tttjjj/elt_bench huggingface dataset:
Perhaps my interpretation was not as mainstream as I believed, but there is nothing intrinsically wrong about putting frequentist and Bayesian methods on the same footing.  See Lehmann and Casella's Theory of Point Estimation, in which frequentist and Bayesian methods are compared via statistical decision theory.
no, since statistical tests "only" check whether the difference in techniques is true or has occurred by chance. See for an example the [Kaggle competition "Dont Overfit"](http://www.kaggle.com/c/overfitting) where the competiton data is purely artificial. Now imagine a statistical sig-test on a crossvalidation-result on the mentioned 250 cases: Real improvement over random model or fluke ?
Please explain why you're not satisfied with suncoolsu's answer to your previous version of the same question http://stats.stackexchange.com/q/3653/449.
Also please indicate what software the code in your question is for, and add an appropriate tag. That way, someone with experience in that software package might be able to suggest explicit code.
I'm unaware of any approaches that "weight", in a continuous manner, the features in a naive Bayesian classifier.  This should not be be required within this approach; the primary confounding feature that you would need to worry about is direct correlations between the feature variables themselves.  So I'm not sure how to address this question; maybe you should sketch out what your overall plan is.
@rapaio Yes, it is.
P.S. If you used all $k$ components in your regressions, not just $l$ components, all the $R^2$'s will be 1. That will help you understand.
Down voters: please provide constructive criticism on how to improve the question. @user1581472: you might get a better response if you provide a bit more detail, for example, some example images might help. Also, this site isn't about "sending codes" - it's for asking advice on how to do something yourself.
A *population* is what you're trying to learn about; the *sample* consists of the data have.  Therefore, *you don't know any of the population parameters* (such as its mean or standard deviation).  Consequently it's impossible to *calculate* the population parameters: you have to *estimate* them from the sample.  I believe that eliminates all these questions, although possibly not question 3, because I cannot make sense of the notation.
@user14075 It seems silly to use $x$ values that are scaled one way (*i.e.*, standardized based on **new** $\\bar{x}$ and $sd(x)$) to predict $\\hat{y}$ from a model that was built using $x$ values that were scaled differently (*i.e.*, standardized based on the **original** $\\bar{x}$ and $sd(x)$). This would be like using an $x$ value that was measured in say inches to build the model and then using $x$ values measured in centimeters (without transformation to inches) to predict $\\hat{y}$ from that model.
If all your variables are the same kind of quantities and are expressed in the same units of measurement, then comparing SDs as you do here is legitimate. But otherwise, this makes no sense. For instance, if the standard deviation of a mass is 0.001 kilograms and the SD of a length is 100 microns, who is to say which is "large" and which not? Could you therefore edit your question to clarify this point? Also mysterious is how you appear to jump from a question about choosing variables for discrimination (evidently) to one about multiple comparisons. What's the connection?
@whuber I do indeed, thanks
Hello. Thanks for your answer. if I use Fisher's exact test, what will be the equation for it please? I am asking because I am familiar with Fisher's exact test when we have only 2 by 2 table, not 6 by 2. Thanks again
Done, and added some information that should have been obvious to me before.
For the OP's edification, the case for using an ANOVA in this situation (that it is essentially a special case of regression) is made [here](http://core.ecu.edu/psyc/wuenschk/docs30/T=ANOVA=Regression.doc).
Thanks for that comprehensive answer!
(+1) I've developed similar ideas using `lattice` but your response is fine.
Do you mean to say that you know the population mean in advance? How can you know that? Some context would help people give a better answer.
I expect it's a formatting typo, and the intention is $(β_0, β_1)'$ (equivalently $(β_0\\;\\; β_1)^T$)- which denotes the *[transpose](http://mathworld.wolfram.com/Transpose.html)* of the row vector $(β_0, β_1)$ -- that is a column vector, consisting of those two elements.
This is a brilliant book about Bayesian *thinking* rather than applying Bayesian methods.  I think this is a good companion text to something which goes more into how do Bayesian computations.
Thank you for the response. It will take me at least a few days to process the materials you presented. I would also like to say your dissertation is incredibly nice and after reading your introduction I look forward to reading the rest.
