idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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4,201 | Interview question: If correlation doesn't imply causation, how do you detect causation? | There are a few ways around this. You are right that A/B testing is one of these. The economics Nobel this year was awarded for the pioneering of field experiments in the study of policies against poverty which do exactly this.
Otherwise, you could go about one of the following alternatives:
Selection on observables. ... | Interview question: If correlation doesn't imply causation, how do you detect causation? | There are a few ways around this. You are right that A/B testing is one of these. The economics Nobel this year was awarded for the pioneering of field experiments in the study of policies against pov | Interview question: If correlation doesn't imply causation, how do you detect causation?
There are a few ways around this. You are right that A/B testing is one of these. The economics Nobel this year was awarded for the pioneering of field experiments in the study of policies against poverty which do exactly this.
Oth... | Interview question: If correlation doesn't imply causation, how do you detect causation?
There are a few ways around this. You are right that A/B testing is one of these. The economics Nobel this year was awarded for the pioneering of field experiments in the study of policies against pov |
4,202 | Interview question: If correlation doesn't imply causation, how do you detect causation? | I would like to give you a philosophical and a scientific answer:
In theory and in principle, causality cannot be observed. It never has and never will. Let's take a simple example: when you hit the buttons of your keyboard and the letters appear on your screen whilst typing a post on this website, you assume a causal ... | Interview question: If correlation doesn't imply causation, how do you detect causation? | I would like to give you a philosophical and a scientific answer:
In theory and in principle, causality cannot be observed. It never has and never will. Let's take a simple example: when you hit the b | Interview question: If correlation doesn't imply causation, how do you detect causation?
I would like to give you a philosophical and a scientific answer:
In theory and in principle, causality cannot be observed. It never has and never will. Let's take a simple example: when you hit the buttons of your keyboard and the... | Interview question: If correlation doesn't imply causation, how do you detect causation?
I would like to give you a philosophical and a scientific answer:
In theory and in principle, causality cannot be observed. It never has and never will. Let's take a simple example: when you hit the b |
4,203 | Interview question: If correlation doesn't imply causation, how do you detect causation? | Briefly...
Option 1:
Randomized Controlled Trial. The 'gold standard'.
Option 2:
Draw a causal diagram of your system. A directed acyclic graph of
how you and others think the system operates.
Decide if one can infer causation from observational study, by the
back door criterion, front door criterion, or other condit... | Interview question: If correlation doesn't imply causation, how do you detect causation? | Briefly...
Option 1:
Randomized Controlled Trial. The 'gold standard'.
Option 2:
Draw a causal diagram of your system. A directed acyclic graph of
how you and others think the system operates.
Decid | Interview question: If correlation doesn't imply causation, how do you detect causation?
Briefly...
Option 1:
Randomized Controlled Trial. The 'gold standard'.
Option 2:
Draw a causal diagram of your system. A directed acyclic graph of
how you and others think the system operates.
Decide if one can infer causation fr... | Interview question: If correlation doesn't imply causation, how do you detect causation?
Briefly...
Option 1:
Randomized Controlled Trial. The 'gold standard'.
Option 2:
Draw a causal diagram of your system. A directed acyclic graph of
how you and others think the system operates.
Decid |
4,204 | Interview question: If correlation doesn't imply causation, how do you detect causation? | Not sure this adds anything, but if you need another thought from philosophy, back in the day, (1960s) we were taught in a philosophy class that Hume’s 3 criteria of causality required:
(1) temporal precedence (presumed cause prior in time);
(2) an observable empirical correlation; and
(3) that all rival hypotheses had... | Interview question: If correlation doesn't imply causation, how do you detect causation? | Not sure this adds anything, but if you need another thought from philosophy, back in the day, (1960s) we were taught in a philosophy class that Hume’s 3 criteria of causality required:
(1) temporal p | Interview question: If correlation doesn't imply causation, how do you detect causation?
Not sure this adds anything, but if you need another thought from philosophy, back in the day, (1960s) we were taught in a philosophy class that Hume’s 3 criteria of causality required:
(1) temporal precedence (presumed cause prior... | Interview question: If correlation doesn't imply causation, how do you detect causation?
Not sure this adds anything, but if you need another thought from philosophy, back in the day, (1960s) we were taught in a philosophy class that Hume’s 3 criteria of causality required:
(1) temporal p |
4,205 | Interview question: If correlation doesn't imply causation, how do you detect causation? | In short, to detect causation directly, we need to control for everything else. For example, you plant two trees using the same soil, the same amount of water, the same time under the light, and so on but with two different fertilizers. If everything is the same and tree A is growing faster, then we may say that the fe... | Interview question: If correlation doesn't imply causation, how do you detect causation? | In short, to detect causation directly, we need to control for everything else. For example, you plant two trees using the same soil, the same amount of water, the same time under the light, and so on | Interview question: If correlation doesn't imply causation, how do you detect causation?
In short, to detect causation directly, we need to control for everything else. For example, you plant two trees using the same soil, the same amount of water, the same time under the light, and so on but with two different fertili... | Interview question: If correlation doesn't imply causation, how do you detect causation?
In short, to detect causation directly, we need to control for everything else. For example, you plant two trees using the same soil, the same amount of water, the same time under the light, and so on |
4,206 | Interview question: If correlation doesn't imply causation, how do you detect causation? | You can not find causation with analysis of the same data which shows correlation.
Sammy above gave an example of hypothesis: living in big cities causes mental disorders. The study he proposes have only two features: location and mental disorder status, and it can show only correlation, not causation. There is always... | Interview question: If correlation doesn't imply causation, how do you detect causation? | You can not find causation with analysis of the same data which shows correlation.
Sammy above gave an example of hypothesis: living in big cities causes mental disorders. The study he proposes have | Interview question: If correlation doesn't imply causation, how do you detect causation?
You can not find causation with analysis of the same data which shows correlation.
Sammy above gave an example of hypothesis: living in big cities causes mental disorders. The study he proposes have only two features: location and... | Interview question: If correlation doesn't imply causation, how do you detect causation?
You can not find causation with analysis of the same data which shows correlation.
Sammy above gave an example of hypothesis: living in big cities causes mental disorders. The study he proposes have |
4,207 | Interview question: If correlation doesn't imply causation, how do you detect causation? | I'm going to focus on a narrow topic: what if you can't do a two group experiment, either randomized or observational? What if you have only one group? Or what if you are talking about some national policy change where, because the change happened to the entire country, there's no obvious control group? I think you can... | Interview question: If correlation doesn't imply causation, how do you detect causation? | I'm going to focus on a narrow topic: what if you can't do a two group experiment, either randomized or observational? What if you have only one group? Or what if you are talking about some national p | Interview question: If correlation doesn't imply causation, how do you detect causation?
I'm going to focus on a narrow topic: what if you can't do a two group experiment, either randomized or observational? What if you have only one group? Or what if you are talking about some national policy change where, because the... | Interview question: If correlation doesn't imply causation, how do you detect causation?
I'm going to focus on a narrow topic: what if you can't do a two group experiment, either randomized or observational? What if you have only one group? Or what if you are talking about some national p |
4,208 | Why do transformers use layer norm instead of batch norm? | It seems that it has been the standard to use batchnorm in CV tasks, and layernorm in NLP tasks. The original Attention is All you Need paper tested only NLP tasks, and thus used layernorm. It does seem that even with the rise of transformers in CV applications, layernorm is still the most standardly used, so I'm not c... | Why do transformers use layer norm instead of batch norm? | It seems that it has been the standard to use batchnorm in CV tasks, and layernorm in NLP tasks. The original Attention is All you Need paper tested only NLP tasks, and thus used layernorm. It does se | Why do transformers use layer norm instead of batch norm?
It seems that it has been the standard to use batchnorm in CV tasks, and layernorm in NLP tasks. The original Attention is All you Need paper tested only NLP tasks, and thus used layernorm. It does seem that even with the rise of transformers in CV applications,... | Why do transformers use layer norm instead of batch norm?
It seems that it has been the standard to use batchnorm in CV tasks, and layernorm in NLP tasks. The original Attention is All you Need paper tested only NLP tasks, and thus used layernorm. It does se |
4,209 | Why do transformers use layer norm instead of batch norm? | A less known issue of Batch Norm is that how hard it is to parallellize batch-normalized models. Since there is dependence between elements, there is additional need for synchronization across devices. While this is not an issue for most vision models, which tends to be used on a small set of devices, Transformers real... | Why do transformers use layer norm instead of batch norm? | A less known issue of Batch Norm is that how hard it is to parallellize batch-normalized models. Since there is dependence between elements, there is additional need for synchronization across devices | Why do transformers use layer norm instead of batch norm?
A less known issue of Batch Norm is that how hard it is to parallellize batch-normalized models. Since there is dependence between elements, there is additional need for synchronization across devices. While this is not an issue for most vision models, which ten... | Why do transformers use layer norm instead of batch norm?
A less known issue of Batch Norm is that how hard it is to parallellize batch-normalized models. Since there is dependence between elements, there is additional need for synchronization across devices |
4,210 | Why do transformers use layer norm instead of batch norm? | If you want to choose a sample box of data which contains all the feature but smaller in length of single dataframe row wise and small number in group of single dataframe sent as batch to dispatch -> layer norm
For transformer such normalization is efficient as it will be able to create relevance matrix in one go on a... | Why do transformers use layer norm instead of batch norm? | If you want to choose a sample box of data which contains all the feature but smaller in length of single dataframe row wise and small number in group of single dataframe sent as batch to dispatch -> | Why do transformers use layer norm instead of batch norm?
If you want to choose a sample box of data which contains all the feature but smaller in length of single dataframe row wise and small number in group of single dataframe sent as batch to dispatch -> layer norm
For transformer such normalization is efficient as... | Why do transformers use layer norm instead of batch norm?
If you want to choose a sample box of data which contains all the feature but smaller in length of single dataframe row wise and small number in group of single dataframe sent as batch to dispatch -> |
4,211 | How can I change the title of a legend in ggplot2? [closed] | Another option is to use
p + labs(aesthetic='custom text')
For example, Chase's example would look like:
library(ggplot2)
ex.data <- data.frame(DV=rnorm(2*4*3),V2=rep(1:2,each=4*3),V4=rep(1:4,each=3),V3=1:3)
p <- qplot(V4, DV, data=ex.data, geom="line", group=V3, linetype=factor(V3)) + facet_grid(. ~ V2)
p + la... | How can I change the title of a legend in ggplot2? [closed] | Another option is to use
p + labs(aesthetic='custom text')
For example, Chase's example would look like:
library(ggplot2)
ex.data <- data.frame(DV=rnorm(2*4*3),V2=rep(1:2,each=4*3),V4=rep(1:4, | How can I change the title of a legend in ggplot2? [closed]
Another option is to use
p + labs(aesthetic='custom text')
For example, Chase's example would look like:
library(ggplot2)
ex.data <- data.frame(DV=rnorm(2*4*3),V2=rep(1:2,each=4*3),V4=rep(1:4,each=3),V3=1:3)
p <- qplot(V4, DV, data=ex.data, geom="line"... | How can I change the title of a legend in ggplot2? [closed]
Another option is to use
p + labs(aesthetic='custom text')
For example, Chase's example would look like:
library(ggplot2)
ex.data <- data.frame(DV=rnorm(2*4*3),V2=rep(1:2,each=4*3),V4=rep(1:4, |
4,212 | How can I change the title of a legend in ggplot2? [closed] | You can change the title of the legend by modifying the scale for that legend. Here's an example using the CO2 dataset
library(ggplot2)
p <- qplot(conc, uptake, data = CO2, colour = Type) + scale_colour_discrete(name = "Fancy Title")
p <- p + facet_grid(. ~ Treatment)
p
EDIT:
Using the example data from above, here ... | How can I change the title of a legend in ggplot2? [closed] | You can change the title of the legend by modifying the scale for that legend. Here's an example using the CO2 dataset
library(ggplot2)
p <- qplot(conc, uptake, data = CO2, colour = Type) + scale_col | How can I change the title of a legend in ggplot2? [closed]
You can change the title of the legend by modifying the scale for that legend. Here's an example using the CO2 dataset
library(ggplot2)
p <- qplot(conc, uptake, data = CO2, colour = Type) + scale_colour_discrete(name = "Fancy Title")
p <- p + facet_grid(. ~ T... | How can I change the title of a legend in ggplot2? [closed]
You can change the title of the legend by modifying the scale for that legend. Here's an example using the CO2 dataset
library(ggplot2)
p <- qplot(conc, uptake, data = CO2, colour = Type) + scale_col |
4,213 | Resources for learning Markov chain and hidden Markov models | Here are some tutorials (available as PDFs):
Dugad and Desai, A tutorial on hidden markov models
Valeria De Fonzo1, Filippo Aluffi-Pentini2 and Valerio Parisi (2007). Hidden Markov Models in Bioinformatics. Current Bioinformatics, 2, 49-61.
