times? | Since the observation times are non-random, logistic regression can be used to estimate the event rate per each 24h interval. You can even just use proportions tests to estimate CIs, unless there are | Survival analysis with only censored event times?
Since the observation times are non-random, logistic regression can be used to estimate the event rate per each 24h interval. You can even just use proportions tests to estimate CIs, unless there are stratification features you want to implement, like species, weight, e... | Survival analysis with only censored event times?
Since the observation times are non-random, logistic regression can be used to estimate the event rate per each 24h interval. You can even just use proportions tests to estimate CIs, unless there are |
45,540 | Alternative to Friedman Test in R | The tests you cited are not appropriate due to the presence of repeated measures. The common way to deal with repeated measures is via mixed-effects linear models.
I'm considering here the most general model, borrowing from one of your earlier posts.
> leach_lme <- lme(fixed = cl_conc ~ soil_type*treatment*days,
+ ... | Alternative to Friedman Test in R | The tests you cited are not appropriate due to the presence of repeated measures. The common way to deal with repeated measures is via mixed-effects linear models.
I'm considering here the most genera | Alternative to Friedman Test in R
The tests you cited are not appropriate due to the presence of repeated measures. The common way to deal with repeated measures is via mixed-effects linear models.
I'm considering here the most general model, borrowing from one of your earlier posts.
> leach_lme <- lme(fixed = cl_conc ... | Alternative to Friedman Test in R
The tests you cited are not appropriate due to the presence of repeated measures. The common way to deal with repeated measures is via mixed-effects linear models.
I'm considering here the most genera |
45,541 | Why is Neyman-Pearson lemma a lemma or is it a theorem? | As Thomas Lumley asserted, Neyman and Pearson in $\rm [I]$ didn't mention lemma. They frequently used the word principle, basis while deducing the critical regions in various cases.
When was the first time it was marked as a lemma?
$\bullet$ Wilks in his book did outline the theory but again refrained from calling it a... | Why is Neyman-Pearson lemma a lemma or is it a theorem? | As Thomas Lumley asserted, Neyman and Pearson in $\rm [I]$ didn't mention lemma. They frequently used the word principle, basis while deducing the critical regions in various cases.
When was the first | Why is Neyman-Pearson lemma a lemma or is it a theorem?
As Thomas Lumley asserted, Neyman and Pearson in $\rm [I]$ didn't mention lemma. They frequently used the word principle, basis while deducing the critical regions in various cases.
When was the first time it was marked as a lemma?
$\bullet$ Wilks in his book did ... | Why is Neyman-Pearson lemma a lemma or is it a theorem?
As Thomas Lumley asserted, Neyman and Pearson in $\rm [I]$ didn't mention lemma. They frequently used the word principle, basis while deducing the critical regions in various cases.
When was the first |
45,542 | Why is Neyman-Pearson lemma a lemma or is it a theorem? | What people often describe as the Neyman Pearson lemma is a result proven by the lemma but not the lemma itself. The description of the lemma by cross validated is for instance:
A theorem stating that likelihood ratio test is the most powerful test of point null hypothesis against point alternative hypothesis
However... | Why is Neyman-Pearson lemma a lemma or is it a theorem? | What people often describe as the Neyman Pearson lemma is a result proven by the lemma but not the lemma itself. The description of the lemma by cross validated is for instance:
A theorem stating tha | Why is Neyman-Pearson lemma a lemma or is it a theorem?
What people often describe as the Neyman Pearson lemma is a result proven by the lemma but not the lemma itself. The description of the lemma by cross validated is for instance:
A theorem stating that likelihood ratio test is the most powerful test of point null ... | Why is Neyman-Pearson lemma a lemma or is it a theorem?
What people often describe as the Neyman Pearson lemma is a result proven by the lemma but not the lemma itself. The description of the lemma by cross validated is for instance:
A theorem stating tha |
45,543 | Compute median of continuous distribution using integrate() in R | CAUTION!
As was pointed out and explained by whuber in the comments, the current code below does not check if it is fed a density that integrates to one (or to some other finite value which we could use to renormalize). It is therefore useful to call ff(1)+0.5 (or whatever the support for a given density is) as a sanit... | Compute median of continuous distribution using integrate() in R | CAUTION!
As was pointed out and explained by whuber in the comments, the current code below does not check if it is fed a density that integrates to one (or to some other finite value which we could u | Compute median of continuous distribution using integrate() in R
CAUTION!
As was pointed out and explained by whuber in the comments, the current code below does not check if it is fed a density that integrates to one (or to some other finite value which we could use to renormalize). It is therefore useful to call ff(1... | Compute median of continuous distribution using integrate() in R
CAUTION!
As was pointed out and explained by whuber in the comments, the current code below does not check if it is fed a density that integrates to one (or to some other finite value which we could u |
45,544 | Normalization of conditional probabilities | Not necessarily. Here is a counter-example: consider the vectors
$$
p = \begin{bmatrix}
0.5 \\
0.5
\end{bmatrix}
$$
and
$$
\pi = \begin{bmatrix}
0.5 \\
0.5
\end{bmatrix}
$$
Then the matrix
$$
W = \begin{bmatrix}
1 & 0 \\
1 & 0
\end{bmatrix}
$$
verifies $Wp = \pi$, while the elemen... | Normalization of conditional probabilities | Not necessarily. Here is a counter-example: consider the vectors
$$
p = \begin{bmatrix}
0.5 \\
0.5
\end{bmatrix}
$$
and
$$
\pi = \begin{bmatrix}
0.5 \\
0.5
\end{bmatrix}
$$
T | Normalization of conditional probabilities
Not necessarily. Here is a counter-example: consider the vectors
$$
p = \begin{bmatrix}
0.5 \\
0.5
\end{bmatrix}
$$
and
$$
\pi = \begin{bmatrix}
0.5 \\
0.5
\end{bmatrix}
$$
Then the matrix
$$
W = \begin{bmatrix}
1 & 0 \\
1 & 0
\end{bmatri... | Normalization of conditional probabilities
Not necessarily. Here is a counter-example: consider the vectors
$$
p = \begin{bmatrix}
0.5 \\
0.5
\end{bmatrix}
$$
and
$$
\pi = \begin{bmatrix}
0.5 \\
0.5
\end{bmatrix}
$$
T |
45,545 | Normalization of conditional probabilities | The answer by @CamilleGontier has pushed me in the right direction: what is implicit in the question (but was not explicitly stated in the OP) is that it should work for an arbitrary vector $p_i$ (as long as it satisfies conditions $p_i>0$ and $\sum_i p_i=1$.) We can then consider a set of linearly independent vectors ... | Normalization of conditional probabilities | The answer by @CamilleGontier has pushed me in the right direction: what is implicit in the question (but was not explicitly stated in the OP) is that it should work for an arbitrary vector $p_i$ (as | Normalization of conditional probabilities
The answer by @CamilleGontier has pushed me in the right direction: what is implicit in the question (but was not explicitly stated in the OP) is that it should work for an arbitrary vector $p_i$ (as long as it satisfies conditions $p_i>0$ and $\sum_i p_i=1$.) We can then cons... | Normalization of conditional probabilities
The answer by @CamilleGontier has pushed me in the right direction: what is implicit in the question (but was not explicitly stated in the OP) is that it should work for an arbitrary vector $p_i$ (as |
45,546 | Structural Causal Models with cycles | Most of the current causal literature restricts itself to acyclic SCMs, but there has recently been a lot of research advancing the theory of cyclic causal systems. Although one of the first algorithms for cyclic causation, the CCD by Richardson, was already published in 1996, it was only in recent years that the amoun... | Structural Causal Models with cycles | Most of the current causal literature restricts itself to acyclic SCMs, but there has recently been a lot of research advancing the theory of cyclic causal systems. Although one of the first algorithm | Structural Causal Models with cycles
Most of the current causal literature restricts itself to acyclic SCMs, but there has recently been a lot of research advancing the theory of cyclic causal systems. Although one of the first algorithms for cyclic causation, the CCD by Richardson, was already published in 1996, it wa... | Structural Causal Models with cycles
Most of the current causal literature restricts itself to acyclic SCMs, but there has recently been a lot of research advancing the theory of cyclic causal systems. Although one of the first algorithm |
