tttjjj/elt_bench huggingface dataset:
Thank you both for the very thoughtful and helpful answers. I really appreciate it and will follow through on the suggested reading.
But it's more than interpretation: my point is that your transformation ruins the defining property of the interval. For instance, suppose $\\log(x)$ has a standard Normal distribution and there are $100$ iid draws. The usual symmetric $5$% two-sided (Student t) CI for the mean of $\\sqrt{x}$ has coverage of about $94.6$%, close to what we want, but your back-transformed CI for the mean of $x$ only has coverage around $32$%. That's a big error, regardless of how you choose to interpret it.
+1 One *huge* problem with assuming a uniform distribution of the parameters is that ML problems are often reformulated by exploiting the invariance of their solutions to reparameterization: however, that would change the prior distribution on the parameters. Thus taking an "expectation" as if the parameters have a uniform distribution is an arbitrary artifact and can lead to mistaken and meaningless results.
it is mathematics heavy book therefore it may be difficult for self learner to follow.
I don't know where you heard that Lasso handles the problem of collinearity, that's absolutely not true.
30 tests will need a huge sample size to keep the experiment wise error rate low.
I would think in terms of a regression model using indicator or dummy variables for vegetation, but make sure you plot your data first. Consider also log scale for erosion, or more generally a scale on which variability of erosion is about the same in each category.
The error message is pretty clear, isn't it? The test itself may work for any sample size, but the sf.test function doesn't. Also, tests of normality are of little use. With such a large sample size, the null hypothesis is almost certain to be rejected if it's real data (as opposed to simulated data).
PLS regression maximises factor scores (which are computed as the product of raw data with loadings vector(s)) *covariance*, not *correlation* (as is done in Canonical Correlation Analysis). There's a good overview of the `pls` package and PLS regression in this [JSS paper](http://www.jstatsoft.org/v18/i02/).
I have tried with R=10000 instead of R=1000 (and specifying type='bca' instead of type='all' since this is what you really want) and it works. So my conclusion would be that what is causing this error is not enough bootstrap replications... but I cannot say more...
How many clusters to you want?  What do you want the users who are the same cluster to have in common?
The evidences are words in documents and $t is a specific topic from a topic set (in topic modeling domain). I have the distribution probability of topics per word, and I would like to determine the topic when a subset of words is observed.
I don't understand the effect sizes for the difference in gender between light and dark hair. Gender is dichotomous, so what are those effect sizes supposed to represent?
I should probably rephrase, the answer then. My point was exactly that the crux is in the definition of the "elbow". Additionally, I tend to not trust the application of some change-point procedure to (time-series) data, as I never know how much does the authors definition of the "elbow" differ from mine. Therefore I advocated creating a personal rule for identifying the "elbow", rather than using some of the shelf tool. You might not have a statistical test, but at least if you create it, you know what it does and how it tends to label curves.
This may be drawing on definitions in some literature. It does not seem related at all to the mainstream statistical sense in which "confidence" implies "confidence interval". Giving some sources and/or more explanation would help greatly. Otherwise $(X|Y)$ suggests only $X$ given $Y$; are you reaching towards conditional probability? In any case, how does your last sentence relate to the rest of the question?
You'll probably need to provide raw data, and not just a correlation matrix, if you want to compute regression scores. Try this instead: `fac(data.frame(v1,v2,v3,v4,v5,v6), nfactors=3, rotate="varimax", scores="Bartlett")$scores`.
Concerning the reply to the second question: there actually is a sense in which regressing $X$ on $Y$ is fine.  It gives you an estimated relationship $X = \\widehat{\\beta}Y + \\widehat{\\alpha}$.  Algebraically inverting this yields $Y = (1/\\widehat{\\beta})(X - \\widehat{\\alpha})$.  In light of this, your reasoning is insufficient, because it does not explain why this derived relationship is incorrect.
Sorry, I should have explained better. The right axis shows normalized variables so that counts and inverse counts can fit onto the same axis. The actual counts can vary from 0 to a some larger value (here between about 2 and 85) and are what I am actually trying to use as my weights at each data point. The "x" axis is a size where independent measurements are made for each raw data point. These counts relate to the precision and accuracy of my measurement, so as counts get smaller I expect both more noise and less accuracy in the raw data values shown on the left axis.
@Denise: Have you tried Poisson regression on the two events and divide? Might work a lot better than the division you did previously between the two improper regressions.
@conjugateprior In general, yes, but for my particular question, no. It still discusses models where the standard deviations of the groups are not modelled, like in the first model sketch in my question.
Do you know the standard error of the instrument/method?
+1 Thanks for your INFO. Probably I might get more by reading "practical guide to training restricted Boltzmann machines" paper.
@Patrick - no, definitely not.  In classical hypothesis testing, $\\Pr(H_0|\\text{anything})$ makes no sense.
HINT: What is the interpretation of the combinatorial term in the first density you have provided? What exactly is the interpretation of that probability? How is the ordering of events accounted for?
Yes, Just take a look at the book's link: _The BRMLtool box is provided to help readers see how mathematical models translate into actual MAT-LAB code._
You can sample from your data set to obtain a balanced sample or penalize the model for missclassifying the minority class. Interesting article here: http://statistics.berkeley.edu/sites/default/files/tech-reports/666.pdf.
See synonymous examples of [*interval regression*](http://stats.stackexchange.com/a/65184/1036).
Please show us your thoughts about tackling this problem and share with us the progress we have made, so we can focus on what will help you understand this material.