Smith, K. Hidden Markov Models in Bioinformatics with Application to Gene Find... | Resources for learning Markov chain and hidden Markov models | Here are some tutorials (available as PDFs):
Dugad and Desai, A tutorial on hidden markov models
Valeria De Fonzo1, Filippo Aluffi-Pentini2 and Valerio Parisi (2007). Hidden Markov Models in Bioinfor | Resources for learning Markov chain and hidden Markov models
Here are some tutorials (available as PDFs):
Dugad and Desai, A tutorial on hidden markov models
Valeria De Fonzo1, Filippo Aluffi-Pentini2 and Valerio Parisi (2007). Hidden Markov Models in Bioinformatics. Current Bioinformatics, 2, 49-61.
Smith, K. Hidden ... | Resources for learning Markov chain and hidden Markov models
Here are some tutorials (available as PDFs):
Dugad and Desai, A tutorial on hidden markov models
Valeria De Fonzo1, Filippo Aluffi-Pentini2 and Valerio Parisi (2007). Hidden Markov Models in Bioinfor |
4,214 | Resources for learning Markov chain and hidden Markov models | There is also a really good book by Oliver Cappe et. al: Inference in Hidden Markov Models. However, it is fairly theoretical and very light on the applications.
There is another book with examples in R, but I couldn't stand it - Hidden Markov Models for Time Series.
P.s. The speech recognition community also has a to... | Resources for learning Markov chain and hidden Markov models | There is also a really good book by Oliver Cappe et. al: Inference in Hidden Markov Models. However, it is fairly theoretical and very light on the applications.
There is another book with examples i | Resources for learning Markov chain and hidden Markov models
There is also a really good book by Oliver Cappe et. al: Inference in Hidden Markov Models. However, it is fairly theoretical and very light on the applications.
There is another book with examples in R, but I couldn't stand it - Hidden Markov Models for Tim... | Resources for learning Markov chain and hidden Markov models
There is also a really good book by Oliver Cappe et. al: Inference in Hidden Markov Models. However, it is fairly theoretical and very light on the applications.
There is another book with examples i |
4,215 | Resources for learning Markov chain and hidden Markov models | It is quite surprising to see that none of the answers mention the Rabiner tutorial paper on HMMs.
While the practical implementation (the latter part of the paper) is focused on speech recognition, this paper is probably the most commonly cited one in the HMM literature, thanks to its clear and well-presented nature.
... | Resources for learning Markov chain and hidden Markov models | It is quite surprising to see that none of the answers mention the Rabiner tutorial paper on HMMs.
While the practical implementation (the latter part of the paper) is focused on speech recognition, t | Resources for learning Markov chain and hidden Markov models
It is quite surprising to see that none of the answers mention the Rabiner tutorial paper on HMMs.
While the practical implementation (the latter part of the paper) is focused on speech recognition, this paper is probably the most commonly cited one in the HM... | Resources for learning Markov chain and hidden Markov models
It is quite surprising to see that none of the answers mention the Rabiner tutorial paper on HMMs.
While the practical implementation (the latter part of the paper) is focused on speech recognition, t |
4,216 | Resources for learning Markov chain and hidden Markov models | For bioinformatics applications, the classic text on HMMs would be Durbin, Eddy, Krough & Michison, "Biological Sequence Analsysis - Probabilistic Models of Proteins and Nucleic Acids", Cambridge University Press, 1998, ISBN 0-521-62971-3. It is technical, but very clear and I found it very useful.
For MCMC there is a... | Resources for learning Markov chain and hidden Markov models | For bioinformatics applications, the classic text on HMMs would be Durbin, Eddy, Krough & Michison, "Biological Sequence Analsysis - Probabilistic Models of Proteins and Nucleic Acids", Cambridge Univ | Resources for learning Markov chain and hidden Markov models
For bioinformatics applications, the classic text on HMMs would be Durbin, Eddy, Krough & Michison, "Biological Sequence Analsysis - Probabilistic Models of Proteins and Nucleic Acids", Cambridge University Press, 1998, ISBN 0-521-62971-3. It is technical, b... | Resources for learning Markov chain and hidden Markov models
For bioinformatics applications, the classic text on HMMs would be Durbin, Eddy, Krough & Michison, "Biological Sequence Analsysis - Probabilistic Models of Proteins and Nucleic Acids", Cambridge Univ |
4,217 | Resources for learning Markov chain and hidden Markov models | Already nice suggestions, I would like to add the following articles that describe HMMs from perspective of application in biology by Sean Eddy.
Hidden Markov Models
Profile hidden Markov models
What is a hidden Markov model? | Resources for learning Markov chain and hidden Markov models | Already nice suggestions, I would like to add the following articles that describe HMMs from perspective of application in biology by Sean Eddy.
Hidden Markov Models
Profile hidden Markov models
W | Resources for learning Markov chain and hidden Markov models
Already nice suggestions, I would like to add the following articles that describe HMMs from perspective of application in biology by Sean Eddy.
Hidden Markov Models
Profile hidden Markov models
What is a hidden Markov model? | Resources for learning Markov chain and hidden Markov models
Already nice suggestions, I would like to add the following articles that describe HMMs from perspective of application in biology by Sean Eddy.
Hidden Markov Models
Profile hidden Markov models
W |
4,218 | Resources for learning Markov chain and hidden Markov models | I learned HMMs using the great book by Walter Zucchini and Iain L. MacDonald
Hidden Markov Models for Time Series: An Introduction Using R
It's really good and features examples in R. | Resources for learning Markov chain and hidden Markov models | I learned HMMs using the great book by Walter Zucchini and Iain L. MacDonald
Hidden Markov Models for Time Series: An Introduction Using R
It's really good and features examples in R. | Resources for learning Markov chain and hidden Markov models
I learned HMMs using the great book by Walter Zucchini and Iain L. MacDonald
Hidden Markov Models for Time Series: An Introduction Using R
It's really good and features examples in R. | Resources for learning Markov chain and hidden Markov models
I learned HMMs using the great book by Walter Zucchini and Iain L. MacDonald
Hidden Markov Models for Time Series: An Introduction Using R
It's really good and features examples in R. |
4,219 | Resources for learning Markov chain and hidden Markov models | Take a look at the (HMM) Toolbox for Matlab by Kevin Murphy and also section Recommended reading on HMMs on this site.
You can also get Probabilistic modeling toolkit for Matlab/Octave with some examples of using Markov Chains and HMM.
You can also find lectures and labs on HMM, for example:
Labs
Lecture1 and Lecture2 | Resources for learning Markov chain and hidden Markov models | Take a look at the (HMM) Toolbox for Matlab by Kevin Murphy and also section Recommended reading on HMMs on this site.
You can also get Probabilistic modeling toolkit for Matlab/Octave with some examp | Resources for learning Markov chain and hidden Markov models
Take a look at the (HMM) Toolbox for Matlab by Kevin Murphy and also section Recommended reading on HMMs on this site.
You can also get Probabilistic modeling toolkit for Matlab/Octave with some examples of using Markov Chains and HMM.
You can also find lectu... | Resources for learning Markov chain and hidden Markov models
Take a look at the (HMM) Toolbox for Matlab by Kevin Murphy and also section Recommended reading on HMMs on this site.
You can also get Probabilistic modeling toolkit for Matlab/Octave with some examp |
4,220 | Resources for learning Markov chain and hidden Markov models | My 2 cents
Beautifully explained and free.
Hidden Markov Models, Theory and Applications
University of Leeds Tutorial | Resources for learning Markov chain and hidden Markov models | My 2 cents
Beautifully explained and free.
Hidden Markov Models, Theory and Applications
University of Leeds Tutorial | Resources for learning Markov chain and hidden Markov models
My 2 cents
Beautifully explained and free.
Hidden Markov Models, Theory and Applications
University of Leeds Tutorial | Resources for learning Markov chain and hidden Markov models
My 2 cents
Beautifully explained and free.
Hidden Markov Models, Theory and Applications
University of Leeds Tutorial |
4,221 | Resources for learning Markov chain and hidden Markov models | Here are some notes by Ramon van Handel at Princeton:
This course is an introduction to some of the basic mathematical,
statistical and computational methods for hidden Markov models.
The first section includes a nice set of applications of HMMs in biology, finance,... | Resources for learning Markov chain and hidden Markov models | Here are some notes by Ramon van Handel at Princeton:
This course is an introduction to some of the basic mathematical,
statistical and computational methods for hidden Markov models.
The first s | Resources for learning Markov chain and hidden Markov models
Here are some notes by Ramon van Handel at Princeton:
This course is an introduction to some of the basic mathematical,
statistical and computational methods for hidden Markov models.
The first section includes a nice set of applications of HMMs in biolo... | Resources for learning Markov chain and hidden Markov models
Here are some notes by Ramon van Handel at Princeton:
This course is an introduction to some of the basic mathematical,
statistical and computational methods for hidden Markov models.
The first s |
4,222 | Resources for learning Markov chain and hidden Markov models | Here is a nice interactive introduction to Markov Chains http://setosa.io/ev/markov-chains/ | Resources for learning Markov chain and hidden Markov models | Here is a nice interactive introduction to Markov Chains http://setosa.io/ev/markov-chains/ | Resources for learning Markov chain and hidden Markov models
Here is a nice interactive introduction to Markov Chains http://setosa.io/ev/markov-chains/ | Resources for learning Markov chain and hidden Markov models
Here is a nice interactive introduction to Markov Chains http://setosa.io/ev/markov-chains/ |
4,223 | Resources for learning Markov chain and hidden Markov models | There are only 3 video i have found very useful for understanding maths behind hidden markov models-
https://www.youtube.com/watch?v=E3qrns5f3Fw
https://www.youtube.com/watch?v=cjlhpaDXihE
https://www.youtube.com/watch?v=5sGEF-e82yY
These are really good and taught by one the best Indian professors from IIT krg. | Resources for learning Markov chain and hidden Markov models | There are only 3 video i have found very useful for understanding maths behind hidden markov models-
https://www.youtube.com/watch?v=E3qrns5f3Fw
https://www.youtube.com/watch?v=cjlhpaDXihE
https://w | Resources for learning Markov chain and hidden Markov models
There are only 3 video i have found very useful for understanding maths behind hidden markov models-
https://www.youtube.com/watch?v=E3qrns5f3Fw
https://www.youtube.com/watch?v=cjlhpaDXihE
https://www.youtube.com/watch?v=5sGEF-e82yY
These are really good an... | Resources for learning Markov chain and hidden Markov models
There are only 3 video i have found very useful for understanding maths behind hidden markov models-
https://www.youtube.com/watch?v=E3qrns5f3Fw
https://www.youtube.com/watch?v=cjlhpaDXihE
https://w |
4,224 | Resources for learning Markov chain and hidden Markov models | This playlist is a great explanation and is based on the paper by Rabiner mentioned in the answer above. -
https://www.youtube.com/watch?v=J_y5hx_ySCg&list=PLix7MmR3doRo3NGNzrq48FItR3TDyuLCo
This above playlist is a 12 series lecture which begins with explanation of Markov Chains/ observable Markov Models and then move... | Resources for learning Markov chain and hidden Markov models | This playlist is a great explanation and is based on the paper by Rabiner mentioned in the answer above. -
https://www.youtube.com/watch?v=J_y5hx_ySCg&list=PLix7MmR3doRo3NGNzrq48FItR3TDyuLCo
This abov | Resources for learning Markov chain and hidden Markov models
This playlist is a great explanation and is based on the paper by Rabiner mentioned in the answer above. -
https://www.youtube.com/watch?v=J_y5hx_ySCg&list=PLix7MmR3doRo3NGNzrq48FItR3TDyuLCo
This above playlist is a 12 series lecture which begins with explana... | Resources for learning Markov chain and hidden Markov models
This playlist is a great explanation and is based on the paper by Rabiner mentioned in the answer above. -
https://www.youtube.com/watch?v=J_y5hx_ySCg&list=PLix7MmR3doRo3NGNzrq48FItR3TDyuLCo
This abov |
4,225 | Why does shrinkage work? | Roughly speaking, there are three different sources of prediction error:
the bias of your model
the variance of your model
unexplainable variance
We can't do anything about point 3 (except for attempting to estimate the unexplained variance and incorporating it in our predictive densities and prediction intervals). T... | Why does shrinkage work? | Roughly speaking, there are three different sources of prediction error:
the bias of your model
the variance of your model
unexplainable variance
We can't do anything about point 3 (except for attem | Why does shrinkage work?