45,547 | Structural Causal Models with cycles | Well, the fundamental rule of causality is that causes must precede effects - that is a strict inequality in time. So it is not permissible to have $X_i(t)=f_i(X_j(t),\dots,U_i(t)),$ but then turn around and have $X_j(t)=f_j(X_i(t),\dots,U_j(t)).$ But you can have feedback show up in subsequent moments in time: $X(t)=f... | Structural Causal Models with cycles | Well, the fundamental rule of causality is that causes must precede effects - that is a strict inequality in time. So it is not permissible to have $X_i(t)=f_i(X_j(t),\dots,U_i(t)),$ but then turn aro | Structural Causal Models with cycles
Well, the fundamental rule of causality is that causes must precede effects - that is a strict inequality in time. So it is not permissible to have $X_i(t)=f_i(X_j(t),\dots,U_i(t)),$ but then turn around and have $X_j(t)=f_j(X_i(t),\dots,U_j(t)).$ But you can have feedback show up i... | Structural Causal Models with cycles
Well, the fundamental rule of causality is that causes must precede effects - that is a strict inequality in time. So it is not permissible to have $X_i(t)=f_i(X_j(t),\dots,U_i(t)),$ but then turn aro |
45,548 | ALS vs SGD in parallelization | SGD can not be parallelised for a single model in vanilla form because it is a single update sequential algorithm by construction. However, SGD-based parallelisation is possible, running multiple streams of batches to construct (build) multiple models and then combine these models, i.e., model averaging. For neural net... | ALS vs SGD in parallelization | SGD can not be parallelised for a single model in vanilla form because it is a single update sequential algorithm by construction. However, SGD-based parallelisation is possible, running multiple stre | ALS vs SGD in parallelization
SGD can not be parallelised for a single model in vanilla form because it is a single update sequential algorithm by construction. However, SGD-based parallelisation is possible, running multiple streams of batches to construct (build) multiple models and then combine these models, i.e., m... | ALS vs SGD in parallelization
SGD can not be parallelised for a single model in vanilla form because it is a single update sequential algorithm by construction. However, SGD-based parallelisation is possible, running multiple stre |
45,549 | ALS vs SGD in parallelization | Note that first update is the standard linear least squares estimation equation, more traditionally written as $(X^T X)^{-1} X^T y =X^\dagger y$, whereas your SGD version formulation comes down to solving this system one row at a time. Hence you get the same issue in parallelizing SGD as with a standard least squares p... | ALS vs SGD in parallelization | Note that first update is the standard linear least squares estimation equation, more traditionally written as $(X^T X)^{-1} X^T y =X^\dagger y$, whereas your SGD version formulation comes down to sol | ALS vs SGD in parallelization
Note that first update is the standard linear least squares estimation equation, more traditionally written as $(X^T X)^{-1} X^T y =X^\dagger y$, whereas your SGD version formulation comes down to solving this system one row at a time. Hence you get the same issue in parallelizing SGD as w... | ALS vs SGD in parallelization
Note that first update is the standard linear least squares estimation equation, more traditionally written as $(X^T X)^{-1} X^T y =X^\dagger y$, whereas your SGD version formulation comes down to sol |
45,550 | Is there a non-parametric form of a 3-way ANOVA? | ANOVA, even a 3-way ANOVA, is a special case of linear regression.
For one-way ANOVA, the typical "nonparametric" flavor is the Kruskal-Wallis test, so it seems like you would want some kind of 3-way Kruskal-Wallis test.
Much as ANOVA is a special case of linear regression, the Kruskal-Wallis test is a special case of ... | Is there a non-parametric form of a 3-way ANOVA? | ANOVA, even a 3-way ANOVA, is a special case of linear regression.
For one-way ANOVA, the typical "nonparametric" flavor is the Kruskal-Wallis test, so it seems like you would want some kind of 3-way | Is there a non-parametric form of a 3-way ANOVA?
ANOVA, even a 3-way ANOVA, is a special case of linear regression.
For one-way ANOVA, the typical "nonparametric" flavor is the Kruskal-Wallis test, so it seems like you would want some kind of 3-way Kruskal-Wallis test.
Much as ANOVA is a special case of linear regressi... | Is there a non-parametric form of a 3-way ANOVA?
ANOVA, even a 3-way ANOVA, is a special case of linear regression.
For one-way ANOVA, the typical "nonparametric" flavor is the Kruskal-Wallis test, so it seems like you would want some kind of 3-way |
45,551 | Is there a non-parametric form of a 3-way ANOVA? | The exchange in comments now makes this clearer. The OP has three species of shark, two level of maturity, and two sexes of shark. This forms a $3\times2\times2$ design. There will be 2 degrees of freedom for species, 1 for sex, 1 for maturity. There will be 2 for species by sex, 2 for species by maturity, and 1 for se... | Is there a non-parametric form of a 3-way ANOVA? | The exchange in comments now makes this clearer. The OP has three species of shark, two level of maturity, and two sexes of shark. This forms a $3\times2\times2$ design. There will be 2 degrees of fre | Is there a non-parametric form of a 3-way ANOVA?
The exchange in comments now makes this clearer. The OP has three species of shark, two level of maturity, and two sexes of shark. This forms a $3\times2\times2$ design. There will be 2 degrees of freedom for species, 1 for sex, 1 for maturity. There will be 2 for specie... | Is there a non-parametric form of a 3-way ANOVA?
The exchange in comments now makes this clearer. The OP has three species of shark, two level of maturity, and two sexes of shark. This forms a $3\times2\times2$ design. There will be 2 degrees of fre |
45,552 | Is there a non-parametric form of a 3-way ANOVA? | You can do an anova per permutation (non-parametric) with the aovp function from lmperm package. I suggest you use perm = "exact", to have a more robust test.
For a following post hoc test you can also use pairwise.perm.t.test from RVaideMemoire package (it allows you to do a correction, and to defined the number of pe... | Is there a non-parametric form of a 3-way ANOVA? | You can do an anova per permutation (non-parametric) with the aovp function from lmperm package. I suggest you use perm = "exact", to have a more robust test.
For a following post hoc test you can als | Is there a non-parametric form of a 3-way ANOVA?
You can do an anova per permutation (non-parametric) with the aovp function from lmperm package. I suggest you use perm = "exact", to have a more robust test.
For a following post hoc test you can also use pairwise.perm.t.test from RVaideMemoire package (it allows you to... | Is there a non-parametric form of a 3-way ANOVA?
You can do an anova per permutation (non-parametric) with the aovp function from lmperm package. I suggest you use perm = "exact", to have a more robust test.
For a following post hoc test you can als |
45,553 | Is there a non-parametric form of a 3-way ANOVA? | Just to add to the other answers, a relatively flexible method for non-parametric multi-way anova is aligned ranks transformation anova (ART anova).
At least in the implementation in R, it can handle mixed effects and has methods for post-hoc analysis.
It has its limitations, so it's important to read up on the backgro... | Is there a non-parametric form of a 3-way ANOVA? | Just to add to the other answers, a relatively flexible method for non-parametric multi-way anova is aligned ranks transformation anova (ART anova).
At least in the implementation in R, it can handle | Is there a non-parametric form of a 3-way ANOVA?
Just to add to the other answers, a relatively flexible method for non-parametric multi-way anova is aligned ranks transformation anova (ART anova).
At least in the implementation in R, it can handle mixed effects and has methods for post-hoc analysis.
It has its limitat... | Is there a non-parametric form of a 3-way ANOVA?
Just to add to the other answers, a relatively flexible method for non-parametric multi-way anova is aligned ranks transformation anova (ART anova).
At least in the implementation in R, it can handle |
45,554 | Ridge or multiple linear regression following PCA? | 85 predictor dimensions with only 150 samples is likely to lead to overfitting in clinical data, even though you now have p < n. You typically need 10-20 cases per predictor to avoid overfitting.
Ridge regression can be thought of as a continuous version of principal components regression (PCR). Ridge weights the princ... | Ridge or multiple linear regression following PCA? | 85 predictor dimensions with only 150 samples is likely to lead to overfitting in clinical data, even though you now have p < n. You typically need 10-20 cases per predictor to avoid overfitting.
Ridg | Ridge or multiple linear regression following PCA?
85 predictor dimensions with only 150 samples is likely to lead to overfitting in clinical data, even though you now have p < n. You typically need 10-20 cases per predictor to avoid overfitting.
Ridge regression can be thought of as a continuous version of principal c... | Ridge or multiple linear regression following PCA?