+1 for SJDM!$.$
Interesting point. If the proposal distribution is not altered and stationarity given, I have no argument why the samples of the burn-in phase should not be used to compute the acceptance rate.
I believe that the usage is ambiguous.  Categorical variables have *levels*.  Data is merely observations *of* a categorical variable, with some specified *level*.  One could abuse the notion of levels to produce infinitely many.  A level itself could, say, count the infinities encountered in a data set (e.g. $X/Y$ where both are drawn from the two element set ${0,1}$.  I do not disagree with your answer, but suggest clarifying to address the issue of levels (or categories).
If this question is not about statistics and is solely about getting things done in MATLAB, the question might be more appropriate for Stack Overflow.
@whuber Thank you for the answer. I made the plots in R http://cs9579.userapi.com/u17020874/153949434/z_9fa17c02.jpg http://cs9579.userapi.com/u17020874/153949434/z_7fa6891c.jpg
Correlations can change dramatically after aggregation: see http://en.wikipedia.org/wiki/Ecological_fallacy.
1. Is yes (see, e.g., Gelman & Hill 2007: http://www.stat.columbia.edu/~gelman/arm/)
The inverse of a strictly increasing function is also strictly increasing!
I do not understand, do you want  samples of $B$ and $A$, but this are distributions! Do you really want these? Moreover, can you please explain better the sampling scheme?
(+1) for statistics being "the science of using data and information to understand the world in the face of variation"
Good point. To be honest, I can't remember what the context around this question was, and I have a feeling that my comments were misleading. I was specifically interested in not losing variability common to all stations, but out of phase. Think of stations all over a continent, and a cold front passing across. A simple spatial average might basically remove the cold front, which is not really a good thing, as each station would exhibit it strongly, but at different times. Probably running some kind of PCA on each station and then averaging the results somehow might be a way to get around that.
Glad that I could help. And good luck!
The response is not a proportion. The SAS notation "r/n" juste means "r among n".
What exactly are you asking for with "What do we know"?
A level shift is a jump .
Thanks. I'm now reading the reference you mention: Yin, P., & Fan, X. (2001). Estimating $R^2$ shrinkage in multiple regression: A comparison of different analytical methods. The Journal of Experimental Education, 69(2), 203-224.
There was some suppression by your confounders
Thank you for such a detailed answers with diagrams.
+1 Very nice idea, especially for the consistent focus on the purpose of the analysis.
Which website and what effect size? It's a bit hard to educate third parties through intermediaries, especially when I don't even know what they actually said.
It's awfully hard to eyeball a distribution, but one can usually say what it's *not*.  In this case, the right tail is so heavy that the Gamma shape parameter $k$ has to exceed 1, but the nonzero mode shows it has to be less than 1; *ergo*, no Gamma is going to be a reasonable approximation for most purposes.
Not in general.  You can go further with knowledge of the joint distribution of the $X_i$'s, though.
I dont'quite understand this. I understand that by compuate part, you create a holdout and testset. I already got those. Then you perform OLS on the testset and save the residuals. But then I'm lost. You then just run descriptives on the residuals from the trainingset?
Machine learning as opposed to what? (I'm serious, not sarcastic here.) Without an alternative hypothesis, as it were, I think we'll end up following in the footsteps of other threads that ask for the difference between AI, machine learning, and pattern recognition (etc).
No, not ANOVA but logistic regression. That is one way to determine if the rates are different.
I don't think that I can use a repeated-measures ANOVA, as the treatments are based on different samples, i.e. the subjects are not the same for the different treatments.
1. This will be more easily done using the ANOVA format/framework, though mathematically ANOVA and regression are equivalent. 2. What do you mean by "based on the control factors without the levels"?  3. If you use just the optimal level for each factor you'll have no way to assign coefficients. Regression requires that the factors have the opportunity to vary, so you can show how the outcome varies with them.
I see. CV performance is pretty good in the example I mentioned above. Does the shape of the response really matter if the residuals look fairly normal?
could be right if what you want to test is whether the observed and expected have different means. But in one place you just say "different" without defining exactly what you intend. Did you want to test for a difference in means?