Roughly speaking, there are three different sources of prediction error:
the bias of your model
the variance of your model
unexplainable variance
We can't do anything about point 3 (except for attempting to estimate the unexplained variance and incorporating it in our predictive densities and... | Why does shrinkage work?
Roughly speaking, there are three different sources of prediction error:
the bias of your model
the variance of your model
unexplainable variance
We can't do anything about point 3 (except for attem |
4,226 | Why does shrinkage work? | Just to add something to @Kolassa's fine answer, the whole question of shrinkage estimates is bound up with Stein's paradox. For multivariate processes with $p \geq 3$, the vector of sample averages is not admissible. In other words, for some parameter value, there is a different estimator with lower expected risk. Ste... | Why does shrinkage work? | Just to add something to @Kolassa's fine answer, the whole question of shrinkage estimates is bound up with Stein's paradox. For multivariate processes with $p \geq 3$, the vector of sample averages i | Why does shrinkage work?
Just to add something to @Kolassa's fine answer, the whole question of shrinkage estimates is bound up with Stein's paradox. For multivariate processes with $p \geq 3$, the vector of sample averages is not admissible. In other words, for some parameter value, there is a different estimator with... | Why does shrinkage work?
Just to add something to @Kolassa's fine answer, the whole question of shrinkage estimates is bound up with Stein's paradox. For multivariate processes with $p \geq 3$, the vector of sample averages i |
4,227 | Why does shrinkage work? | @Kolassa has a great mathematical answer. For a more intuitive visual answer here is a picture. I'm doing simple linear regression here with a slope and y-intercept. A population of 17 points are loosely correlated. At random I picked two points and created a regression. In general, 2 points is not enough observat... | Why does shrinkage work? | @Kolassa has a great mathematical answer. For a more intuitive visual answer here is a picture. I'm doing simple linear regression here with a slope and y-intercept. A population of 17 points are l | Why does shrinkage work?
@Kolassa has a great mathematical answer. For a more intuitive visual answer here is a picture. I'm doing simple linear regression here with a slope and y-intercept. A population of 17 points are loosely correlated. At random I picked two points and created a regression. In general, 2 poin... | Why does shrinkage work?
@Kolassa has a great mathematical answer. For a more intuitive visual answer here is a picture. I'm doing simple linear regression here with a slope and y-intercept. A population of 17 points are l |
4,228 | What is maxout in neural network? | A maxout layer is simply a layer where the activation function is the max of the inputs. As stated in the paper, even an MLP with 2 maxout units can approximate any function. They give a couple of reasons as to why maxout may be performing well, but the main reason they give is the following --
Dropout can be thought o... | What is maxout in neural network? | A maxout layer is simply a layer where the activation function is the max of the inputs. As stated in the paper, even an MLP with 2 maxout units can approximate any function. They give a couple of rea | What is maxout in neural network?
A maxout layer is simply a layer where the activation function is the max of the inputs. As stated in the paper, even an MLP with 2 maxout units can approximate any function. They give a couple of reasons as to why maxout may be performing well, but the main reason they give is the fol... | What is maxout in neural network?
A maxout layer is simply a layer where the activation function is the max of the inputs. As stated in the paper, even an MLP with 2 maxout units can approximate any function. They give a couple of rea |
4,229 | What is maxout in neural network? | A maxout unit can learn a piecewise linear, convex function with up to k pieces. 1
So when k is 2, you can implement the ReLU, absolute ReLU, leaky ReLU, etc., or it can learn to implement a new function. If k is let's say 10, you can even approximately learn the convex function.
When k is 2:
the Maxout neuron comput... | What is maxout in neural network? | A maxout unit can learn a piecewise linear, convex function with up to k pieces. 1
So when k is 2, you can implement the ReLU, absolute ReLU, leaky ReLU, etc., or it can learn to implement a new func | What is maxout in neural network?
A maxout unit can learn a piecewise linear, convex function with up to k pieces. 1
So when k is 2, you can implement the ReLU, absolute ReLU, leaky ReLU, etc., or it can learn to implement a new function. If k is let's say 10, you can even approximately learn the convex function.
When... | What is maxout in neural network?
A maxout unit can learn a piecewise linear, convex function with up to k pieces. 1
So when k is 2, you can implement the ReLU, absolute ReLU, leaky ReLU, etc., or it can learn to implement a new func |
4,230 | What is the difference between a particle filter (sequential Monte Carlo) and a Kalman filter? | From Dan Simon's "Optimal State Estimation":
In a linear system with Gaussian noise, the Kalman filter is optimal. In a system that is nonlinear, the Kalman filter can be used for state estimation, but the particle filter may give better results at the price of additional computational effort. In a system that has non... | What is the difference between a particle filter (sequential Monte Carlo) and a Kalman filter? | From Dan Simon's "Optimal State Estimation":
In a linear system with Gaussian noise, the Kalman filter is optimal. In a system that is nonlinear, the Kalman filter can be used for state estimation, b | What is the difference between a particle filter (sequential Monte Carlo) and a Kalman filter?
From Dan Simon's "Optimal State Estimation":
In a linear system with Gaussian noise, the Kalman filter is optimal. In a system that is nonlinear, the Kalman filter can be used for state estimation, but the particle filter ma... | What is the difference between a particle filter (sequential Monte Carlo) and a Kalman filter?
From Dan Simon's "Optimal State Estimation":
In a linear system with Gaussian noise, the Kalman filter is optimal. In a system that is nonlinear, the Kalman filter can be used for state estimation, b |
4,231 | What is the difference between a particle filter (sequential Monte Carlo) and a Kalman filter? | From A Tutorial on Particle Filtering and Smoothing:
Fifteen years later:
Since their introduction in 1993, particle filters have become a very popular class of numerical methods
for the solution of optimal estimation problems in non-linear non-Gaussian scenarios. In comparison with
standard approximation methods,... | What is the difference between a particle filter (sequential Monte Carlo) and a Kalman filter? | From A Tutorial on Particle Filtering and Smoothing:
Fifteen years later:
Since their introduction in 1993, particle filters have become a very popular class of numerical methods
for the solution o | What is the difference between a particle filter (sequential Monte Carlo) and a Kalman filter?
From A Tutorial on Particle Filtering and Smoothing:
Fifteen years later:
Since their introduction in 1993, particle filters have become a very popular class of numerical methods
for the solution of optimal estimation prob... | What is the difference between a particle filter (sequential Monte Carlo) and a Kalman filter?
From A Tutorial on Particle Filtering and Smoothing:
Fifteen years later:
Since their introduction in 1993, particle filters have become a very popular class of numerical methods
for the solution o |
4,232 | ANOVA assumption normality/normal distribution of residuals | Let's assume this is a fixed effects model. (The advice doesn't really change for random-effects models, it just gets a little more complicated.)
First let us distinguish the "residuals" from the "errors:" the former are the differences between the responses and their predicted values, while the latter are random vari... | ANOVA assumption normality/normal distribution of residuals | Let's assume this is a fixed effects model. (The advice doesn't really change for random-effects models, it just gets a little more complicated.)
First let us distinguish the "residuals" from the "er | ANOVA assumption normality/normal distribution of residuals
Let's assume this is a fixed effects model. (The advice doesn't really change for random-effects models, it just gets a little more complicated.)
First let us distinguish the "residuals" from the "errors:" the former are the differences between the responses ... | ANOVA assumption normality/normal distribution of residuals
Let's assume this is a fixed effects model. (The advice doesn't really change for random-effects models, it just gets a little more complicated.)
First let us distinguish the "residuals" from the "er |
4,233 | ANOVA assumption normality/normal distribution of residuals | Standard Classical one-way ANOVA can be viewed as an extension to the classical "2-sample T-test" to an "n-sample T-test". This can be seen from comparing a one-way ANOVA with only two groups to the classical 2-sample T-test.
I think where you are getting confused is that (under the assumptions of the model) the resid... | ANOVA assumption normality/normal distribution of residuals | Standard Classical one-way ANOVA can be viewed as an extension to the classical "2-sample T-test" to an "n-sample T-test". This can be seen from comparing a one-way ANOVA with only two groups to the | ANOVA assumption normality/normal distribution of residuals
Standard Classical one-way ANOVA can be viewed as an extension to the classical "2-sample T-test" to an "n-sample T-test". This can be seen from comparing a one-way ANOVA with only two groups to the classical 2-sample T-test.
I think where you are getting con... | ANOVA assumption normality/normal distribution of residuals
Standard Classical one-way ANOVA can be viewed as an extension to the classical "2-sample T-test" to an "n-sample T-test". This can be seen from comparing a one-way ANOVA with only two groups to the |
4,234 | ANOVA assumption normality/normal distribution of residuals | In the one-way case with $p$ groups of size $n_{j}$:
$F = \frac{SS_{b} / df_{b}}{SS_{w} / df_{w}}$ where
$SS_{b} = \sum_{j=1}^{p}{n_{j} (M - M_{j}})^{2}$ and
$SS_{w} = \sum_{j=1}^{p}\sum_{i=1}^{n_{j}}{(y_{ij} - M_{j})^{2}}$
$F$ follows an $F$-distribution if $SS_{b} / df_{b}$ and $SS_{w} / df_{w}$ are independent, $\ch... | ANOVA assumption normality/normal distribution of residuals | In the one-way case with $p$ groups of size $n_{j}$:
$F = \frac{SS_{b} / df_{b}}{SS_{w} / df_{w}}$ where
$SS_{b} = \sum_{j=1}^{p}{n_{j} (M - M_{j}})^{2}$ and
$SS_{w} = \sum_{j=1}^{p}\sum_{i=1}^{n_{j}} | ANOVA assumption normality/normal distribution of residuals
In the one-way case with $p$ groups of size $n_{j}$:
$F = \frac{SS_{b} / df_{b}}{SS_{w} / df_{w}}$ where
$SS_{b} = \sum_{j=1}^{p}{n_{j} (M - M_{j}})^{2}$ and
$SS_{w} = \sum_{j=1}^{p}\sum_{i=1}^{n_{j}}{(y_{ij} - M_{j})^{2}}$
$F$ follows an $F$-distribution if $... | ANOVA assumption normality/normal distribution of residuals
In the one-way case with $p$ groups of size $n_{j}$:
$F = \frac{SS_{b} / df_{b}}{SS_{w} / df_{w}}$ where
$SS_{b} = \sum_{j=1}^{p}{n_{j} (M - M_{j}})^{2}$ and
$SS_{w} = \sum_{j=1}^{p}\sum_{i=1}^{n_{j}} |
4,235 | Should I normalize word2vec's word vectors before using them? | When the downstream applications only care about the direction of the word vectors (e.g. they only pay attention to the cosine similarity of two words), then normalize, and forget about length.
However, if the downstream applications are able to (or need to) consider more sensible aspects, such as word significance, or... | Should I normalize word2vec's word vectors before using them? | When the downstream applications only care about the direction of the word vectors (e.g. they only pay attention to the cosine similarity of two words), then normalize, and forget about length.
Howeve | Should I normalize word2vec's word vectors before using them?
When the downstream applications only care about the direction of the word vectors (e.g. they only pay attention to the cosine similarity of two words), then normalize, and forget about length.
However, if the downstream applications are able to (or need to)... | Should I normalize word2vec's word vectors before using them?
When the downstream applications only care about the direction of the word vectors (e.g. they only pay attention to the cosine similarity of two words), then normalize, and forget about length.
Howeve |
4,236 | A/B tests: z-test vs t-test vs chi square vs fisher exact test | We use these tests for different reasons and under different circumstances.
$z$-test. A $z$-test assumes that our observations are independently drawn from a Normal distribution with unknown mean and known variance. A $z$-test is used primarily when we have quantitative data. (i.e. weights of rodents, ages of individu... | A/B tests: z-test vs t-test vs chi square vs fisher exact test | We use these tests for different reasons and under different circumstances.
$z$-test. A $z$-test assumes that our observations are independently drawn from a Normal distribution with unknown mean and | A/B tests: z-test vs t-test vs chi square vs fisher exact test
We use these tests for different reasons and under different circumstances.
$z$-test. A $z$-test assumes that our observations are independently drawn from a Normal distribution with unknown mean and known variance. A $z$-test is used primarily when we hav... | A/B tests: z-test vs t-test vs chi square vs fisher exact test
We use these tests for different reasons and under different circumstances.
$z$-test. A $z$-test assumes that our observations are independently drawn from a Normal distribution with unknown mean and |
4,237 | A/B tests: z-test vs t-test vs chi square vs fisher exact test | For a 3 way test you usually use an ANOVA rather than 3 separate tests. Please also check on the Bonferroni correction before multiple testing.