85 predictor dimensions with only 150 samples is likely to lead to overfitting in clinical data, even though you now have p < n. You typically need 10-20 cases per predictor to avoid overfitting.
Ridg |
45,555 | Frequentist inference with a null hypothesis that reflects theory a good-enough belt around it | I agree that the null hypothesis of equivalence is, in many cases, a rather useless hypothesis. In such cases, a superiority hypothesis informed by theory/other empirical results may be preferred. However, I don't see the need for a new procedure here. I'd suggest you 1) set a superiority hypothesis and 2) use a t-test... | Frequentist inference with a null hypothesis that reflects theory a good-enough belt around it | I agree that the null hypothesis of equivalence is, in many cases, a rather useless hypothesis. In such cases, a superiority hypothesis informed by theory/other empirical results may be preferred. How | Frequentist inference with a null hypothesis that reflects theory a good-enough belt around it
I agree that the null hypothesis of equivalence is, in many cases, a rather useless hypothesis. In such cases, a superiority hypothesis informed by theory/other empirical results may be preferred. However, I don't see the nee... | Frequentist inference with a null hypothesis that reflects theory a good-enough belt around it
I agree that the null hypothesis of equivalence is, in many cases, a rather useless hypothesis. In such cases, a superiority hypothesis informed by theory/other empirical results may be preferred. How |
45,556 | Frequentist inference with a null hypothesis that reflects theory a good-enough belt around it | As far as I can see, your main question can be addressed by the answer of num_39 or probably also by a confidence interval (maybe one-sided).
I will address some other issues raised in the question. I think that it is very important to distinguish between the formal concept of a significance test (and p-value) and the ... | Frequentist inference with a null hypothesis that reflects theory a good-enough belt around it | As far as I can see, your main question can be addressed by the answer of num_39 or probably also by a confidence interval (maybe one-sided).
I will address some other issues raised in the question. I | Frequentist inference with a null hypothesis that reflects theory a good-enough belt around it
As far as I can see, your main question can be addressed by the answer of num_39 or probably also by a confidence interval (maybe one-sided).
I will address some other issues raised in the question. I think that it is very im... | Frequentist inference with a null hypothesis that reflects theory a good-enough belt around it
As far as I can see, your main question can be addressed by the answer of num_39 or probably also by a confidence interval (maybe one-sided).
I will address some other issues raised in the question. I |
45,557 | How to prove this inequality? | It's convenient to define $U$ once and for all to be a uniform variable on the interval $[-1,1]$ and simply multiply it by $t$ to produce the $U$ used in the question.
Two useful, easily proven, but not widely known facts about random variables $X$ in general are
No matter what the distribution function (CDF) $F_X$ of... | How to prove this inequality? | It's convenient to define $U$ once and for all to be a uniform variable on the interval $[-1,1]$ and simply multiply it by $t$ to produce the $U$ used in the question.
Two useful, easily proven, but n | How to prove this inequality?
It's convenient to define $U$ once and for all to be a uniform variable on the interval $[-1,1]$ and simply multiply it by $t$ to produce the $U$ used in the question.
Two useful, easily proven, but not widely known facts about random variables $X$ in general are
No matter what the distri... | How to prove this inequality?
It's convenient to define $U$ once and for all to be a uniform variable on the interval $[-1,1]$ and simply multiply it by $t$ to produce the $U$ used in the question.
Two useful, easily proven, but n |
45,558 | How to prove this inequality? | Yes, your comment is on the right track. This looks like it's going to be Markov's Inequality:
$$P(Z\geq z)\leq \frac{E[Z]}{z}$$
for non-negative $Z$. As you have noted, $X+U+t$ is non-negative, so it's a candidate for $Z$, and $X+U+t\geq 2t$ when $X+U\geq t$. So, consider the mean of $Z$. | How to prove this inequality? | Yes, your comment is on the right track. This looks like it's going to be Markov's Inequality:
$$P(Z\geq z)\leq \frac{E[Z]}{z}$$
for non-negative $Z$. As you have noted, $X+U+t$ is non-negative, so i | How to prove this inequality?
Yes, your comment is on the right track. This looks like it's going to be Markov's Inequality:
$$P(Z\geq z)\leq \frac{E[Z]}{z}$$
for non-negative $Z$. As you have noted, $X+U+t$ is non-negative, so it's a candidate for $Z$, and $X+U+t\geq 2t$ when $X+U\geq t$. So, consider the mean of $Z$... | How to prove this inequality?
Yes, your comment is on the right track. This looks like it's going to be Markov's Inequality:
$$P(Z\geq z)\leq \frac{E[Z]}{z}$$
for non-negative $Z$. As you have noted, $X+U+t$ is non-negative, so i |
45,559 | Why is GARCH offering no predictive value? | First of all, your results look a bit strange. I would advise you to check your code. Nevertheless, I will describe a method that you can use to obtain one-step-ahead forecasts for the conditional variance using a GARCH(1,1)-model.
Method
Assume that you observe a time series $(r_t)_{t=1}^T$ of log-returns and you want... | Why is GARCH offering no predictive value? | First of all, your results look a bit strange. I would advise you to check your code. Nevertheless, I will describe a method that you can use to obtain one-step-ahead forecasts for the conditional var | Why is GARCH offering no predictive value?
First of all, your results look a bit strange. I would advise you to check your code. Nevertheless, I will describe a method that you can use to obtain one-step-ahead forecasts for the conditional variance using a GARCH(1,1)-model.
Method
Assume that you observe a time series ... | Why is GARCH offering no predictive value?
First of all, your results look a bit strange. I would advise you to check your code. Nevertheless, I will describe a method that you can use to obtain one-step-ahead forecasts for the conditional var |
45,560 | Why is GARCH offering no predictive value? | Your observation is correct. GARCH is an autoregressive model and its $h$-step-ahead predictions tend to lag $h$ steps behind, as is the case with most autoregressive models.
We often model time series processes as being hit by a new zero-mean stochastic shock every period. A special case that illustrates the lagging p... | Why is GARCH offering no predictive value? | Your observation is correct. GARCH is an autoregressive model and its $h$-step-ahead predictions tend to lag $h$ steps behind, as is the case with most autoregressive models.
We often model time serie | Why is GARCH offering no predictive value?
Your observation is correct. GARCH is an autoregressive model and its $h$-step-ahead predictions tend to lag $h$ steps behind, as is the case with most autoregressive models.
We often model time series processes as being hit by a new zero-mean stochastic shock every period. A ... | Why is GARCH offering no predictive value?
Your observation is correct. GARCH is an autoregressive model and its $h$-step-ahead predictions tend to lag $h$ steps behind, as is the case with most autoregressive models.
We often model time serie |
45,561 | How can I better understand this covariance equation? | Let's write this in matrix forms:
$$\overline{\mathbf{x}} =
\left[\matrix{\bar{x}_1\\\bar{x}_2\\\vdots\\\bar{x}_d}\right]
=
\frac{1}{N}\sum_{i=1}^N\mathbf{x}_i
=
\frac{1}{N}\sum_{i=1}^N\left[\matrix{x_{i,1}\\x_{i,2}\\\vdots\\x_{i,d}}\right]
$$
So the (biased) estimate of the covariance matrix is a square matrix, like b... | How can I better understand this covariance equation? | Let's write this in matrix forms:
$$\overline{\mathbf{x}} =
\left[\matrix{\bar{x}_1\\\bar{x}_2\\\vdots\\\bar{x}_d}\right]
=
\frac{1}{N}\sum_{i=1}^N\mathbf{x}_i
=
\frac{1}{N}\sum_{i=1}^N\left[\matrix{x | How can I better understand this covariance equation?
Let's write this in matrix forms:
$$\overline{\mathbf{x}} =
\left[\matrix{\bar{x}_1\\\bar{x}_2\\\vdots\\\bar{x}_d}\right]
=
\frac{1}{N}\sum_{i=1}^N\mathbf{x}_i
=
\frac{1}{N}\sum_{i=1}^N\left[\matrix{x_{i,1}\\x_{i,2}\\\vdots\\x_{i,d}}\right]
$$
So the (biased) estima... | How can I better understand this covariance equation?