If the quadratic function is both increasing and decreasing in the domain of the data points, then the linear regression will miss the association between $x$ and $y$. (It would report a slope close to 0.) Although some die-hard statisticians discourage it, it is often useful to plot out the data before your analysis, if possible (i.e. exploratory analysis). If the data is highly multidimensional, you may wish to consider using mutual information to first determine whether there is any association between the response and the predictor variables.
"One intermediate strategy is to choose a large number of random nodes, similar to what happens when you initialize a neural network, and fix the input-to-hidden weights. The optimization over the *-to-output weights stays linear." => you mean that there will be a single global maximum for the solution in this case?
Sorry, but a good example on why one _should_ always start with a plot and not confuse likelihood or its maximum as involving derivatives
Because without constraining/regularizing/whatever to dramatically reduce the way that the parameters grow, you can rapidly overwhelm *any* ability to estimate - there's no point in having 2^40 points if you have 2^60 parameters. More points simply doesn't cut it - even if it wasn't prohibitively expensive, there are all manner of other constraints that will bite (space, time, ...). Hence, for example, the focus in statistics on using additive models (possibly after transformation) with nonparametric methods.
Since you have used the `normal-distribution` tag, which part of the problem do _you_ think involves the normal distribution?
I'm glad you figured this out. Any thoughts on which normalization method makes more sense? I've actually gotten worse results using normalization in glmnet (for lasso) and I'm still not sure why.
Thank you for bringing this interesting and little-known approach to our attention.
I should have noticed before that the Laplace distribution is symmetric, so that is something I can add to my write-up, thanks a lot!
@Dalmo MDS needs a dissimilarity; he is asking how to compute a reasonable similarity on such data. Afterwards, he can use MDS to project the data to Euclidean space.
@mpiktas $p(y)$ is not given. I have added example tables, but I am not sure if these numeric values are correct since I cannot calculate correctly.
I think John Tukey might disagree http://en.wikipedia.org/wiki/Exploratory_data_analysis ;o)
"curvilinear" can't mean just "quadratic". If your question boils down to how I do fit a quadratic, then the answer is using a linear and a squared term as predictors. Newtonian mechanics aside, there are rarely theory-based reasons for fitting quadratics; at best they are used empirically.
Site and SiteSize look like they will be perfectly colinear - each site has one size, right? And they are all different? If so, I don't think you can include both.
Could you please give the full reference to "Chris Bishop's book"?
Hi and welcome to CV. With questions that are routine book-work like this (this sort of question is explicitly solved in many textbooks), the treatment is somewhat different, as discussed [here](http://stats.stackexchange.com/tags/self-study/info). Please read the link and modify your tags and the body of your post accordingly.
(meadian, not mode - cheers)
install.packages("TeachingDemos", repos="http://R-Forge.R-project.org")
OK, so for cortisol, you definitely want some way to account for diurnal profiles, e.g., with splines. Unfortunately, I have no idea at all about SPSS. Would some example code in R help you? (I'd rather not spend a lot of time on this unless it would really be helpful, and if you are stuck with SPSS, you would probably better look for a SPSS guru.)
I am already using junction tree - I am trying to figure out if there is some way to do this when I can't guarantee a tree of bipartite components.
i'm using the standard error to estimate a confidence interval. true, this could be directly estimated using the bootstrap, but i'd like to ultimately use the formulas given for the SE approximation.
Welcome to the site, @StephenCrowley. If you have your own question, please do not post it as ( / as part of) an answer. Click on the gray "ASK QUESTION" button at the top of the page & ask it there. If you have a question for clarification from the OP, you should ask it in a comment to the question post above. (Although frustratingly, you cannot do that until you reach 50 rep.)
+1  Your discussion in point 1 leads to the crux of the question: how is one to test a *post hoc* hypothesis that was developed (essentially on the spur of the moment, it seems) from an examination of the data?  It's unclear what the hypothesis is even supposed to be.  This is the old data-snooping problem looming large.  A good case can be made that the proper answer is that trying to apply the mechanics of hypothesis testing to such one-off observations just makes nonsense of statistical significance.
Are you saying you want to know if there is a statistical relationship between any of the first 4 scales and any of the last 3 scales?  Or is your question more sophisticated than that?  In any case, keeping the scale scores (rather than dichotomizing) will give you more information and should result in a more powerful statistical analysis.