Please use this
https://www.google.com/search?q=testing+multiple+means&rlz=1C1CHBD_enIN817IN817&oq=testing+multiple+means+&aqs=chrome..69i57j69i60l3j69i61j0.3564j0j7&sourceid... | A/B tests: z-test vs t-test vs chi square vs fisher exact test | For a 3 way test you usually use an ANOVA rather than 3 separate tests. Please also check on the Bonferroni correction before multiple testing.
Please use this
https://www.google.com/search?q=testin | A/B tests: z-test vs t-test vs chi square vs fisher exact test
For a 3 way test you usually use an ANOVA rather than 3 separate tests. Please also check on the Bonferroni correction before multiple testing.
Please use this
https://www.google.com/search?q=testing+multiple+means&rlz=1C1CHBD_enIN817IN817&oq=testing+mult... | A/B tests: z-test vs t-test vs chi square vs fisher exact test
For a 3 way test you usually use an ANOVA rather than 3 separate tests. Please also check on the Bonferroni correction before multiple testing.
Please use this
https://www.google.com/search?q=testin |
4,238 | Graph for relationship between two ordinal variables | A spineplot (mosaic plot) works well for the example data here, but can be difficult to read or interpret if some combinations of categories are rare or don't exist. Naturally it's reasonable, and expected, that a low frequency is represented by a small tile, and zero by no tile at all, but the psychological difficulty... | Graph for relationship between two ordinal variables | A spineplot (mosaic plot) works well for the example data here, but can be difficult to read or interpret if some combinations of categories are rare or don't exist. Naturally it's reasonable, and exp | Graph for relationship between two ordinal variables
A spineplot (mosaic plot) works well for the example data here, but can be difficult to read or interpret if some combinations of categories are rare or don't exist. Naturally it's reasonable, and expected, that a low frequency is represented by a small tile, and zer... | Graph for relationship between two ordinal variables
A spineplot (mosaic plot) works well for the example data here, but can be difficult to read or interpret if some combinations of categories are rare or don't exist. Naturally it's reasonable, and exp |
4,239 | Graph for relationship between two ordinal variables | Here is a quick attempt at a heat map, I have used black cell borders to break up the cells, but perhaps the tiles should be separated more as in Glen_b's answer.
library(ggplot2)
runningcounts.df <- as.data.frame(table(importance, often))
ggplot(runningcounts.df, aes(importance, often)) +
geom_tile(aes(fill = Freq... | Graph for relationship between two ordinal variables | Here is a quick attempt at a heat map, I have used black cell borders to break up the cells, but perhaps the tiles should be separated more as in Glen_b's answer.
library(ggplot2)
runningcounts.df <- | Graph for relationship between two ordinal variables
Here is a quick attempt at a heat map, I have used black cell borders to break up the cells, but perhaps the tiles should be separated more as in Glen_b's answer.
library(ggplot2)
runningcounts.df <- as.data.frame(table(importance, often))
ggplot(runningcounts.df, a... | Graph for relationship between two ordinal variables
Here is a quick attempt at a heat map, I have used black cell borders to break up the cells, but perhaps the tiles should be separated more as in Glen_b's answer.
library(ggplot2)
runningcounts.df <- |
4,240 | Graph for relationship between two ordinal variables | Here's an example of what a spineplot of the data would look like. I did this in Stata pretty quickly, but there's an R implementation. I think in R it should be just:
spineplot(factor(often)~factor(importance))
The spineplot actually seems to be the default if you give R categorical variables:
plot(factor(often)~fact... | Graph for relationship between two ordinal variables | Here's an example of what a spineplot of the data would look like. I did this in Stata pretty quickly, but there's an R implementation. I think in R it should be just:
spineplot(factor(often)~factor( | Graph for relationship between two ordinal variables
Here's an example of what a spineplot of the data would look like. I did this in Stata pretty quickly, but there's an R implementation. I think in R it should be just:
spineplot(factor(often)~factor(importance))
The spineplot actually seems to be the default if you ... | Graph for relationship between two ordinal variables
Here's an example of what a spineplot of the data would look like. I did this in Stata pretty quickly, but there's an R implementation. I think in R it should be just:
spineplot(factor(often)~factor( |
4,241 | Graph for relationship between two ordinal variables | The way I've done this is a bit of a fudge, but it could be fixed up easily enough.
This is a modified version of the jittering approach.
Removing the axes reduces the temptation to interpret the scale as continuous; drawing boxes around the jittered combinations emphasizes there's something like a "scale break" - that... | Graph for relationship between two ordinal variables | The way I've done this is a bit of a fudge, but it could be fixed up easily enough.
This is a modified version of the jittering approach.
Removing the axes reduces the temptation to interpret the scal | Graph for relationship between two ordinal variables
The way I've done this is a bit of a fudge, but it could be fixed up easily enough.
This is a modified version of the jittering approach.
Removing the axes reduces the temptation to interpret the scale as continuous; drawing boxes around the jittered combinations emp... | Graph for relationship between two ordinal variables
The way I've done this is a bit of a fudge, but it could be fixed up easily enough.
This is a modified version of the jittering approach.
Removing the axes reduces the temptation to interpret the scal |
4,242 | Graph for relationship between two ordinal variables | Using the R package riverplot:
data$importance <- factor(data$importance,
labels = c("not at all important",
"somewhat unimportant",
"neither important nor unimportant",
"s... | Graph for relationship between two ordinal variables | Using the R package riverplot:
data$importance <- factor(data$importance,
labels = c("not at all important",
"somewhat unimportant | Graph for relationship between two ordinal variables
Using the R package riverplot:
data$importance <- factor(data$importance,
labels = c("not at all important",
"somewhat unimportant",
"neither important nor un... | Graph for relationship between two ordinal variables
Using the R package riverplot:
data$importance <- factor(data$importance,
labels = c("not at all important",
"somewhat unimportant |
4,243 | Graph for relationship between two ordinal variables | A faceted bar chart in R. It shows the distribution of "often" at each level of "importance" very clearly. But it wouldn't have worked so well if the maximum count had varied more between levels of "importance"; it's easy enough to set scales="free_y" in ggplot (see here) to avoid lots of empty space, but the shape of ... | Graph for relationship between two ordinal variables | A faceted bar chart in R. It shows the distribution of "often" at each level of "importance" very clearly. But it wouldn't have worked so well if the maximum count had varied more between levels of "i | Graph for relationship between two ordinal variables
A faceted bar chart in R. It shows the distribution of "often" at each level of "importance" very clearly. But it wouldn't have worked so well if the maximum count had varied more between levels of "importance"; it's easy enough to set scales="free_y" in ggplot (see ... | Graph for relationship between two ordinal variables
A faceted bar chart in R. It shows the distribution of "often" at each level of "importance" very clearly. But it wouldn't have worked so well if the maximum count had varied more between levels of "i |
4,244 | Graph for relationship between two ordinal variables | A different idea that I didn't think of originally was a sieve plot.
Size of each tile is proportional to expected frequency; the little squares inside the rectangles represent actual frequencies. Hence greater density of the squares indicates higher than expected frequency (and is shaded blue); lower density of squar... | Graph for relationship between two ordinal variables | A different idea that I didn't think of originally was a sieve plot.
Size of each tile is proportional to expected frequency; the little squares inside the rectangles represent actual frequencies. He | Graph for relationship between two ordinal variables
A different idea that I didn't think of originally was a sieve plot.
Size of each tile is proportional to expected frequency; the little squares inside the rectangles represent actual frequencies. Hence greater density of the squares indicates higher than expected f... | Graph for relationship between two ordinal variables
A different idea that I didn't think of originally was a sieve plot.
Size of each tile is proportional to expected frequency; the little squares inside the rectangles represent actual frequencies. He |
4,245 | Can a random forest be used for feature selection in multiple linear regression? | Since RF can handle non-linearity but can't provide coefficients, would it be wise to use Random Forest to gather the most important Features and then plug those features into a Multiple Linear Regression model in order to explain their signs?
I interpret OP's one-sentence question to mean that OP wishes to understand... | Can a random forest be used for feature selection in multiple linear regression? | Since RF can handle non-linearity but can't provide coefficients, would it be wise to use Random Forest to gather the most important Features and then plug those features into a Multiple Linear Regres | Can a random forest be used for feature selection in multiple linear regression?
Since RF can handle non-linearity but can't provide coefficients, would it be wise to use Random Forest to gather the most important Features and then plug those features into a Multiple Linear Regression model in order to explain their si... | Can a random forest be used for feature selection in multiple linear regression?
Since RF can handle non-linearity but can't provide coefficients, would it be wise to use Random Forest to gather the most important Features and then plug those features into a Multiple Linear Regres |
4,246 | Can a random forest be used for feature selection in multiple linear regression? | The answer by @Sycorax is fantastic. In addition to those fully described aspects of the problem related to model fit, there is another reason not to pursue a multi-step process such as running random forests, lasso, or elastic net to "learn" which features to feed to traditional regression. Ordinary regression would... | Can a random forest be used for feature selection in multiple linear regression? | The answer by @Sycorax is fantastic. In addition to those fully described aspects of the problem related to model fit, there is another reason not to pursue a multi-step process such as running rando | Can a random forest be used for feature selection in multiple linear regression?
The answer by @Sycorax is fantastic. In addition to those fully described aspects of the problem related to model fit, there is another reason not to pursue a multi-step process such as running random forests, lasso, or elastic net to "le... | Can a random forest be used for feature selection in multiple linear regression?
The answer by @Sycorax is fantastic. In addition to those fully described aspects of the problem related to model fit, there is another reason not to pursue a multi-step process such as running rando |
4,247 | Can a random forest be used for feature selection in multiple linear regression? | A properly executed random forest applied to a problem that is more "random forest appropriate" can work as a filter to remove noise, and make results that are more useful as inputs to other analysis tools.
Disclaimers:
Is it a "silver bullet"? No way. Mileage will vary. It works where it works, and not elsewhere... | Can a random forest be used for feature selection in multiple linear regression? | A properly executed random forest applied to a problem that is more "random forest appropriate" can work as a filter to remove noise, and make results that are more useful as inputs to other analysis | Can a random forest be used for feature selection in multiple linear regression?
A properly executed random forest applied to a problem that is more "random forest appropriate" can work as a filter to remove noise, and make results that are more useful as inputs to other analysis tools.
Disclaimers:
Is it a "silver ... | Can a random forest be used for feature selection in multiple linear regression?
A properly executed random forest applied to a problem that is more "random forest appropriate" can work as a filter to remove noise, and make results that are more useful as inputs to other analysis |
4,248 | Can a random forest be used for feature selection in multiple linear regression? | Despite the legitimate warnings that this approach might fail in some cases, this should not discourage you from trying it out! Breimann reports an example (Breimann 2001) that selecting features by variable importance from a random forest and plugging them into logistic regresission outperformed variable selections sp... | Can a random forest be used for feature selection in multiple linear regression? | Despite the legitimate warnings that this approach might fail in some cases, this should not discourage you from trying it out! Breimann reports an example (Breimann 2001) that selecting features by v | Can a random forest be used for feature selection in multiple linear regression?
Despite the legitimate warnings that this approach might fail in some cases, this should not discourage you from trying it out! Breimann reports an example (Breimann 2001) that selecting features by variable importance from a random forest... | Can a random forest be used for feature selection in multiple linear regression?
Despite the legitimate warnings that this approach might fail in some cases, this should not discourage you from trying it out! Breimann reports an example (Breimann 2001) that selecting features by v |
4,249 | What is the difference between posterior and posterior predictive distribution? | The simple difference between the two is that the posterior distribution depends on the unknown parameter $\theta$, i.e., the posterior distribution is:
$$p(\theta|x)=c\times p(x|\theta)p(\theta)$$
where $c$ is the normalizing constant.
While on the other hand, the posterior predictive distribution does not depend on t... | What is the difference between posterior and posterior predictive distribution? | The simple difference between the two is that the posterior distribution depends on the unknown parameter $\theta$, i.e., the posterior distribution is:
$$p(\theta|x)=c\times p(x|\theta)p(\theta)$$
wh | What is the difference between posterior and posterior predictive distribution?
The simple difference between the two is that the posterior distribution depends on the unknown parameter $\theta$, i.e., the posterior distribution is:
$$p(\theta|x)=c\times p(x|\theta)p(\theta)$$
where $c$ is the normalizing constant.
Whi... | What is the difference between posterior and posterior predictive distribution?
The simple difference between the two is that the posterior distribution depends on the unknown parameter $\theta$, i.e., the posterior distribution is:
$$p(\theta|x)=c\times p(x|\theta)p(\theta)$$
wh |
4,250 | What is the difference between posterior and posterior predictive distribution? | The predictive distribution is usually used when you have learned a posterior distribution for the parameter of some sort of predictive model. For example in Bayesian linear regression, you learn a posterior distribution over the w parameter of the model y=wX given some observed data X.