Let's write this in matrix forms:
$$\overline{\mathbf{x}} =
\left[\matrix{\bar{x}_1\\\bar{x}_2\\\vdots\\\bar{x}_d}\right]
=
\frac{1}{N}\sum_{i=1}^N\mathbf{x}_i
=
\frac{1}{N}\sum_{i=1}^N\left[\matrix{x |
45,562 | Equivalent ways of parametrizing Gamma distribution | This distribution $f(x, \alpha) = \frac{x^{\alpha - 1} e^{-x}}{\Gamma(\alpha)}$ is the distribution with a fixed scale parameter $1/\beta = \theta = 1$.
The article states further on
The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale param... | Equivalent ways of parametrizing Gamma distribution | This distribution $f(x, \alpha) = \frac{x^{\alpha - 1} e^{-x}}{\Gamma(\alpha)}$ is the distribution with a fixed scale parameter $1/\beta = \theta = 1$.
The article states further on
The probability | Equivalent ways of parametrizing Gamma distribution
This distribution $f(x, \alpha) = \frac{x^{\alpha - 1} e^{-x}}{\Gamma(\alpha)}$ is the distribution with a fixed scale parameter $1/\beta = \theta = 1$.
The article states further on
The probability density above is defined in the “standardized” form. To shift and/o... | Equivalent ways of parametrizing Gamma distribution
This distribution $f(x, \alpha) = \frac{x^{\alpha - 1} e^{-x}}{\Gamma(\alpha)}$ is the distribution with a fixed scale parameter $1/\beta = \theta = 1$.
The article states further on
The probability |
45,563 | Equivalent ways of parametrizing Gamma distribution | A change of variables in the density requires more than substitution. In particular you need to multiply by the absolute value of the derivative of the inverse function. This would be more obvious if you considered the cumulative distribution function and then differentiated to get the density: the extra multiplicat... | Equivalent ways of parametrizing Gamma distribution | A change of variables in the density requires more than substitution. In particular you need to multiply by the absolute value of the derivative of the inverse function. This would be more obvious | Equivalent ways of parametrizing Gamma distribution
A change of variables in the density requires more than substitution. In particular you need to multiply by the absolute value of the derivative of the inverse function. This would be more obvious if you considered the cumulative distribution function and then diff... | Equivalent ways of parametrizing Gamma distribution
A change of variables in the density requires more than substitution. In particular you need to multiply by the absolute value of the derivative of the inverse function. This would be more obvious |
45,564 | Zero-inflated Gaussian for weights below zero recorded as 0? | I think the model is more appropriately a left-censored Gaussian, since the process you describe is about discarding information below some value (in this case, the location is known to be 0, which is simpler than the case of an unknown censoring value). In other words, there's some real quantity which can (hypothetica... | Zero-inflated Gaussian for weights below zero recorded as 0? | I think the model is more appropriately a left-censored Gaussian, since the process you describe is about discarding information below some value (in this case, the location is known to be 0, which is | Zero-inflated Gaussian for weights below zero recorded as 0?
I think the model is more appropriately a left-censored Gaussian, since the process you describe is about discarding information below some value (in this case, the location is known to be 0, which is simpler than the case of an unknown censoring value). In o... | Zero-inflated Gaussian for weights below zero recorded as 0?
I think the model is more appropriately a left-censored Gaussian, since the process you describe is about discarding information below some value (in this case, the location is known to be 0, which is |
45,565 | What does comparing mean rank mean? | When comparing two independent samples, you want to rank all the data together.
Revising your example:
Sample A
value rank
20 7.5
20 7.5
20 7.5
20 7.5
25 10
and Sample B
value rank
1 1
2 2
3 3
4 4
5 5
What is going on?
Sample B's value of 1 is the lowest ordered va... | What does comparing mean rank mean? | When comparing two independent samples, you want to rank all the data together.
Revising your example:
Sample A
value rank
20 7.5
20 7.5
20 7.5
20 7.5
25 10
and Sample B
va | What does comparing mean rank mean?
When comparing two independent samples, you want to rank all the data together.
Revising your example:
Sample A
value rank
20 7.5
20 7.5
20 7.5
20 7.5
25 10
and Sample B
value rank
1 1
2 2
3 3
4 4
5 5
What is going on?
Sample B's... | What does comparing mean rank mean?
When comparing two independent samples, you want to rank all the data together.
Revising your example:
Sample A
value rank
20 7.5
20 7.5
20 7.5
20 7.5
25 10
and Sample B
va |
45,566 | Cyclicality in causal relationships | Because causes must precede effects, acyclic is preferred. Ultimately, there can be no true cycles: if event $A$ causes event $B,$ then $A$ must precede $B.$ The time $t_a$ at which $A$ occurs must be smaller than the time $t_b$ at which $B$ occurs, for time flowing in the usual direction. If $t_a<t_b,$ it is impossibl... | Cyclicality in causal relationships | Because causes must precede effects, acyclic is preferred. Ultimately, there can be no true cycles: if event $A$ causes event $B,$ then $A$ must precede $B.$ The time $t_a$ at which $A$ occurs must be | Cyclicality in causal relationships
Because causes must precede effects, acyclic is preferred. Ultimately, there can be no true cycles: if event $A$ causes event $B,$ then $A$ must precede $B.$ The time $t_a$ at which $A$ occurs must be smaller than the time $t_b$ at which $B$ occurs, for time flowing in the usual dire... | Cyclicality in causal relationships
Because causes must precede effects, acyclic is preferred. Ultimately, there can be no true cycles: if event $A$ causes event $B,$ then $A$ must precede $B.$ The time $t_a$ at which $A$ occurs must be |
45,567 | How to decide the best form of BMI used in cox regression, categorical or continuous? | BMI might be associated continuously with outcome but not necessarily linearly. The best way to test that is to fit BMI as a continuous predictor flexibly, for example with restricted cubic splines as in the rms package in R. If you use the tools in that package, then you can use its anova() function to test the signif... | How to decide the best form of BMI used in cox regression, categorical or continuous? | BMI might be associated continuously with outcome but not necessarily linearly. The best way to test that is to fit BMI as a continuous predictor flexibly, for example with restricted cubic splines as | How to decide the best form of BMI used in cox regression, categorical or continuous?
BMI might be associated continuously with outcome but not necessarily linearly. The best way to test that is to fit BMI as a continuous predictor flexibly, for example with restricted cubic splines as in the rms package in R. If you u... | How to decide the best form of BMI used in cox regression, categorical or continuous?
BMI might be associated continuously with outcome but not necessarily linearly. The best way to test that is to fit BMI as a continuous predictor flexibly, for example with restricted cubic splines as |
45,568 | Simple constant-width prediction interval for a regression model | As described in your question, you should expect that the prediction intervals in production to have the desired coverage.
During training you come up with a fitted model $f$, which need not be equal to, or even close to, the true data generating function.
Using the test set you get a sample $e_1,\dots ,e_{n_\text{test... | Simple constant-width prediction interval for a regression model | As described in your question, you should expect that the prediction intervals in production to have the desired coverage.
During training you come up with a fitted model $f$, which need not be equal | Simple constant-width prediction interval for a regression model
As described in your question, you should expect that the prediction intervals in production to have the desired coverage.
During training you come up with a fitted model $f$, which need not be equal to, or even close to, the true data generating function... | Simple constant-width prediction interval for a regression model
As described in your question, you should expect that the prediction intervals in production to have the desired coverage.
During training you come up with a fitted model $f$, which need not be equal |
45,569 | Simple constant-width prediction interval for a regression model | I think the fundamental thing to realize here is that if your test set is really a test set (used in no way for training) and your test data are really i.i.d., and test and production really have the same distribution, then $f$ can be considered as any other function determined independently of your data. The fact that... | Simple constant-width prediction interval for a regression model | I think the fundamental thing to realize here is that if your test set is really a test set (used in no way for training) and your test data are really i.i.d., and test and production really have the | Simple constant-width prediction interval for a regression model
I think the fundamental thing to realize here is that if your test set is really a test set (used in no way for training) and your test data are really i.i.d., and test and production really have the same distribution, then $f$ can be considered as any ot... | Simple constant-width prediction interval for a regression model
I think the fundamental thing to realize here is that if your test set is really a test set (used in no way for training) and your test data are really i.i.d., and test and production really have the |
45,570 | Is there a generalized concept of noncentrality of a distribution? | It's hard to understand how to answer this question.