@whuber But at the moment, we have no reason to suppose that it is bad either.  And I am not referring to the absence of any indication of error in the estimate that is given to $\\lambda$.  But the error in the estimate for $\\lambda$ is not the same thing as the standard deviation.  From my perspective, if $\\lambda$ was known with certainty, what is the use of a std dev estimator?  For normal, if mean is known, then standard deviation is still worth estimating.  But, if mean and std dev of a normal are known, what is the use of a kurtosis estimator?
I would suggest to stop using the term "arithmetic mean" in order to refer to the "sample mean". Let me put it this way: the "sample mean" _is_ an arithmetic mean. And yes the sample mean is an unbiased estimator of the expected value of any distribution, where "unbiased estimator" means, that the expected value of the estimator equals the true value that the estimator estimates. In our case, since the sample mean $\\bar X = \\frac 1n\\sum_{i=1}^{n}X_i$ attempts to estimate the expected value $EX$ of the distribution that _all_ $X_i$ follow, we have $E(\\bar X) = E(X)$.
df should not be 0, something is wrong. If you remove an effect and rerun, there should be a difference in the df of at least 1 (if the variable removed is continuous) or more than 1 (if it is categorical with > 2 levels)
Thanks for the response.  I have a couple of follow up questions to your response.  For plot(analysis) I'm able to see residuals vs. fitted, a q-q plot, etc.  Is this what you are referring to by "representation of your model"?  Also, assuming I know my model is quadratic, could I do something like: lm(y ~ x + I(x^2) + I(x^3)), or is there another way I could do it assuming I have used nlm(y~x^3+x^2)?
@whuber, thank you, I suppose $(N_i/N)/S$ would be better, yes. So, what should I use in this case as $\\sigma$? $\\sqrt{N_i}/N/S$, not $\\sqrt{N_i/N}/S$, I suppose?
see http://glmm.wikidot.com/faq#overdispersion_est (by the way, did you google "lme4 overdispersion" ... ?
@Andy Thank you!  That's a real find.  This software looks like it reproduces GeoDa's capabilities with the addition of logistic regression and GWR.  I look forward to exploring it.
I guess you mean "Strongly disagree". You can do all kinds of analysis on it, yet it depends on what type of arguments you want to make.
I have some questions about the usage of time for building a Bayesian Network, I added these as extra comments under my first question. @Learnerbeaver
As you can see from my update (below) I realised this soon after completing the post - but many thanks for your help!
@NRH actually it depends upon the ratio $\\mu/S$, so the density is independent of $S$ only if the mean is zero.
@ Peter Flom....ok the questionnaire consists of 15 items and each is answered according to the 6 point scale.... would that qualify as interval?
The R package irlba is fantastic for SVD on sparse data, which will get you most of the way to PCA.
Are you only interested in the severity of those who do have cancer, or also of the characteristics of those who develop cancer compared to those who don't?
Thank you - I will look into the instrumental variable test. And thanks everyone for very helpful comments.
Becouse in this case the conditional probability will be different from prior probability: __P(toxic|X=True)=0.75; P(toxic|X=False)=0.25__ against prior __P(toxic)=0.5__
Thank you. I met a optimization problem and the constraint is  
$Pr\\left( \\sum_{i}^{}{x_{i}+a_{i}}\\leq c \\right)\\geq 1-p$  
where $a_{i}$ is random variable.   
So I wanted to decompose the constraint into separated constraints:  
$Pr\\left( x_{i}+a_{i}\\leq b_{i} \\right)\\geq 1-p_{i}\\; \\forall i$  
$\\sum_{i}^{}{b_{i}}\\leq c\\; $  
$ \\sum_{i}^{}{p_{i}}\\leq p$ It seems that they are not equivalent. Thank you.
Welcome to the site, @RiccardoCavallari. Please don't sign your posts. Notice that your username (with a link to your user page) & your flair are automatically added to your posts. Regarding your question, do you care if the mean or SD is similar, or only if the shape & ranking is similar? Could you just correlate the 2?