Then when a new unseen data poi... | What is the difference between posterior and posterior predictive distribution? | The predictive distribution is usually used when you have learned a posterior distribution for the parameter of some sort of predictive model. For example in Bayesian linear regression, you learn a p | What is the difference between posterior and posterior predictive distribution?
The predictive distribution is usually used when you have learned a posterior distribution for the parameter of some sort of predictive model. For example in Bayesian linear regression, you learn a posterior distribution over the w paramet... | What is the difference between posterior and posterior predictive distribution?
The predictive distribution is usually used when you have learned a posterior distribution for the parameter of some sort of predictive model. For example in Bayesian linear regression, you learn a p |
4,251 | What is the difference between posterior and posterior predictive distribution? | They refer to distributions of two different things.
The posterior distribution refers to the distribution of the parameter, while the predictive posterior distribution (PPD) refers to the distribution of future observations of data. | What is the difference between posterior and posterior predictive distribution? | They refer to distributions of two different things.
The posterior distribution refers to the distribution of the parameter, while the predictive posterior distribution (PPD) refers to the distributi | What is the difference between posterior and posterior predictive distribution?
They refer to distributions of two different things.
The posterior distribution refers to the distribution of the parameter, while the predictive posterior distribution (PPD) refers to the distribution of future observations of data. | What is the difference between posterior and posterior predictive distribution?
They refer to distributions of two different things.
The posterior distribution refers to the distribution of the parameter, while the predictive posterior distribution (PPD) refers to the distributi |
4,252 | Explanation of min_child_weight in xgboost algorithm | For a regression, the loss of each point in a node is
$\frac{1}{2}(y_i - \hat{y_i})^2$
The second derivative of this expression with respect to $\hat{y_i}$ is $1$. So when you sum the second derivative over all points in the node, you get the number of points in the node. Here, min_child_weight means something like "st... | Explanation of min_child_weight in xgboost algorithm | For a regression, the loss of each point in a node is
$\frac{1}{2}(y_i - \hat{y_i})^2$
The second derivative of this expression with respect to $\hat{y_i}$ is $1$. So when you sum the second derivativ | Explanation of min_child_weight in xgboost algorithm
For a regression, the loss of each point in a node is
$\frac{1}{2}(y_i - \hat{y_i})^2$
The second derivative of this expression with respect to $\hat{y_i}$ is $1$. So when you sum the second derivative over all points in the node, you get the number of points in the ... | Explanation of min_child_weight in xgboost algorithm
For a regression, the loss of each point in a node is
$\frac{1}{2}(y_i - \hat{y_i})^2$
The second derivative of this expression with respect to $\hat{y_i}$ is $1$. So when you sum the second derivativ |
4,253 | Explanation of min_child_weight in xgboost algorithm | When there is little information, gradients of the loss function will tend to change slower, hence a smaller hessian. In the MLE framework, the negative of the hessian is known as the observed Fisher information. Ignoring the sign, a larger hessian will mean that more information is available. You don't want splits to ... | Explanation of min_child_weight in xgboost algorithm | When there is little information, gradients of the loss function will tend to change slower, hence a smaller hessian. In the MLE framework, the negative of the hessian is known as the observed Fisher | Explanation of min_child_weight in xgboost algorithm
When there is little information, gradients of the loss function will tend to change slower, hence a smaller hessian. In the MLE framework, the negative of the hessian is known as the observed Fisher information. Ignoring the sign, a larger hessian will mean that mor... | Explanation of min_child_weight in xgboost algorithm
When there is little information, gradients of the loss function will tend to change slower, hence a smaller hessian. In the MLE framework, the negative of the hessian is known as the observed Fisher |
4,254 | Regression when the OLS residuals are not normally distributed | The ordinary least squares estimate is still a reasonable estimator in the face of non-normal errors. In particular, the Gauss-Markov Theorem states that the ordinary least squares estimate is the best linear unbiased estimator (BLUE) of the regression coefficients ('Best' meaning optimal in terms of minimizing mean sq... | Regression when the OLS residuals are not normally distributed | The ordinary least squares estimate is still a reasonable estimator in the face of non-normal errors. In particular, the Gauss-Markov Theorem states that the ordinary least squares estimate is the bes | Regression when the OLS residuals are not normally distributed
The ordinary least squares estimate is still a reasonable estimator in the face of non-normal errors. In particular, the Gauss-Markov Theorem states that the ordinary least squares estimate is the best linear unbiased estimator (BLUE) of the regression coef... | Regression when the OLS residuals are not normally distributed
The ordinary least squares estimate is still a reasonable estimator in the face of non-normal errors. In particular, the Gauss-Markov Theorem states that the ordinary least squares estimate is the bes |
4,255 | Regression when the OLS residuals are not normally distributed | I think you want to look at all the properties of the residuals.
normality
constant variance
correlated to a covariate.
combinations of the above
If it is just 1 and it is due to heavytails or skewness due to one heavy tail, robust regression might be a good approach or possibly a transformation to normality. If it ... | Regression when the OLS residuals are not normally distributed | I think you want to look at all the properties of the residuals.
normality
constant variance
correlated to a covariate.
combinations of the above
If it is just 1 and it is due to heavytails or skewn | Regression when the OLS residuals are not normally distributed
I think you want to look at all the properties of the residuals.
normality
constant variance
correlated to a covariate.
combinations of the above
If it is just 1 and it is due to heavytails or skewness due to one heavy tail, robust regression might be a g... | Regression when the OLS residuals are not normally distributed
I think you want to look at all the properties of the residuals.
normality
constant variance
correlated to a covariate.
combinations of the above
If it is just 1 and it is due to heavytails or skewn |
4,256 | Regression when the OLS residuals are not normally distributed | For non-normal conditions one would sometimes resort to robust regression, especially using the links to methods.
In order to present the context for non-normality it may help to review the assumptions for linear OLS regression, which are:
Weak exogeneity. This essentially means that the predictor variables, x, can be... | Regression when the OLS residuals are not normally distributed | For non-normal conditions one would sometimes resort to robust regression, especially using the links to methods.
In order to present the context for non-normality it may help to review the assumption | Regression when the OLS residuals are not normally distributed
For non-normal conditions one would sometimes resort to robust regression, especially using the links to methods.
In order to present the context for non-normality it may help to review the assumptions for linear OLS regression, which are:
Weak exogeneity.... | Regression when the OLS residuals are not normally distributed
For non-normal conditions one would sometimes resort to robust regression, especially using the links to methods.
In order to present the context for non-normality it may help to review the assumption |
4,257 | Regression when the OLS residuals are not normally distributed | Macro (jsut above) stated the correct answer. Just some precision because I had the same question
The condition of normality of the residuals is useful when residuals are also homoskedastic. The result is then that OLS has the smallest variance between all of the estimator (linear OR non-linear).
The extended OLS assum... | Regression when the OLS residuals are not normally distributed | Macro (jsut above) stated the correct answer. Just some precision because I had the same question
The condition of normality of the residuals is useful when residuals are also homoskedastic. The resul | Regression when the OLS residuals are not normally distributed
Macro (jsut above) stated the correct answer. Just some precision because I had the same question
The condition of normality of the residuals is useful when residuals are also homoskedastic. The result is then that OLS has the smallest variance between all ... | Regression when the OLS residuals are not normally distributed
Macro (jsut above) stated the correct answer. Just some precision because I had the same question
The condition of normality of the residuals is useful when residuals are also homoskedastic. The resul |
4,258 | Regression when the OLS residuals are not normally distributed | My experience is completely in accord with Michael Chernick. Not only at times does applying a data transformation makes the modeling error normally distributed, it can also correct heteroskedasticity.
Sorry, but to suggest otherwise like gather an insane amount of data, or employ less efficient robust regression meth... | Regression when the OLS residuals are not normally distributed | My experience is completely in accord with Michael Chernick. Not only at times does applying a data transformation makes the modeling error normally distributed, it can also correct heteroskedasticity | Regression when the OLS residuals are not normally distributed
My experience is completely in accord with Michael Chernick. Not only at times does applying a data transformation makes the modeling error normally distributed, it can also correct heteroskedasticity.
Sorry, but to suggest otherwise like gather an insane ... | Regression when the OLS residuals are not normally distributed
My experience is completely in accord with Michael Chernick. Not only at times does applying a data transformation makes the modeling error normally distributed, it can also correct heteroskedasticity |
4,259 | Is there a test to determine whether GLM overdispersion is significant? | In the R package AER you will find the function dispersiontest, which implements a Test for Overdispersion by Cameron & Trivedi (1990).
It follows a simple idea: In a Poisson model, the mean is $E(Y)=\mu$ and the variance is $Var(Y)=\mu$ as well. They are equal. The test simply tests this assumption as a null hypothes... | Is there a test to determine whether GLM overdispersion is significant? | In the R package AER you will find the function dispersiontest, which implements a Test for Overdispersion by Cameron & Trivedi (1990).
It follows a simple idea: In a Poisson model, the mean is $E(Y) | Is there a test to determine whether GLM overdispersion is significant?
In the R package AER you will find the function dispersiontest, which implements a Test for Overdispersion by Cameron & Trivedi (1990).
It follows a simple idea: In a Poisson model, the mean is $E(Y)=\mu$ and the variance is $Var(Y)=\mu$ as well. ... | Is there a test to determine whether GLM overdispersion is significant?
In the R package AER you will find the function dispersiontest, which implements a Test for Overdispersion by Cameron & Trivedi (1990).
It follows a simple idea: In a Poisson model, the mean is $E(Y) |
4,260 | Is there a test to determine whether GLM overdispersion is significant? | An alternative is the odTest from the pscl library which compares the log-likelihood ratios of a Negative Binomial regression to the restriction of a Poisson regression $\mu =\mathrm{Var}$. The following result is obtained:
>library(pscl)
>odTest(NegBinModel)
Likelihood ratio test of H0: Poisson, as restricted NB mo... | Is there a test to determine whether GLM overdispersion is significant? | An alternative is the odTest from the pscl library which compares the log-likelihood ratios of a Negative Binomial regression to the restriction of a Poisson regression $\mu =\mathrm{Var}$. The follow | Is there a test to determine whether GLM overdispersion is significant?
An alternative is the odTest from the pscl library which compares the log-likelihood ratios of a Negative Binomial regression to the restriction of a Poisson regression $\mu =\mathrm{Var}$. The following result is obtained:
>library(pscl)
>odTest(... | Is there a test to determine whether GLM overdispersion is significant?
An alternative is the odTest from the pscl library which compares the log-likelihood ratios of a Negative Binomial regression to the restriction of a Poisson regression $\mu =\mathrm{Var}$. The follow |
4,261 | Is there a test to determine whether GLM overdispersion is significant? | Another alternative is to use the P__disp function from the msme package. The P__disp function can be used to calculate the Pearson $\chi^2$ and Pearson dispersion statistics after fitting the model with glm or glm.nb. | Is there a test to determine whether GLM overdispersion is significant? | Another alternative is to use the P__disp function from the msme package. The P__disp function can be used to calculate the Pearson $\chi^2$ and Pearson dispersion statistics after fitting the model w | Is there a test to determine whether GLM overdispersion is significant?
Another alternative is to use the P__disp function from the msme package. The P__disp function can be used to calculate the Pearson $\chi^2$ and Pearson dispersion statistics after fitting the model with glm or glm.nb. | Is there a test to determine whether GLM overdispersion is significant?
Another alternative is to use the P__disp function from the msme package. The P__disp function can be used to calculate the Pearson $\chi^2$ and Pearson dispersion statistics after fitting the model w |
4,262 | Is there a test to determine whether GLM overdispersion is significant? | Yet another option would be to use a likelihood-ratio test to show that a quasipoisson GLM with overdispersion is significantly better than a regular poisson GLM without overdispersion :
fit = glm(count ~ treatment,family="poisson",data=data)
fit.overdisp = glm(count ~ treatment,family="quasipoisson",data=data)
summa... | Is there a test to determine whether GLM overdispersion is significant? | Yet another option would be to use a likelihood-ratio test to show that a quasipoisson GLM with overdispersion is significantly better than a regular poisson GLM without overdispersion :
fit = glm(cou | Is there a test to determine whether GLM overdispersion is significant?
Yet another option would be to use a likelihood-ratio test to show that a quasipoisson GLM with overdispersion is significantly better than a regular poisson GLM without overdispersion :
fit = glm(count ~ treatment,family="poisson",data=data)
fit.... | Is there a test to determine whether GLM overdispersion is significant?