For any given hypothesis and any given test statistic, the distribution under an alternative hypothesis is considered a "non-central" version of the distribution of the same statistic under the null.
In some lucky cases, the test-statistic under the alternative hypot... | Is there a generalized concept of noncentrality of a distribution? | It's hard to understand how to answer this question.
For any given hypothesis and any given test statistic, the distribution under an alternative hypothesis is considered a "non-central" version of th | Is there a generalized concept of noncentrality of a distribution?
It's hard to understand how to answer this question.
For any given hypothesis and any given test statistic, the distribution under an alternative hypothesis is considered a "non-central" version of the distribution of the same statistic under the null.
... | Is there a generalized concept of noncentrality of a distribution?
It's hard to understand how to answer this question.
For any given hypothesis and any given test statistic, the distribution under an alternative hypothesis is considered a "non-central" version of th |
45,571 | Is there a generalized concept of noncentrality of a distribution? | I think a simple way to think about noncentral distributions is to consider how they're built from normal distribution, e.g., non central t variable is $\frac{Z+\mu}{\sqrt{V/\nu}}$, where $Z$ is standard normal and $V\sim\chi_\nu^2$. When noncentrality parameter $\mu=0$, we have the standard normal in numerator, and th... | Is there a generalized concept of noncentrality of a distribution? | I think a simple way to think about noncentral distributions is to consider how they're built from normal distribution, e.g., non central t variable is $\frac{Z+\mu}{\sqrt{V/\nu}}$, where $Z$ is stand | Is there a generalized concept of noncentrality of a distribution?
I think a simple way to think about noncentral distributions is to consider how they're built from normal distribution, e.g., non central t variable is $\frac{Z+\mu}{\sqrt{V/\nu}}$, where $Z$ is standard normal and $V\sim\chi_\nu^2$. When noncentrality ... | Is there a generalized concept of noncentrality of a distribution?
I think a simple way to think about noncentral distributions is to consider how they're built from normal distribution, e.g., non central t variable is $\frac{Z+\mu}{\sqrt{V/\nu}}$, where $Z$ is stand |
45,572 | Is there a generalized concept of noncentrality of a distribution? | I agree with Aksakal and AdamO, the non-central varieties are a result of investigating the power of a test. The test itself assumes a particular null hypothesis for the purposes of argument and inference using ex-post sampling probability as evidence. Power explores the ex-ante sampling probability of the test when ... | Is there a generalized concept of noncentrality of a distribution? | I agree with Aksakal and AdamO, the non-central varieties are a result of investigating the power of a test. The test itself assumes a particular null hypothesis for the purposes of argument and infe | Is there a generalized concept of noncentrality of a distribution?
I agree with Aksakal and AdamO, the non-central varieties are a result of investigating the power of a test. The test itself assumes a particular null hypothesis for the purposes of argument and inference using ex-post sampling probability as evidence.... | Is there a generalized concept of noncentrality of a distribution?
I agree with Aksakal and AdamO, the non-central varieties are a result of investigating the power of a test. The test itself assumes a particular null hypothesis for the purposes of argument and infe |
45,573 | Is there a generalized concept of noncentrality of a distribution? | The intuitive way to grasp noncentral distributions is through their central counterparts. There are several noncentral distributions like noncentral chi-squared, noncentral F, noncentral T, noncentral beta, noncentral negative hypergeometric, noncentral Wishart, and so on. All of them can be expressed as infinite mixt... | Is there a generalized concept of noncentrality of a distribution? | The intuitive way to grasp noncentral distributions is through their central counterparts. There are several noncentral distributions like noncentral chi-squared, noncentral F, noncentral T, noncentra | Is there a generalized concept of noncentrality of a distribution?
The intuitive way to grasp noncentral distributions is through their central counterparts. There are several noncentral distributions like noncentral chi-squared, noncentral F, noncentral T, noncentral beta, noncentral negative hypergeometric, noncentra... | Is there a generalized concept of noncentrality of a distribution?
The intuitive way to grasp noncentral distributions is through their central counterparts. There are several noncentral distributions like noncentral chi-squared, noncentral F, noncentral T, noncentra |
45,574 | Why doesn't this work as a backdoor? | Your assumption is that conditioning on a variable (i.e., $X_4$) blocks all paths through that variable, but that is not so. Conditioning on a variable opens a path between the antecedents of the variable. $X_1$ and $X_2$ are d-connected after conditioning on $X_4$. $X_4$ is a collider of $X_1$ and $X_2$. | Why doesn't this work as a backdoor? | Your assumption is that conditioning on a variable (i.e., $X_4$) blocks all paths through that variable, but that is not so. Conditioning on a variable opens a path between the antecedents of the vari | Why doesn't this work as a backdoor?
Your assumption is that conditioning on a variable (i.e., $X_4$) blocks all paths through that variable, but that is not so. Conditioning on a variable opens a path between the antecedents of the variable. $X_1$ and $X_2$ are d-connected after conditioning on $X_4$. $X_4$ is a colli... | Why doesn't this work as a backdoor?
Your assumption is that conditioning on a variable (i.e., $X_4$) blocks all paths through that variable, but that is not so. Conditioning on a variable opens a path between the antecedents of the vari |
45,575 | Plot profile likelihood | I'll use $\mu_i = \eta_1 - 2\theta\eta_2x_i + \eta_2 x_i^2$ for convenience. If we're thinking of $\mu_i$ as a function of $\theta$, so only $\eta_1$ and $\eta_2$ are parameters, then we can write this as
$$
\mu_i = \eta_1 + \eta_2(-2\theta x_i + x_i^2) = \eta_1 + \eta_2 z_i
$$
for $z_i = -2\theta x_i + x_i^2$. This is... | Plot profile likelihood | I'll use $\mu_i = \eta_1 - 2\theta\eta_2x_i + \eta_2 x_i^2$ for convenience. If we're thinking of $\mu_i$ as a function of $\theta$, so only $\eta_1$ and $\eta_2$ are parameters, then we can write thi | Plot profile likelihood
I'll use $\mu_i = \eta_1 - 2\theta\eta_2x_i + \eta_2 x_i^2$ for convenience. If we're thinking of $\mu_i$ as a function of $\theta$, so only $\eta_1$ and $\eta_2$ are parameters, then we can write this as
$$
\mu_i = \eta_1 + \eta_2(-2\theta x_i + x_i^2) = \eta_1 + \eta_2 z_i
$$
for $z_i = -2\the... | Plot profile likelihood
I'll use $\mu_i = \eta_1 - 2\theta\eta_2x_i + \eta_2 x_i^2$ for convenience. If we're thinking of $\mu_i$ as a function of $\theta$, so only $\eta_1$ and $\eta_2$ are parameters, then we can write thi |
45,576 | Plot profile likelihood | This is an appendix to @jld's answer (+1), which assumes that the error variance $\sigma^2$ is known.
Alternatively, we can treat $\sigma^2$ as another parameter to maximize while profiling the log-likelihood for $\theta$. This is straightforward to do in a linear regression:
$$
\begin{aligned}
\widehat{\sigma}_\mu^2 =... | Plot profile likelihood | This is an appendix to @jld's answer (+1), which assumes that the error variance $\sigma^2$ is known.
Alternatively, we can treat $\sigma^2$ as another parameter to maximize while profiling the log-li | Plot profile likelihood
This is an appendix to @jld's answer (+1), which assumes that the error variance $\sigma^2$ is known.
Alternatively, we can treat $\sigma^2$ as another parameter to maximize while profiling the log-likelihood for $\theta$. This is straightforward to do in a linear regression:
$$
\begin{aligned}
... | Plot profile likelihood
This is an appendix to @jld's answer (+1), which assumes that the error variance $\sigma^2$ is known.
Alternatively, we can treat $\sigma^2$ as another parameter to maximize while profiling the log-li |
45,577 | How should I proceed when the minimum sample size in an experiment is not reached? | Elaborating a bit on Jeremy's answer, let's think for a minute about what a power analysis is. The purpose is to determine how many participants one would need to "detect" an effect of a specific size. So in discussing the results of your experiment vis a vis the sample size you originally designed, and what the pandem... | How should I proceed when the minimum sample size in an experiment is not reached? | Elaborating a bit on Jeremy's answer, let's think for a minute about what a power analysis is. The purpose is to determine how many participants one would need to "detect" an effect of a specific size | How should I proceed when the minimum sample size in an experiment is not reached?