As @Glen_b indicates, this beast has a simple name, cube root. http://www.stata-journal.com/sjpdf.html?articlenum=st0223 has more on cube roots. Some but not all of the content is Stata-specific.
You need some amount of measure theory even to define random variables, expectations, and variance. Moreover, this theorem is false unless it is understood that $X$ is a constant *except possibly on a set of measure zero*. What, then, are you really looking for in a "non-measure theoretic argument"?
I think that you should conceptualize what is "centrality" or "purity". For example, which cluster is more topic centered for you: this `{a,b,c},{a,d,e},{b,d,f}` or this `{a,b,c},{a,b,d},{a,e,f}`? Both have the same number of matches inside (3).
Are you interested in interactions between factors? If this is not a crucial part of your analysis then you may run separate MANOVA (or Repeated Measures) and consider a correction in your type I error.
The same logic (taking "absence of evidence in favor H1" as "evidence of absence of H1") essentially underlies all goodness-of-fit tests. The reasoning also often crops up when people state "the test was non significant, we can therefore conclude there is no effect of factor X / no influence of variable Y". I guess the sin is less severe if accompanied by reasoning about the test's power (e.g., a-priori estimation of sample size to reach a certain power given a certain relevant effect size).
You can use any integration method you want. But in this case you do not need to use any.
Also see [Python as a statistics workbench](http://stats.stackexchange.com/q/1595/2981) for some discussion of R and Python for data analysis.
Argh, no. The REASON that R has imported your numbers as factors is because of the embedded comma. Changing them to integers just means you're swapping one meaningless result for another. What you SHOULD do is go back to your Excel sheet, remove the formatting, re-export and re-import your data.
@RomanLuštrik, a Poisson regression is something to consider, but the choice should be made based on the science, not the data.  The above data has non-integers for $y$, so there would need to be some type of weight or observation window for the non-integers to make sense in a Poisson regression.  It should only be considered if the response variable represents counts and the science behind the data is consistent with the Poisson distribution.
@Pedro: I suppose you can click on the "share" link at the bottom of this answer. It should be a stable link. [Math.SE has a citation mechanism](http://meta.math.stackexchange.com/a/8218) , which doesn't appear to be enabled on this site, but you may be able to adapt it.
@Glen_b Yes--the short durations lend importance to the role of the time-reversal machines! :-)  Taken collectively, our comments indicate that although the thrust of this question is evident, it will be impossible to answer in detail without stipulating the meaning of the parameters in the "N" and "Gamma" distributions.
Assuming that the expectations exist (cf. Paul Staab's comment on his answer), the [law of the unconscious statistician](http://en.wikipedia.org/wiki/Law_of_the_unconscious_statistician) gives $$\\begin{align}E\\left[\\frac{X}{Y}\\right]&=\\int\\int\\frac{x}{y}f_{X,Y}(x,y)\\,dx\\,dy\\\\&= \\int\\int\\frac{x}{y}f_X(x)f_Y(y)\\,dx\\,dy\\\\&=\\int xf_X(x)\\,dx\\int \\frac{1}{y}f_Y(y)\\,dy\\\\&=E[X]E\\left[\\frac{1}{Y}\\right]\\end{align}$$
Dear Maarten Buis ! Nice explanation. My written Upvote to you :) ..my current reputation score does not permit me to vote :( !!
One way to understand the issue is to consider a different model, the ordinary multiple regression model.  This model involves a residual variance.  Stepwise variable selection results in an underestimate of this variance.  Two unbiased estimators for the variance have been developed: (1) fit a full pre-specified model and compute the residual variance; or (2) run stepwise selection or other data mining procedure and use Ye's generalized degrees of freedom (d.f.) to estimate the "effective d.f." of the modeling process (close to # candidate variables), then use it to estimate the variance.
Thanks for giving a source, but are readers expected to read the presentation to seek out everything else? You are asking (very busy) people to do you a favour; it's not a good idea to expect that people will work at your question if they can't understand it from reading.
Sorry I lost the rest of my reply here - I just wanted to say that I reached the same conclusion using ARCH LM, too. Thank you.
The `ols` function in the R `rms` package can use numerical optimization to find the optimum penalty using effective AIC.  But you have to provide the maximum penalty which is not always easy.