Yet another option would be to use a likelihood-ratio test to show that a quasipoisson GLM with overdispersion is significantly better than a regular poisson GLM without overdispersion :
fit = glm(cou |
4,263 | Adam optimizer with exponential decay | Empirically speaking: definitely try it out, you may find some very useful training heuristics, in which case, please do share!
Usually people use some kind of decay, for Adam it seems uncommon. Is there any theoretical reason for this? Can it be useful to combine Adam optimizer with decay?
I haven't seen enough peop... | Adam optimizer with exponential decay | Empirically speaking: definitely try it out, you may find some very useful training heuristics, in which case, please do share!
Usually people use some kind of decay, for Adam it seems uncommon. Is t | Adam optimizer with exponential decay
Empirically speaking: definitely try it out, you may find some very useful training heuristics, in which case, please do share!
Usually people use some kind of decay, for Adam it seems uncommon. Is there any theoretical reason for this? Can it be useful to combine Adam optimizer w... | Adam optimizer with exponential decay
Empirically speaking: definitely try it out, you may find some very useful training heuristics, in which case, please do share!
Usually people use some kind of decay, for Adam it seems uncommon. Is t |
4,264 | Adam optimizer with exponential decay | Adam uses the initial learning rate, or step size according to the original paper's terminology, while adaptively computing updates. Step size also gives an approximate bound for updates. In this regard, I think it is a good idea to reduce step size towards the end of training. This is also supported by a recent work f... | Adam optimizer with exponential decay | Adam uses the initial learning rate, or step size according to the original paper's terminology, while adaptively computing updates. Step size also gives an approximate bound for updates. In this rega | Adam optimizer with exponential decay
Adam uses the initial learning rate, or step size according to the original paper's terminology, while adaptively computing updates. Step size also gives an approximate bound for updates. In this regard, I think it is a good idea to reduce step size towards the end of training. Thi... | Adam optimizer with exponential decay
Adam uses the initial learning rate, or step size according to the original paper's terminology, while adaptively computing updates. Step size also gives an approximate bound for updates. In this rega |
4,265 | Adam optimizer with exponential decay | The reason why most people don't use learning rate decay with Adam is that the algorithm itself does a learning rate decay in the following way:
t <- t + 1
lr_t <- learning_rate * sqrt(1 - beta2^t) / (1 - beta1^t)
where t0 is the initial timestep, and lr_t is the new learning rate used. | Adam optimizer with exponential decay | The reason why most people don't use learning rate decay with Adam is that the algorithm itself does a learning rate decay in the following way:
t <- t + 1
lr_t <- learning_rate * sqrt(1 - beta2^t) / | Adam optimizer with exponential decay
The reason why most people don't use learning rate decay with Adam is that the algorithm itself does a learning rate decay in the following way:
t <- t + 1
lr_t <- learning_rate * sqrt(1 - beta2^t) / (1 - beta1^t)
where t0 is the initial timestep, and lr_t is the new learning rat... | Adam optimizer with exponential decay
The reason why most people don't use learning rate decay with Adam is that the algorithm itself does a learning rate decay in the following way:
t <- t + 1
lr_t <- learning_rate * sqrt(1 - beta2^t) / |
4,266 | Adam optimizer with exponential decay | I agree with @Indie AI's opinion, here I supply some other information:
From CS231n:
... Many of these methods may still require other hyperparameter settings, but the argument is that they are well-behaved for a broader range of hyperparameter values than the raw learning rate. ...
And Also from the Paper Rethinking... | Adam optimizer with exponential decay | I agree with @Indie AI's opinion, here I supply some other information:
From CS231n:
... Many of these methods may still require other hyperparameter settings, but the argument is that they are well- | Adam optimizer with exponential decay
I agree with @Indie AI's opinion, here I supply some other information:
From CS231n:
... Many of these methods may still require other hyperparameter settings, but the argument is that they are well-behaved for a broader range of hyperparameter values than the raw learning rate. .... | Adam optimizer with exponential decay
I agree with @Indie AI's opinion, here I supply some other information:
From CS231n:
... Many of these methods may still require other hyperparameter settings, but the argument is that they are well- |
4,267 | Adam optimizer with exponential decay | I trained a dataset with real easy data, if a person is considered fat or not, height and weight - creating data calculating bmi, and if over 27, the person is fat. So very easy basic data. When using Adam as optimizer, and learning rate at 0.001, the accuracy will only get me around 85% for 5 epocs, topping at max 90%... | Adam optimizer with exponential decay | I trained a dataset with real easy data, if a person is considered fat or not, height and weight - creating data calculating bmi, and if over 27, the person is fat. So very easy basic data. When using | Adam optimizer with exponential decay
I trained a dataset with real easy data, if a person is considered fat or not, height and weight - creating data calculating bmi, and if over 27, the person is fat. So very easy basic data. When using Adam as optimizer, and learning rate at 0.001, the accuracy will only get me arou... | Adam optimizer with exponential decay
I trained a dataset with real easy data, if a person is considered fat or not, height and weight - creating data calculating bmi, and if over 27, the person is fat. So very easy basic data. When using |
4,268 | Adam optimizer with exponential decay | The learning rate decay in the Adam is the same as that in RSMProp(as you can see from this answer), and that is kind of mostly based on the magnitude of the previous gradients to dump out the oscillations. So the exponential decay(for a decreasing learning rate along the training process) can be adopted at the same ti... | Adam optimizer with exponential decay | The learning rate decay in the Adam is the same as that in RSMProp(as you can see from this answer), and that is kind of mostly based on the magnitude of the previous gradients to dump out the oscilla | Adam optimizer with exponential decay
The learning rate decay in the Adam is the same as that in RSMProp(as you can see from this answer), and that is kind of mostly based on the magnitude of the previous gradients to dump out the oscillations. So the exponential decay(for a decreasing learning rate along the training ... | Adam optimizer with exponential decay
The learning rate decay in the Adam is the same as that in RSMProp(as you can see from this answer), and that is kind of mostly based on the magnitude of the previous gradients to dump out the oscilla |
4,269 | Logistic Regression: Scikit Learn vs Statsmodels | Your clue to figuring this out should be that the parameter estimates from the scikit-learn estimation are uniformly smaller in magnitude than the statsmodels counterpart. This might lead you to believe that scikit-learn applies some kind of parameter regularization. You can confirm this by reading the scikit-learn doc... | Logistic Regression: Scikit Learn vs Statsmodels | Your clue to figuring this out should be that the parameter estimates from the scikit-learn estimation are uniformly smaller in magnitude than the statsmodels counterpart. This might lead you to belie | Logistic Regression: Scikit Learn vs Statsmodels
Your clue to figuring this out should be that the parameter estimates from the scikit-learn estimation are uniformly smaller in magnitude than the statsmodels counterpart. This might lead you to believe that scikit-learn applies some kind of parameter regularization. You... | Logistic Regression: Scikit Learn vs Statsmodels
Your clue to figuring this out should be that the parameter estimates from the scikit-learn estimation are uniformly smaller in magnitude than the statsmodels counterpart. This might lead you to belie |
4,270 | Logistic Regression: Scikit Learn vs Statsmodels | What tripped me up:
disable sklearn regularization LogisticRegression(C=1e9)
add statsmodels intercept sm.Logit(y, sm.add_constant(X)) OR disable sklearn intercept LogisticRegression(C=1e9, fit_intercept=False)
sklearn returns probability for each class so model_sklearn.predict_proba(X)[:, 1] == model_statsmodel.pre... | Logistic Regression: Scikit Learn vs Statsmodels | What tripped me up:
disable sklearn regularization LogisticRegression(C=1e9)
add statsmodels intercept sm.Logit(y, sm.add_constant(X)) OR disable sklearn intercept LogisticRegression(C=1e9, fit_inte | Logistic Regression: Scikit Learn vs Statsmodels
What tripped me up:
disable sklearn regularization LogisticRegression(C=1e9)
add statsmodels intercept sm.Logit(y, sm.add_constant(X)) OR disable sklearn intercept LogisticRegression(C=1e9, fit_intercept=False)
sklearn returns probability for each class so model_sklea... | Logistic Regression: Scikit Learn vs Statsmodels
What tripped me up:
disable sklearn regularization LogisticRegression(C=1e9)
add statsmodels intercept sm.Logit(y, sm.add_constant(X)) OR disable sklearn intercept LogisticRegression(C=1e9, fit_inte |
4,271 | Logistic Regression: Scikit Learn vs Statsmodels | Another difference is that you've set fit_intercept=False, which effectively is a different model. You can see that Statsmodel includes the intercept. Not having an intercept surely changes the expected weights on the features. Try the following and see how it compares:
model = LogisticRegression(C=1e9) | Logistic Regression: Scikit Learn vs Statsmodels | Another difference is that you've set fit_intercept=False, which effectively is a different model. You can see that Statsmodel includes the intercept. Not having an intercept surely changes the expect | Logistic Regression: Scikit Learn vs Statsmodels
Another difference is that you've set fit_intercept=False, which effectively is a different model. You can see that Statsmodel includes the intercept. Not having an intercept surely changes the expected weights on the features. Try the following and see how it compares:
... | Logistic Regression: Scikit Learn vs Statsmodels
Another difference is that you've set fit_intercept=False, which effectively is a different model. You can see that Statsmodel includes the intercept. Not having an intercept surely changes the expect |
4,272 | Manually Calculating P value from t-value in t-test | Use pt and make it two-tailed.
> 2*pt(11.244, 30, lower=FALSE)
[1] 2.785806e-12 | Manually Calculating P value from t-value in t-test | Use pt and make it two-tailed.
> 2*pt(11.244, 30, lower=FALSE)
[1] 2.785806e-12 | Manually Calculating P value from t-value in t-test
Use pt and make it two-tailed.
> 2*pt(11.244, 30, lower=FALSE)
[1] 2.785806e-12 | Manually Calculating P value from t-value in t-test
Use pt and make it two-tailed.
> 2*pt(11.244, 30, lower=FALSE)
[1] 2.785806e-12 |
4,273 | Manually Calculating P value from t-value in t-test | I posted this as a comment but when I wanted to add a bit more in edit, it became too long so I've moved it down here.
Edit: Your test statistic and d.f are correct. The other answer notes the issue with the calculation of the tail area in the call to pt(), and the doubling for two-tails, which resolves your difference... | Manually Calculating P value from t-value in t-test | I posted this as a comment but when I wanted to add a bit more in edit, it became too long so I've moved it down here.
Edit: Your test statistic and d.f are correct. The other answer notes the issue w | Manually Calculating P value from t-value in t-test
I posted this as a comment but when I wanted to add a bit more in edit, it became too long so I've moved it down here.
Edit: Your test statistic and d.f are correct. The other answer notes the issue with the calculation of the tail area in the call to pt(), and the do... | Manually Calculating P value from t-value in t-test
I posted this as a comment but when I wanted to add a bit more in edit, it became too long so I've moved it down here.
Edit: Your test statistic and d.f are correct. The other answer notes the issue w |
4,274 | Manually Calculating P value from t-value in t-test | The best way to calculate it manually is:
t.value = (mean(data) - 10) / (sd(data) / sqrt(length(data)))
p.value = 2*pt(-abs(t.value), df=length(data)-1)
You need the abs() function because otherwise you run the risk of getting p-values bigger than $1$ (when the mean of the data is bigger than the given mean)! | Manually Calculating P value from t-value in t-test | The best way to calculate it manually is:
t.value = (mean(data) - 10) / (sd(data) / sqrt(length(data)))
p.value = 2*pt(-abs(t.value), df=length(data)-1)
You need the abs() function because otherwise | Manually Calculating P value from t-value in t-test
The best way to calculate it manually is:
t.value = (mean(data) - 10) / (sd(data) / sqrt(length(data)))
p.value = 2*pt(-abs(t.value), df=length(data)-1)
You need the abs() function because otherwise you run the risk of getting p-values bigger than $1$ (when the mean... | Manually Calculating P value from t-value in t-test
The best way to calculate it manually is:
t.value = (mean(data) - 10) / (sd(data) / sqrt(length(data)))
p.value = 2*pt(-abs(t.value), df=length(data)-1)
You need the abs() function because otherwise |
4,275 | Manually Calculating P value from t-value in t-test | I really like the answer @Aaron provided, along with the abs comments. I find a handy confirmation is to run
pt(1.96, 1000000, lower.tail = F) * 2
which yields 0.04999607.
Here, we're using the well-known property that 95% of the area under the normal distribution occurs at ~1.96 standard deviations, thus the output ... | Manually Calculating P value from t-value in t-test | I really like the answer @Aaron provided, along with the abs comments. I find a handy confirmation is to run
pt(1.96, 1000000, lower.tail = F) * 2
which yields 0.04999607.