Elaborating a bit on Jeremy's answer, let's think for a minute about what a power analysis is. The purpose is to determine how many participants one would need to "detect" an effect of a specific size. So in discussing the results of you... | How should I proceed when the minimum sample size in an experiment is not reached?
Elaborating a bit on Jeremy's answer, let's think for a minute about what a power analysis is. The purpose is to determine how many participants one would need to "detect" an effect of a specific size |
45,578 | How should I proceed when the minimum sample size in an experiment is not reached? | I would just explain what happened. You powered for N, and you got N*. It's not the first time this has happened (and won't be the last).
Post hoc power would not be especially useful (as you have realized.) | How should I proceed when the minimum sample size in an experiment is not reached? | I would just explain what happened. You powered for N, and you got N*. It's not the first time this has happened (and won't be the last).
Post hoc power would not be especially useful (as you have rea | How should I proceed when the minimum sample size in an experiment is not reached?
I would just explain what happened. You powered for N, and you got N*. It's not the first time this has happened (and won't be the last).
Post hoc power would not be especially useful (as you have realized.) | How should I proceed when the minimum sample size in an experiment is not reached?
I would just explain what happened. You powered for N, and you got N*. It's not the first time this has happened (and won't be the last).
Post hoc power would not be especially useful (as you have rea |
45,579 | Getting understand HAC estimators | In a linear model, we have $\hat\beta = (X^TX)^{-1}X^TY$.
A basic property of variances and matrices is that
$$\mathrm{var}[A^TY] = A^T\mathrm{var}[Y]A$$
So
$$\mathrm{var}[\hat\beta] = (X^TX)^{-1}X^T \mathrm{var}[Y] X(X^TX)^{-1}$$
It's usual when considering HAC estimators to break this into three pieces, two of whic... | Getting understand HAC estimators | In a linear model, we have $\hat\beta = (X^TX)^{-1}X^TY$.
A basic property of variances and matrices is that
$$\mathrm{var}[A^TY] = A^T\mathrm{var}[Y]A$$
So
$$\mathrm{var}[\hat\beta] = (X^TX)^{-1}X^T | Getting understand HAC estimators
In a linear model, we have $\hat\beta = (X^TX)^{-1}X^TY$.
A basic property of variances and matrices is that
$$\mathrm{var}[A^TY] = A^T\mathrm{var}[Y]A$$
So
$$\mathrm{var}[\hat\beta] = (X^TX)^{-1}X^T \mathrm{var}[Y] X(X^TX)^{-1}$$
It's usual when considering HAC estimators to break t... | Getting understand HAC estimators
In a linear model, we have $\hat\beta = (X^TX)^{-1}X^TY$.
A basic property of variances and matrices is that
$$\mathrm{var}[A^TY] = A^T\mathrm{var}[Y]A$$
So
$$\mathrm{var}[\hat\beta] = (X^TX)^{-1}X^T |
45,580 | Getting understand HAC estimators | The ideas the HAC estimators implemented in the sandwich package are explained in an accompanying paper that is also listed in the references in ?vcovHAC:
Zeileis A (2004).
"Econometric Computing with HC and HAC Covariance Matrix Estimators."
Journal of Statistical Software, 11(10), 1-17.
doi:10.18637/jss.v011.i10
Th... | Getting understand HAC estimators | The ideas the HAC estimators implemented in the sandwich package are explained in an accompanying paper that is also listed in the references in ?vcovHAC:
Zeileis A (2004).
"Econometric Computing wit | Getting understand HAC estimators
The ideas the HAC estimators implemented in the sandwich package are explained in an accompanying paper that is also listed in the references in ?vcovHAC:
Zeileis A (2004).
"Econometric Computing with HC and HAC Covariance Matrix Estimators."
Journal of Statistical Software, 11(10), 1... | Getting understand HAC estimators
The ideas the HAC estimators implemented in the sandwich package are explained in an accompanying paper that is also listed in the references in ?vcovHAC:
Zeileis A (2004).
"Econometric Computing wit |
45,581 | Is a sample i.i.d or is a collection of random variables i.i.d.? | From Wikipedia, two Random Variables (RVs) (remark: you can generalize this to any number of RVs) are independent and identically distributed (i.i.d.) if their Cumulative Distribution Function (CDF) is the same for any element of the domain $I$ and if their joint CDF factorizes in the product of the marginal CDFs. This... | Is a sample i.i.d or is a collection of random variables i.i.d.? | From Wikipedia, two Random Variables (RVs) (remark: you can generalize this to any number of RVs) are independent and identically distributed (i.i.d.) if their Cumulative Distribution Function (CDF) i | Is a sample i.i.d or is a collection of random variables i.i.d.?
From Wikipedia, two Random Variables (RVs) (remark: you can generalize this to any number of RVs) are independent and identically distributed (i.i.d.) if their Cumulative Distribution Function (CDF) is the same for any element of the domain $I$ and if the... | Is a sample i.i.d or is a collection of random variables i.i.d.?
From Wikipedia, two Random Variables (RVs) (remark: you can generalize this to any number of RVs) are independent and identically distributed (i.i.d.) if their Cumulative Distribution Function (CDF) i |
45,582 | How to fit this linear regression with constraints? | The model is overparametrised: you don't need $\beta_1$, which can be set to anything convenient, like 1.
One thing I thought of was to fit iteratively. Start out with some guess at $w$ and $\beta_2$. Then compute $Z=(\sum_i \hat{w}_iX_i)^2$ and fit the linear model
Y~ X1+X2+...+X_k + Z
The coefficients of the $X$s a... | How to fit this linear regression with constraints? | The model is overparametrised: you don't need $\beta_1$, which can be set to anything convenient, like 1.
One thing I thought of was to fit iteratively. Start out with some guess at $w$ and $\beta_2 | How to fit this linear regression with constraints?
The model is overparametrised: you don't need $\beta_1$, which can be set to anything convenient, like 1.
One thing I thought of was to fit iteratively. Start out with some guess at $w$ and $\beta_2$. Then compute $Z=(\sum_i \hat{w}_iX_i)^2$ and fit the linear model... | How to fit this linear regression with constraints?
The model is overparametrised: you don't need $\beta_1$, which can be set to anything convenient, like 1.
One thing I thought of was to fit iteratively. Start out with some guess at $w$ and $\beta_2 |
45,583 | How to fit this linear regression with constraints? | If you write out the expression, you get a polynomial in terms of $X_1,X_2,..,X_k$, including their interactions, where the new "coefficients" are all function of $\beta$s and $w$s and twos. For k=2, you get a polynomial that has 5 coefficients (or 6 including the intercept) with 4 unknowns:
$$ \begin{align*} Y &= \be... | How to fit this linear regression with constraints? | If you write out the expression, you get a polynomial in terms of $X_1,X_2,..,X_k$, including their interactions, where the new "coefficients" are all function of $\beta$s and $w$s and twos. For k=2, | How to fit this linear regression with constraints?
If you write out the expression, you get a polynomial in terms of $X_1,X_2,..,X_k$, including their interactions, where the new "coefficients" are all function of $\beta$s and $w$s and twos. For k=2, you get a polynomial that has 5 coefficients (or 6 including the int... | How to fit this linear regression with constraints?
If you write out the expression, you get a polynomial in terms of $X_1,X_2,..,X_k$, including their interactions, where the new "coefficients" are all function of $\beta$s and $w$s and twos. For k=2, |
45,584 | Dirichlet distribution vs Multinomial distribution? | Multinomial distribution is a discrete, multivariate distribution for $k$ variables $x_1,x_2,\dots,x_k$ where each $x_i \in \{0,1,\dots,n\}$ and $\sum_{i=1}^k x_i = n$. Dirichlet distribution is a continuous, multivariate distribution for $k$ variables $x_1,x_2,\dots,x_k$ where each $x_i \in (0,1)$ and $\sum_{i=1}^k x_... | Dirichlet distribution vs Multinomial distribution? | Multinomial distribution is a discrete, multivariate distribution for $k$ variables $x_1,x_2,\dots,x_k$ where each $x_i \in \{0,1,\dots,n\}$ and $\sum_{i=1}^k x_i = n$. Dirichlet distribution is a con | Dirichlet distribution vs Multinomial distribution?