Here, we're using the well | Manually Calculating P value from t-value in t-test
I really like the answer @Aaron provided, along with the abs comments. I find a handy confirmation is to run
pt(1.96, 1000000, lower.tail = F) * 2
which yields 0.04999607.
Here, we're using the well-known property that 95% of the area under the normal distribution o... | Manually Calculating P value from t-value in t-test
I really like the answer @Aaron provided, along with the abs comments. I find a handy confirmation is to run
pt(1.96, 1000000, lower.tail = F) * 2
which yields 0.04999607.
Here, we're using the well |
4,276 | Multinomial logistic regression vs one-vs-rest binary logistic regression | If $Y$ has more than two categories your question about "advantage" of one regression over the other is probably meaningless if you aim to compare the models' parameters, because the models will be fundamentally different:
$\bf log \frac{P(i)}{P(not~i)}=logit_i=linear~combination$ for each $i$ binary logistic regressio... | Multinomial logistic regression vs one-vs-rest binary logistic regression | If $Y$ has more than two categories your question about "advantage" of one regression over the other is probably meaningless if you aim to compare the models' parameters, because the models will be fu | Multinomial logistic regression vs one-vs-rest binary logistic regression
If $Y$ has more than two categories your question about "advantage" of one regression over the other is probably meaningless if you aim to compare the models' parameters, because the models will be fundamentally different:
$\bf log \frac{P(i)}{P(... | Multinomial logistic regression vs one-vs-rest binary logistic regression
If $Y$ has more than two categories your question about "advantage" of one regression over the other is probably meaningless if you aim to compare the models' parameters, because the models will be fu |
4,277 | Multinomial logistic regression vs one-vs-rest binary logistic regression | Because of the title, I'm assuming that "advantages of multiple logistic regression" means "multinomial regression". There are often advantages when the model is fit simultaneously. This particular situation is described in Agresti (Categorical Data Analysis, 2002) pg 273. In sum (paraphrasing Agresti), you expect the ... | Multinomial logistic regression vs one-vs-rest binary logistic regression | Because of the title, I'm assuming that "advantages of multiple logistic regression" means "multinomial regression". There are often advantages when the model is fit simultaneously. This particular si | Multinomial logistic regression vs one-vs-rest binary logistic regression
Because of the title, I'm assuming that "advantages of multiple logistic regression" means "multinomial regression". There are often advantages when the model is fit simultaneously. This particular situation is described in Agresti (Categorical D... | Multinomial logistic regression vs one-vs-rest binary logistic regression
Because of the title, I'm assuming that "advantages of multiple logistic regression" means "multinomial regression". There are often advantages when the model is fit simultaneously. This particular si |
4,278 | Multinomial logistic regression vs one-vs-rest binary logistic regression | I don't think the previous answers really capture the key difference, although it is implicit in the discussion of Independence of Irrelevant Alternatives (which is a social sciences term rather than a statistical term).
If you use a multinomial model then your predictions for the different options sum to 1; If you use... | Multinomial logistic regression vs one-vs-rest binary logistic regression | I don't think the previous answers really capture the key difference, although it is implicit in the discussion of Independence of Irrelevant Alternatives (which is a social sciences term rather than | Multinomial logistic regression vs one-vs-rest binary logistic regression
I don't think the previous answers really capture the key difference, although it is implicit in the discussion of Independence of Irrelevant Alternatives (which is a social sciences term rather than a statistical term).
If you use a multinomial ... | Multinomial logistic regression vs one-vs-rest binary logistic regression
I don't think the previous answers really capture the key difference, although it is implicit in the discussion of Independence of Irrelevant Alternatives (which is a social sciences term rather than |
4,279 | Multinomial logistic regression vs one-vs-rest binary logistic regression | It seems that the question was not at all about the implementation/structural differences between (a) the softmax (multinomial logistic) regression model and (b) the OvR "composite" model based on multiple binary logistic regression models. In a nutshell, however, skipping all the formulas, these differences can be sum... | Multinomial logistic regression vs one-vs-rest binary logistic regression | It seems that the question was not at all about the implementation/structural differences between (a) the softmax (multinomial logistic) regression model and (b) the OvR "composite" model based on mul | Multinomial logistic regression vs one-vs-rest binary logistic regression
It seems that the question was not at all about the implementation/structural differences between (a) the softmax (multinomial logistic) regression model and (b) the OvR "composite" model based on multiple binary logistic regression models. In a ... | Multinomial logistic regression vs one-vs-rest binary logistic regression
It seems that the question was not at all about the implementation/structural differences between (a) the softmax (multinomial logistic) regression model and (b) the OvR "composite" model based on mul |
4,280 | How to identify a bimodal distribution? | Identifying a mode for a continuous distribution requires smoothing or binning the data.
Binning is typically too procrustean: the results often depend on where you place the bin cutpoints.
Kernel smoothing (specifically, in the form of kernel density estimation) is a good choice. Although many kernel shapes are possi... | How to identify a bimodal distribution? | Identifying a mode for a continuous distribution requires smoothing or binning the data.
Binning is typically too procrustean: the results often depend on where you place the bin cutpoints.
Kernel smo | How to identify a bimodal distribution?
Identifying a mode for a continuous distribution requires smoothing or binning the data.
Binning is typically too procrustean: the results often depend on where you place the bin cutpoints.
Kernel smoothing (specifically, in the form of kernel density estimation) is a good choice... | How to identify a bimodal distribution?
Identifying a mode for a continuous distribution requires smoothing or binning the data.
Binning is typically too procrustean: the results often depend on where you place the bin cutpoints.
Kernel smo |
4,281 | How to identify a bimodal distribution? | There is a well-known paper by Silverman that deals with this issue. It employs kernel-density estimation. See
B. W. Silverman, Using kernel density estimates to investigate multimodality, J. Royal
Stat. Soc. B, vol. 43, no. 1, 1981, pp. 97-99.
Note that there are some errors in the tables of the paper. This is jus... | How to identify a bimodal distribution? | There is a well-known paper by Silverman that deals with this issue. It employs kernel-density estimation. See
B. W. Silverman, Using kernel density estimates to investigate multimodality, J. Royal
| How to identify a bimodal distribution?
There is a well-known paper by Silverman that deals with this issue. It employs kernel-density estimation. See
B. W. Silverman, Using kernel density estimates to investigate multimodality, J. Royal
Stat. Soc. B, vol. 43, no. 1, 1981, pp. 97-99.
Note that there are some errors... | How to identify a bimodal distribution?
There is a well-known paper by Silverman that deals with this issue. It employs kernel-density estimation. See
B. W. Silverman, Using kernel density estimates to investigate multimodality, J. Royal
|
4,282 | How to identify a bimodal distribution? | I came late to the party, but if you are just interested in whether it is multimodal or not, meaning you are not interested in the number of modes, you should look at diptest.
In R the package is called diptest. | How to identify a bimodal distribution? | I came late to the party, but if you are just interested in whether it is multimodal or not, meaning you are not interested in the number of modes, you should look at diptest.
In R the package is call | How to identify a bimodal distribution?
I came late to the party, but if you are just interested in whether it is multimodal or not, meaning you are not interested in the number of modes, you should look at diptest.
In R the package is called diptest. | How to identify a bimodal distribution?
I came late to the party, but if you are just interested in whether it is multimodal or not, meaning you are not interested in the number of modes, you should look at diptest.
In R the package is call |
4,283 | How to identify a bimodal distribution? | The definition in wiki is slightly confusing to me. The probability of a continous data set having just one mode is zero. A simple way to program a bimodal distrubiton is with two seperate normal distributions centered differently. This creates two peaks or what wiki calls modes. You can actually use almost any two... | How to identify a bimodal distribution? | The definition in wiki is slightly confusing to me. The probability of a continous data set having just one mode is zero. A simple way to program a bimodal distrubiton is with two seperate normal di | How to identify a bimodal distribution?
The definition in wiki is slightly confusing to me. The probability of a continous data set having just one mode is zero. A simple way to program a bimodal distrubiton is with two seperate normal distributions centered differently. This creates two peaks or what wiki calls mod... | How to identify a bimodal distribution?
The definition in wiki is slightly confusing to me. The probability of a continous data set having just one mode is zero. A simple way to program a bimodal distrubiton is with two seperate normal di |
4,284 | Visually interesting statistics concepts that are easy to explain | I like images illustrating how different patterns can have similar correlation. The ones below are from Wikipedia articles on correlation and dependence
and Anscombe's quartet with correlations of about $0.816$ | Visually interesting statistics concepts that are easy to explain | I like images illustrating how different patterns can have similar correlation. The ones below are from Wikipedia articles on correlation and dependence
and Anscombe's quartet with correlations of | Visually interesting statistics concepts that are easy to explain
I like images illustrating how different patterns can have similar correlation. The ones below are from Wikipedia articles on correlation and dependence
and Anscombe's quartet with correlations of about $0.816$ | Visually interesting statistics concepts that are easy to explain
I like images illustrating how different patterns can have similar correlation. The ones below are from Wikipedia articles on correlation and dependence
and Anscombe's quartet with correlations of |
4,285 | Visually interesting statistics concepts that are easy to explain | Simpson's Paradox
A phenomenon that appears when a key variable is omitted from the analysis of a relationship between one or more independent variables and a dependent variable. For instance, this shows the more bedrooms houses have, the lower the home price:
(source: ba762researchmethods at sites.google.com)
which ... | Visually interesting statistics concepts that are easy to explain | Simpson's Paradox
A phenomenon that appears when a key variable is omitted from the analysis of a relationship between one or more independent variables and a dependent variable. For instance, this s | Visually interesting statistics concepts that are easy to explain
Simpson's Paradox
A phenomenon that appears when a key variable is omitted from the analysis of a relationship between one or more independent variables and a dependent variable. For instance, this shows the more bedrooms houses have, the lower the home... | Visually interesting statistics concepts that are easy to explain
Simpson's Paradox
A phenomenon that appears when a key variable is omitted from the analysis of a relationship between one or more independent variables and a dependent variable. For instance, this s |
4,286 | Visually interesting statistics concepts that are easy to explain | One of the most interesting concepts that are very important today and very easy to visualize is "overfitting". The green classifier below presents a clear example of overfitting [Edit: "the green classifier is given by the very wiggly line separating red and blue data points" - Nick Cox].
From Wikipedia: | Visually interesting statistics concepts that are easy to explain | One of the most interesting concepts that are very important today and very easy to visualize is "overfitting". The green classifier below presents a clear example of overfitting [Edit: "the green cla | Visually interesting statistics concepts that are easy to explain
One of the most interesting concepts that are very important today and very easy to visualize is "overfitting". The green classifier below presents a clear example of overfitting [Edit: "the green classifier is given by the very wiggly line separating re... | Visually interesting statistics concepts that are easy to explain
One of the most interesting concepts that are very important today and very easy to visualize is "overfitting". The green classifier below presents a clear example of overfitting [Edit: "the green cla |
4,287 | Visually interesting statistics concepts that are easy to explain | How does a 2D dataset where the mean of X is 54 with a SD 17, and for Y 48 and 27, respectively, and the correlation between the two is -0.06?
Introducing the Anscombosaurus:
And its companion, the Datasaurus Dozen: | Visually interesting statistics concepts that are easy to explain | How does a 2D dataset where the mean of X is 54 with a SD 17, and for Y 48 and 27, respectively, and the correlation between the two is -0.06?
Introducing the Anscombosaurus:
And its companion, the D | Visually interesting statistics concepts that are easy to explain
How does a 2D dataset where the mean of X is 54 with a SD 17, and for Y 48 and 27, respectively, and the correlation between the two is -0.06?
Introducing the Anscombosaurus:
And its companion, the Datasaurus Dozen: | Visually interesting statistics concepts that are easy to explain
How does a 2D dataset where the mean of X is 54 with a SD 17, and for Y 48 and 27, respectively, and the correlation between the two is -0.06?
Introducing the Anscombosaurus:
And its companion, the D |
4,288 | Visually interesting statistics concepts that are easy to explain | I think spurious correlations also deserve their own post. I.e. correlation does not equal causation. Perhaps one of the things used most often when trying to bend the truth using statistics. Tyler Vigen has a famous website with lots of examples. To illustrate - see the plot below where the number of polio cases and t... | Visually interesting statistics concepts that are easy to explain | I think spurious correlations also deserve their own post. I.e. correlation does not equal causation. Perhaps one of the things used most often when trying to bend the truth using statistics. Tyler Vi | Visually interesting statistics concepts that are easy to explain
I think spurious correlations also deserve their own post. I.e. correlation does not equal causation. Perhaps one of the things used most often when trying to bend the truth using statistics. Tyler Vigen has a famous website with lots of examples. To ill... | Visually interesting statistics concepts that are easy to explain
I think spurious correlations also deserve their own post. I.e. correlation does not equal causation. Perhaps one of the things used most often when trying to bend the truth using statistics. Tyler Vi |
4,289 | Visually interesting statistics concepts that are easy to explain | Bias can be good
An $\color{orangered}{\text{unbiased estimator}}$ is on average correct. A $\color{steelblue}{\text{biased estimator}}$ is on average not correct.