Multinomial distribution is a discrete, multivariate distribution for $k$ variables $x_1,x_2,\dots,x_k$ where each $x_i \in \{0,1,\dots,n\}$ and $\sum_{i=1}^k x_i = n$. Dirichlet distribution is a continuous, multivariate distribution for $k$ variables $x_1,x_2,\dots,... | Dirichlet distribution vs Multinomial distribution?
Multinomial distribution is a discrete, multivariate distribution for $k$ variables $x_1,x_2,\dots,x_k$ where each $x_i \in \{0,1,\dots,n\}$ and $\sum_{i=1}^k x_i = n$. Dirichlet distribution is a con |
45,585 | Dirichlet distribution vs Multinomial distribution? | A first difference is that multinomial distribution $\mathcal{M}(N, \mathbf{p})$ is discrete (it generalises binomial disrtibution) whereas Dirichlet distribution is continuous (it generalizes Beta distribution).
But if you were to make $N$ go to infinity in order to get an approximately continuous outcome, then the m... | Dirichlet distribution vs Multinomial distribution? | A first difference is that multinomial distribution $\mathcal{M}(N, \mathbf{p})$ is discrete (it generalises binomial disrtibution) whereas Dirichlet distribution is continuous (it generalizes Beta di | Dirichlet distribution vs Multinomial distribution?
A first difference is that multinomial distribution $\mathcal{M}(N, \mathbf{p})$ is discrete (it generalises binomial disrtibution) whereas Dirichlet distribution is continuous (it generalizes Beta distribution).
But if you were to make $N$ go to infinity in order to... | Dirichlet distribution vs Multinomial distribution?
A first difference is that multinomial distribution $\mathcal{M}(N, \mathbf{p})$ is discrete (it generalises binomial disrtibution) whereas Dirichlet distribution is continuous (it generalizes Beta di |
45,586 | Can we get Moment Generating Function(MGF) from data? | Can we define an MGF from data?
The MGF of a random variables $X$ is defined to be
$$M(t) = \mathbf E\left[e^{tX}\right],$$
so given observed data $x_1,\ldots, x_n$ we can certainly define the empirical MGF to be
$$M(t; \underline x) = \frac1n \left( e^{tx_1} + \cdots + e^{tx_n}\right).$$
Is it useful?
The use of this ... | Can we get Moment Generating Function(MGF) from data? | Can we define an MGF from data?
The MGF of a random variables $X$ is defined to be
$$M(t) = \mathbf E\left[e^{tX}\right],$$
so given observed data $x_1,\ldots, x_n$ we can certainly define the empiric | Can we get Moment Generating Function(MGF) from data?
Can we define an MGF from data?
The MGF of a random variables $X$ is defined to be
$$M(t) = \mathbf E\left[e^{tX}\right],$$
so given observed data $x_1,\ldots, x_n$ we can certainly define the empirical MGF to be
$$M(t; \underline x) = \frac1n \left( e^{tx_1} + \cdo... | Can we get Moment Generating Function(MGF) from data?
Can we define an MGF from data?
The MGF of a random variables $X$ is defined to be
$$M(t) = \mathbf E\left[e^{tX}\right],$$
so given observed data $x_1,\ldots, x_n$ we can certainly define the empiric |
45,587 | Can we get Moment Generating Function(MGF) from data? | In parametric problems (i.e., where you have a specified distribution family indexed by a finite number of parameters), both the true density and MGF are functions of the parameters (assuming the latter exists). Both objects summarise the distribution and contain the same information, so neither is less useful in a st... | Can we get Moment Generating Function(MGF) from data? | In parametric problems (i.e., where you have a specified distribution family indexed by a finite number of parameters), both the true density and MGF are functions of the parameters (assuming the latt | Can we get Moment Generating Function(MGF) from data?
In parametric problems (i.e., where you have a specified distribution family indexed by a finite number of parameters), both the true density and MGF are functions of the parameters (assuming the latter exists). Both objects summarise the distribution and contain t... | Can we get Moment Generating Function(MGF) from data?
In parametric problems (i.e., where you have a specified distribution family indexed by a finite number of parameters), both the true density and MGF are functions of the parameters (assuming the latt |
45,588 | Can we get Moment Generating Function(MGF) from data? | Just some additions to the excellent answer by @owen88. Some examples of empirical mgf's (emgf) (and comments on better ways to estimate them) can be found in answers here: How does saddlepoint approximation work?. One use is to approximate the bootstrap distribution, thereby making possible bootstrap without simula... | Can we get Moment Generating Function(MGF) from data? | Just some additions to the excellent answer by @owen88. Some examples of empirical mgf's (emgf) (and comments on better ways to estimate them) can be found in answers here: How does saddlepoint appr | Can we get Moment Generating Function(MGF) from data?
Just some additions to the excellent answer by @owen88. Some examples of empirical mgf's (emgf) (and comments on better ways to estimate them) can be found in answers here: How does saddlepoint approximation work?. One use is to approximate the bootstrap distribu... | Can we get Moment Generating Function(MGF) from data?
Just some additions to the excellent answer by @owen88. Some examples of empirical mgf's (emgf) (and comments on better ways to estimate them) can be found in answers here: How does saddlepoint appr |
45,589 | Will each unique input to an Autoencoder produce a unique coding? | In some setups, not only they can, they need to. An idealized Denoising Autoencoder with a weak decoder would map any input+noise, as well as just input, to the same eventual latent code - its encoder would be just a lossless compression of the noiseless data, plus noise filters.
For a negative case, in a pathological ... | Will each unique input to an Autoencoder produce a unique coding? | In some setups, not only they can, they need to. An idealized Denoising Autoencoder with a weak decoder would map any input+noise, as well as just input, to the same eventual latent code - its encoder | Will each unique input to an Autoencoder produce a unique coding?
In some setups, not only they can, they need to. An idealized Denoising Autoencoder with a weak decoder would map any input+noise, as well as just input, to the same eventual latent code - its encoder would be just a lossless compression of the noiseless... | Will each unique input to an Autoencoder produce a unique coding?
In some setups, not only they can, they need to. An idealized Denoising Autoencoder with a weak decoder would map any input+noise, as well as just input, to the same eventual latent code - its encoder |
45,590 | Will each unique input to an Autoencoder produce a unique coding? | There is more information going to the bottleneck than it is going out, so some input have to produce the same outputs. | Will each unique input to an Autoencoder produce a unique coding? | There is more information going to the bottleneck than it is going out, so some input have to produce the same outputs. | Will each unique input to an Autoencoder produce a unique coding?
There is more information going to the bottleneck than it is going out, so some input have to produce the same outputs. | Will each unique input to an Autoencoder produce a unique coding?
There is more information going to the bottleneck than it is going out, so some input have to produce the same outputs. |
45,591 | Will each unique input to an Autoencoder produce a unique coding? | Trivially, if your bottleneck/representation layer uses ReLU activations and all of the inputs to that layer are less than 0, the encoding will be all 0s. So to produce such encodings, you'd just need to have two inputs that have the property that they get mapped "to the left side" of all the bottleneck layer ReLUs.
Or... | Will each unique input to an Autoencoder produce a unique coding? | Trivially, if your bottleneck/representation layer uses ReLU activations and all of the inputs to that layer are less than 0, the encoding will be all 0s. So to produce such encodings, you'd just need | Will each unique input to an Autoencoder produce a unique coding?
Trivially, if your bottleneck/representation layer uses ReLU activations and all of the inputs to that layer are less than 0, the encoding will be all 0s. So to produce such encodings, you'd just need to have two inputs that have the property that they g... | Will each unique input to an Autoencoder produce a unique coding?
Trivially, if your bottleneck/representation layer uses ReLU activations and all of the inputs to that layer are less than 0, the encoding will be all 0s. So to produce such encodings, you'd just need |
45,592 | Statistical test with violation of independence assumption | I have many questions about the proposed approach, mostly because it is not clearly described. It's unlikely this question can be edited to give us much insight into the setting and rationale for this approach. Nonetheless, a few points can be addressed.
Sums of variances obtained by randomly partitioning a dataset 30-... | Statistical test with violation of independence assumption | I have many questions about the proposed approach, mostly because it is not clearly described. It's unlikely this question can be edited to give us much insight into the setting and rationale for this | Statistical test with violation of independence assumption
I have many questions about the proposed approach, mostly because it is not clearly described. It's unlikely this question can be edited to give us much insight into the setting and rationale for this approach. Nonetheless, a few points can be addressed.
Sums o... | Statistical test with violation of independence assumption
I have many questions about the proposed approach, mostly because it is not clearly described. It's unlikely this question can be edited to give us much insight into the setting and rationale for this |
45,593 | Statistical test with violation of independence assumption | If I understand you correctly, you are asking about testing the significance of the difference between two regressions on the same data set. This is not a standard significance testing problem. A standard significance testing problem states a null hypothesis ($H_0$) about how the data were generated, and uses the distr... | Statistical test with violation of independence assumption | If I understand you correctly, you are asking about testing the significance of the difference between two regressions on the same data set. This is not a standard significance testing problem. A stan | Statistical test with violation of independence assumption
If I understand you correctly, you are asking about testing the significance of the difference between two regressions on the same data set. This is not a standard significance testing problem. A standard significance testing problem states a null hypothesis ($... | Statistical test with violation of independence assumption
If I understand you correctly, you are asking about testing the significance of the difference between two regressions on the same data set. This is not a standard significance testing problem. A stan |
45,594 | What justifies adjusting for proxy variables in the DAG causal inference framework? | Since Interest_in_Acme is unobservable, the average causal effect of Loyalty Club Membership on Spend is unidentifiable. However, there is an important exception to that rule, that is if Interest_in_Acme is perfectly correlated ($r=1.0$ or $r=0.0$) with Spend_in_Prev_Year. If those two variables are perfectly correlate... | What justifies adjusting for proxy variables in the DAG causal inference framework? | Since Interest_in_Acme is unobservable, the average causal effect of Loyalty Club Membership on Spend is unidentifiable. However, there is an important exception to that rule, that is if Interest_in_A | What justifies adjusting for proxy variables in the DAG causal inference framework?
Since Interest_in_Acme is unobservable, the average causal effect of Loyalty Club Membership on Spend is unidentifiable. However, there is an important exception to that rule, that is if Interest_in_Acme is perfectly correlated ($r=1.0$... | What justifies adjusting for proxy variables in the DAG causal inference framework?
Since Interest_in_Acme is unobservable, the average causal effect of Loyalty Club Membership on Spend is unidentifiable. However, there is an important exception to that rule, that is if Interest_in_A |
45,595 | What justifies adjusting for proxy variables in the DAG causal inference framework? | Exact point identification is not possible here, but adjusting for Spend_in_Prev_Year does partially block the backdoor path, so that would be the rationale for it. As a general advice, you should adjust for the proxy in the absence of the true confounder (there are exceptions, the proxy could be opening other backdoo... | What justifies adjusting for proxy variables in the DAG causal inference framework? | Exact point identification is not possible here, but adjusting for Spend_in_Prev_Year does partially block the backdoor path, so that would be the rationale for it. As a general advice, you should ad | What justifies adjusting for proxy variables in the DAG causal inference framework?
Exact point identification is not possible here, but adjusting for Spend_in_Prev_Year does partially block the backdoor path, so that would be the rationale for it. As a general advice, you should adjust for the proxy in the absence of... | What justifies adjusting for proxy variables in the DAG causal inference framework?
Exact point identification is not possible here, but adjusting for Spend_in_Prev_Year does partially block the backdoor path, so that would be the rationale for it. As a general advice, you should ad |
45,596 | When to use Cohen's d and when t-test? | Cohen's d seeks to tell you how big the standardized difference is between the two distributions. It's very popular in areas like psychology where I think there are no obvious units you can use to describe the difference. In medical stats, I could say (for example) that your HbA1c levels were on average 5mg different ... | When to use Cohen's d and when t-test? | Cohen's d seeks to tell you how big the standardized difference is between the two distributions. It's very popular in areas like psychology where I think there are no obvious units you can use to de | When to use Cohen's d and when t-test?
Cohen's d seeks to tell you how big the standardized difference is between the two distributions. It's very popular in areas like psychology where I think there are no obvious units you can use to describe the difference. In medical stats, I could say (for example) that your HbA1... | When to use Cohen's d and when t-test?
Cohen's d seeks to tell you how big the standardized difference is between the two distributions. It's very popular in areas like psychology where I think there are no obvious units you can use to de |
45,597 | When to use Cohen's d and when t-test? | T-test is in complimentary relation with Cohen's $d$ (and equivalence tests using Cohen's $d$).
T-test gives a p-value which is the probability of committing a Type I error. One can reject the null hypothesis, if the p-value is too small, but one cannot claim that the null hypothesis is true on the basis of p-value on... | When to use Cohen's d and when t-test? | T-test is in complimentary relation with Cohen's $d$ (and equivalence tests using Cohen's $d$).
T-test gives a p-value which is the probability of committing a Type I error. One can reject the null h | When to use Cohen's d and when t-test?
T-test is in complimentary relation with Cohen's $d$ (and equivalence tests using Cohen's $d$).
T-test gives a p-value which is the probability of committing a Type I error. One can reject the null hypothesis, if the p-value is too small, but one cannot claim that the null hypoth... | When to use Cohen's d and when t-test?
T-test is in complimentary relation with Cohen's $d$ (and equivalence tests using Cohen's $d$).
T-test gives a p-value which is the probability of committing a Type I error. One can reject the null h |
45,598 | Error while performing multiclass classification using Gridsearch CV | Accuracy might look tempting but not a good metric in general. In multilabel classification, for each class we'll have f1 score, precision, recall values etc. You need to decide how to average them, which is what the error is saying actually. The options are binary (which is the default one), micro, macro, weighted, sa... | Error while performing multiclass classification using Gridsearch CV | Accuracy might look tempting but not a good metric in general. In multilabel classification, for each class we'll have f1 score, precision, recall values etc. You need to decide how to average them, w | Error while performing multiclass classification using Gridsearch CV
Accuracy might look tempting but not a good metric in general. In multilabel classification, for each class we'll have f1 score, precision, recall values etc. You need to decide how to average them, which is what the error is saying actually. The opti... | Error while performing multiclass classification using Gridsearch CV
Accuracy might look tempting but not a good metric in general. In multilabel classification, for each class we'll have f1 score, precision, recall values etc. You need to decide how to average them, w |
45,599 | Error while performing multiclass classification using Gridsearch CV | In addition to gunes' excellent answer, you may also use several scoring functions:
scoring = {'accuracy': make_scorer(accuracy_score),
'precision': make_scorer(precision_score, average = 'macro'),
'recall': make_scorer(recall_score, average = 'macro'),
'f1_macro': make_scorer(f1_score,... | Error while performing multiclass classification using Gridsearch CV | In addition to gunes' excellent answer, you may also use several scoring functions:
scoring = {'accuracy': make_scorer(accuracy_score),
'precision': make_scorer(precision_score, average = ' | Error while performing multiclass classification using Gridsearch CV
In addition to gunes' excellent answer, you may also use several scoring functions:
scoring = {'accuracy': make_scorer(accuracy_score),
'precision': make_scorer(precision_score, average = 'macro'),
'recall': make_scorer(recall_sc... | Error while performing multiclass classification using Gridsearch CV
In addition to gunes' excellent answer, you may also use several scoring functions:
scoring = {'accuracy': make_scorer(accuracy_score),
'precision': make_scorer(precision_score, average = ' |
45,600 | Could someone please translate this code into some mathematical notation? [closed] | Although this question relies heavily on Python, the answer does appear to benefit from some statistical reasoning.
This function creates "training" and "test" datasets of points $(x_i,y_i)$ for a regression model
$$y_i = w_0 x_i + w_1 x_i^2 + \varepsilon_i \sigma$$
where $\varepsilon_i$ are independent variables with ... | Could someone please translate this code into some mathematical notation? [closed] | Although this question relies heavily on Python, the answer does appear to benefit from some statistical reasoning.
This function creates "training" and "test" datasets of points $(x_i,y_i)$ for a reg | Could someone please translate this code into some mathematical notation? [closed]
Although this question relies heavily on Python, the answer does appear to benefit from some statistical reasoning.
This function creates "training" and "test" datasets of points $(x_i,y_i)$ for a regression model
$$y_i = w_0 x_i + w_1 x... | Could someone please translate this code into some mathematical notation? [closed]
Although this question relies heavily on Python, the answer does appear to benefit from some statistical reasoning.
This function creates "training" and "test" datasets of points $(x_i,y_i)$ for a reg |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.