Why then, would you ever want to use a biased estimator (e.g. ridge regression)?
The answer is that introducing bias can reduce variance.
In the picture, ... | Visually interesting statistics concepts that are easy to explain | Bias can be good
An $\color{orangered}{\text{unbiased estimator}}$ is on average correct. A $\color{steelblue}{\text{biased estimator}}$ is on average not correct.
Why then, would you ever want to use | Visually interesting statistics concepts that are easy to explain
Bias can be good
An $\color{orangered}{\text{unbiased estimator}}$ is on average correct. A $\color{steelblue}{\text{biased estimator}}$ is on average not correct.
Why then, would you ever want to use a biased estimator (e.g. ridge regression)?
The answ... | Visually interesting statistics concepts that are easy to explain
Bias can be good
An $\color{orangered}{\text{unbiased estimator}}$ is on average correct. A $\color{steelblue}{\text{biased estimator}}$ is on average not correct.
Why then, would you ever want to use |
4,290 | Visually interesting statistics concepts that are easy to explain | When first understanding estimators and their error, it's useful to understand two sources of error: bias and variance. The below image does a great job illustrating this while highlighting tradeoffs between these two sources of error.
The bullseye is the true value the estimator is trying to estimate and each dot rep... | Visually interesting statistics concepts that are easy to explain | When first understanding estimators and their error, it's useful to understand two sources of error: bias and variance. The below image does a great job illustrating this while highlighting tradeoffs | Visually interesting statistics concepts that are easy to explain
When first understanding estimators and their error, it's useful to understand two sources of error: bias and variance. The below image does a great job illustrating this while highlighting tradeoffs between these two sources of error.
The bullseye is t... | Visually interesting statistics concepts that are easy to explain
When first understanding estimators and their error, it's useful to understand two sources of error: bias and variance. The below image does a great job illustrating this while highlighting tradeoffs |
4,291 | Visually interesting statistics concepts that are easy to explain | Principal component Analysis (PCA)
PCA is a method for dimension reduction. It projects the original variables in the direction that maximizes the variance.
In our figure, the red points come from a bivariate normal distribution. The vectors are the eigenvectors and the size of these vectors are proportional to the va... | Visually interesting statistics concepts that are easy to explain | Principal component Analysis (PCA)
PCA is a method for dimension reduction. It projects the original variables in the direction that maximizes the variance.
In our figure, the red points come from a | Visually interesting statistics concepts that are easy to explain
Principal component Analysis (PCA)
PCA is a method for dimension reduction. It projects the original variables in the direction that maximizes the variance.
In our figure, the red points come from a bivariate normal distribution. The vectors are the eig... | Visually interesting statistics concepts that are easy to explain
Principal component Analysis (PCA)
PCA is a method for dimension reduction. It projects the original variables in the direction that maximizes the variance.
In our figure, the red points come from a |
4,292 | Visually interesting statistics concepts that are easy to explain | Eigenvectors & Eigenvalues
The concept of eigenvectors and eigenvalues which are the basis for principal component analysis (PCA), as explained on wikipedia:
In essence, an eigenvector $v$ of a linear transformation $T$ is a nonzero vector that, when $T$ is applied to it, does not change direction. Applying $T$ to the... | Visually interesting statistics concepts that are easy to explain | Eigenvectors & Eigenvalues
The concept of eigenvectors and eigenvalues which are the basis for principal component analysis (PCA), as explained on wikipedia:
In essence, an eigenvector $v$ of a linea | Visually interesting statistics concepts that are easy to explain
Eigenvectors & Eigenvalues
The concept of eigenvectors and eigenvalues which are the basis for principal component analysis (PCA), as explained on wikipedia:
In essence, an eigenvector $v$ of a linear transformation $T$ is a nonzero vector that, when $T... | Visually interesting statistics concepts that are easy to explain
Eigenvectors & Eigenvalues
The concept of eigenvectors and eigenvalues which are the basis for principal component analysis (PCA), as explained on wikipedia:
In essence, an eigenvector $v$ of a linea |
4,293 | Visually interesting statistics concepts that are easy to explain | Trade-off bias variance is another very important concept in Statistics/Machine Learning.
The data points in blue come from $y(x)=\sin(x)+\epsilon$, where $\epsilon$ has a normal distribution. The red curves are estimated using different samples. The figure "Large Variance and Small Bias" presents the original model, ... | Visually interesting statistics concepts that are easy to explain | Trade-off bias variance is another very important concept in Statistics/Machine Learning.
The data points in blue come from $y(x)=\sin(x)+\epsilon$, where $\epsilon$ has a normal distribution. The re | Visually interesting statistics concepts that are easy to explain
Trade-off bias variance is another very important concept in Statistics/Machine Learning.
The data points in blue come from $y(x)=\sin(x)+\epsilon$, where $\epsilon$ has a normal distribution. The red curves are estimated using different samples. The fi... | Visually interesting statistics concepts that are easy to explain
Trade-off bias variance is another very important concept in Statistics/Machine Learning.
The data points in blue come from $y(x)=\sin(x)+\epsilon$, where $\epsilon$ has a normal distribution. The re |
4,294 | Visually interesting statistics concepts that are easy to explain | Here is very basic one, but in my opinion very powerful because it's not only a visual explanation of a concept but also asks for visualising or imagining a real object depicting the concept:
Neophytes sometimes have a hard time understanding very basic concepts like mean, median and mode.
So, for helping them to bet... | Visually interesting statistics concepts that are easy to explain | Here is very basic one, but in my opinion very powerful because it's not only a visual explanation of a concept but also asks for visualising or imagining a real object depicting the concept:
Neophyte | Visually interesting statistics concepts that are easy to explain
Here is very basic one, but in my opinion very powerful because it's not only a visual explanation of a concept but also asks for visualising or imagining a real object depicting the concept:
Neophytes sometimes have a hard time understanding very basic ... | Visually interesting statistics concepts that are easy to explain
Here is very basic one, but in my opinion very powerful because it's not only a visual explanation of a concept but also asks for visualising or imagining a real object depicting the concept:
Neophyte |
4,295 | Visually interesting statistics concepts that are easy to explain | The figure below shows the importance of defining preciselly the objectives and assumptions of a clustering problem (and a general statistical problem). Different models may provide very different results:
Sources: ScikitLearn | Visually interesting statistics concepts that are easy to explain | The figure below shows the importance of defining preciselly the objectives and assumptions of a clustering problem (and a general statistical problem). Different models may provide very different res | Visually interesting statistics concepts that are easy to explain
The figure below shows the importance of defining preciselly the objectives and assumptions of a clustering problem (and a general statistical problem). Different models may provide very different results:
Sources: ScikitLearn | Visually interesting statistics concepts that are easy to explain
The figure below shows the importance of defining preciselly the objectives and assumptions of a clustering problem (and a general statistical problem). Different models may provide very different res |
4,296 | Visually interesting statistics concepts that are easy to explain | Okay, so this one is less about illustrating a basic concept, but it is very interesting both visually and in terms of applications. I think showing people what they can ultimately accomplish with what they are learning is a great form of motivation, so you can pitch it as an example of developing and applying statisti... | Visually interesting statistics concepts that are easy to explain | Okay, so this one is less about illustrating a basic concept, but it is very interesting both visually and in terms of applications. I think showing people what they can ultimately accomplish with wha | Visually interesting statistics concepts that are easy to explain
Okay, so this one is less about illustrating a basic concept, but it is very interesting both visually and in terms of applications. I think showing people what they can ultimately accomplish with what they are learning is a great form of motivation, so ... | Visually interesting statistics concepts that are easy to explain
Okay, so this one is less about illustrating a basic concept, but it is very interesting both visually and in terms of applications. I think showing people what they can ultimately accomplish with wha |
4,297 | Is the COVID-19 pandemic curve a Gaussian curve? | It seems like there are three questions here:
Is the actual distribution of cases Gaussian? No.
Are the curves given in the graphic Gaussian? Not quite. I think the red one is a little bit skewed, and the blue one is definitely skewed.
Can plots of a value versus time be considered Gaussian? Yes.
In mathematics, a... | Is the COVID-19 pandemic curve a Gaussian curve? | It seems like there are three questions here:
Is the actual distribution of cases Gaussian? No.
Are the curves given in the graphic Gaussian? Not quite. I think the red one is a little bit skewed, a | Is the COVID-19 pandemic curve a Gaussian curve?
It seems like there are three questions here:
Is the actual distribution of cases Gaussian? No.
Are the curves given in the graphic Gaussian? Not quite. I think the red one is a little bit skewed, and the blue one is definitely skewed.
Can plots of a value versus time ... | Is the COVID-19 pandemic curve a Gaussian curve?
It seems like there are three questions here:
Is the actual distribution of cases Gaussian? No.
Are the curves given in the graphic Gaussian? Not quite. I think the red one is a little bit skewed, a |
4,298 | Is the COVID-19 pandemic curve a Gaussian curve? | No.
For example:
Not in the sense of a Gaussian probability distribution: the bell-curve of a normal (Gaussian) distribution is a histogram (a map of probability density against values of a single variable), but the curves you quote are (as you note) a map of the values of one variable (new cases) against a second var... | Is the COVID-19 pandemic curve a Gaussian curve? | No.
For example:
Not in the sense of a Gaussian probability distribution: the bell-curve of a normal (Gaussian) distribution is a histogram (a map of probability density against values of a single va | Is the COVID-19 pandemic curve a Gaussian curve?
No.
For example:
Not in the sense of a Gaussian probability distribution: the bell-curve of a normal (Gaussian) distribution is a histogram (a map of probability density against values of a single variable), but the curves you quote are (as you note) a map of the values... | Is the COVID-19 pandemic curve a Gaussian curve?
No.
For example:
Not in the sense of a Gaussian probability distribution: the bell-curve of a normal (Gaussian) distribution is a histogram (a map of probability density against values of a single va |
4,299 | Is the COVID-19 pandemic curve a Gaussian curve? | Epidemiological curves for respiratory infections are very irregular curves. See for instance the SARS outbreak of 2002/2003
https://www.who.int/csr/sars/epicurve/epiindex/en/index1.html
and for endemic diseases they may have some seasonal pattern. See for instance the euromomo logo
(source: euromomo.eu)
Besides the ... | Is the COVID-19 pandemic curve a Gaussian curve? | Epidemiological curves for respiratory infections are very irregular curves. See for instance the SARS outbreak of 2002/2003
https://www.who.int/csr/sars/epicurve/epiindex/en/index1.html
and for ende | Is the COVID-19 pandemic curve a Gaussian curve?
Epidemiological curves for respiratory infections are very irregular curves. See for instance the SARS outbreak of 2002/2003
https://www.who.int/csr/sars/epicurve/epiindex/en/index1.html
and for endemic diseases they may have some seasonal pattern. See for instance the ... | Is the COVID-19 pandemic curve a Gaussian curve?
Epidemiological curves for respiratory infections are very irregular curves. See for instance the SARS outbreak of 2002/2003
https://www.who.int/csr/sars/epicurve/epiindex/en/index1.html
and for ende |
4,300 | Is the COVID-19 pandemic curve a Gaussian curve? | I'm not an epidemiologist, and you should ask this question to the epidemiologists.
First of all, drawing Gaussian curves is simple, since even basic plotting software has them implemented (e.g. Microsoft Excel), so when people need to draw "a distribution", they often draw Gaussians. The "flatten the curve" figures a... | Is the COVID-19 pandemic curve a Gaussian curve? | I'm not an epidemiologist, and you should ask this question to the epidemiologists.
First of all, drawing Gaussian curves is simple, since even basic plotting software has them implemented (e.g. Micr | Is the COVID-19 pandemic curve a Gaussian curve?
I'm not an epidemiologist, and you should ask this question to the epidemiologists.
First of all, drawing Gaussian curves is simple, since even basic plotting software has them implemented (e.g. Microsoft Excel), so when people need to draw "a distribution", they often ... | Is the COVID-19 pandemic curve a Gaussian curve?
I'm not an epidemiologist, and you should ask this question to the epidemiologists.
First of all, drawing Gaussian curves is simple, since even basic plotting software has them implemented (e.g. Micr |
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