Thank you for the response. Unfortunately this skips most of the key detail that I need, about how to implement a kernal density method for this specific problem, or how exactly to use a variable width kernal. I also forgot to mention (and have now editted in) that we can not rely on the number of flips being large for a given coin (though the number of coins is large)
Provided that you randomized properly, there is no such thing as "sample size bias".  You cannot reliably measure tail behavior with _n_ = 16.  It just isn't happening -- you can't reasonably expect to get much beyond the 5th and 95th percentiles, absent a miracle.  As Goldberger said, the cure for micronumerosity is to take larger samples.  The diagnostics might tell you that your model is inadequate, but whether the problems are due to what the diagnostic is nominally looking for or due to lack of fit is an open question.
Could you explain this a little bit further?  I don't understand why you say that a multinomial distribution is derived from $n$ independent *variables*.  Do you mean outcomes?  The outcomes are definitely dependent since they're mutually exclusive.
Thanks for your answer. That solves the problem of bounding.

For my data it goes to 1 very quickly for my data so I guess the next thing I need to do is to scale this information to concentrate on the interesting range which I could do based on the history of it without fear of leaving the bound, just hitting the limit.
@user1172558 Done. Plus extra comments at the end. I'm not sure why we have a relatively large divergence in the posteriors for our different methods.
See also this nice blog entry on the Stata blog written by Bill Gould - http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/
If you transform variables, it should be to address assumptions of the model; OLS assumes that the residuals are normally distributed, not the variables.
No statistical answer is possible without some probability model for how such graphs might naturally vary.  What is your model?
Note that you should literally print out one of the guideline [checklists](http://www.strobe-statement.org/index.php?id=available-checklists) and go through the paper to be reviewed point-by-point. This is what the reviewers at a reputable medical journal would do. An example systemic review that uses this approach to gauge the quality of tumor marker studies is available [here](http://www.nature.com/bjc/journal/v102/n1/full/6605462a.html).
But are $\\alpha$ and $\\beta$ even in $p(t|\\alpha,\\beta)$? That's what @JuhoKokkala meant. The multivariate normal density isn't typically parameterized by things called $\\alpha$ and $\\beta$.
The expected cost can only be evaluated if you know the false-positive and false-negative costs, which are not necessary for calculation of the AUC, which is a good statistic to use if the costs are unknown or variable.
Hi, thanks for the answer, I had tried to do as you said but got an error. I tried it again and it worked. I took a sample of size 100 instead of 1100 the first time and the error was :
 `Error in stats::arima(x = x, order = order, seasonal = seasonal, include.mean = include.mean, : too few non-missing observations`
 I didn't realize what it was about then... Thanks anyway, I guess I can go back to work !
 Regards.
Well for starters, in your formulation, there's *no noise term at all*. It won't fit much real data without one. Did you mean to write an AR model?
Though not entirely uncommon for this type of thing to occur some people might like to see this as a teaching or learning case.  If you could share the data it would be great.  You also might get good feedback on your specific problem.
Is there more than one tree per site? If not, then this may be a nomenclature problem. If yes, then I think you do need another random effect - the model would be nested both in space and time.
This is very helpful but here is a footnote on "covariate". Some people use that term _much_ more broadly for any kind of predictor or independent variable. (Many other synonyms exist, naturally.)
If you `plot(m)` you should get 4 plots, including a scale-location plot, which should be easier to interpret - if the mean of the scale location plot clearly changes, you don't have homoskedasticity.
I think @NickCox already provided a good answer, given your situation. Just looking at the plot and drawing conclusions is also perfectly fine. You don't need a “test” at all costs, especially if you are confused about what a statistical test can tell you. One thing that might help you understand what you are reading here and elsewhere: From your comments, it seems that you are trying to look at the relationship between two variables or two time series, not two distributions. Better just forget this idea of “comparing the distributions” and read basic material about correlation.
You could help us by specifying the book and providing its definition of risk!  This word "risk" means so many things that it's practically impossible to reverse-engineer a formula like this.
Alright, thanks a lot for the detailed answer. Do you by any chance happen to know how to interpret the output of the acf2A() function, which returns a matrix?
What does your model look like? What are the dependent and explanatory variables?
Scott's pi makes the assumption that annotators have the same distribution of responses. This means that the classifier should have the same prior probabilities of the classes as the the dataset. Many classifiers do enforse this constraint. For example, the true classes may be {a,a,b,c,c}, and predictions may be {a,c,b,c,c} - the prior probabilities of the classes are not the same, but the prediction accuracy is good.
Is this supposed to be an answer to your question? If so, would you mind elaborating on it a little, to make it more unambiguously an answer?
I did not follow the details on the computations you describe but the basic intuition (split the dataset multiple times and repeatedly evaluate the model on the hold-out data) is in fact a well-established technique called “cross-validation”. I don't know if this is a valid approach for your particular goal but using this keyword should help you find some relevant literature.
Thanks. I realized after I posted that this would be the correct way to enter the data. So I agree with this change.
@Stephan is hinting that you should read our [faq], Linda, and heed its guidance concerning how to ask a good question, because that will help you elicit appropriate and useful answers. It would be nice to see you modify your question to reflect your own thoughts and the research you have conducted to get an answer before you came here, so we can focus our replies.
"which you have under normality" You mean the normality of $\\bar{x}$, or are we assuming normality of the $x_i$ that we're averaging to get $\\bar{x}$ ?
Almost: replace *a* by 0 and divide by *k!*.
It's hard to help with this little info. Maybe explain what your variables are, what you goals are, and post some data if possible.
Can you write down how they're specified mathematically? There's definitely some ambiguity about what a linear model is and about what a mixed effect model is.
Define "optimal"
(+1) For being explicit. Good answer. :)
*As a result, points above the mean can't typically get too far above the mean (because otherwise the mean would shift!). Near p=12 the endpoints don't really "push it up" the same way.*

Too perfect. This is a great explanation.
Thank you very much for the explanation of xcorr()! Do you know why I get a different output in 1) ? From the documentation I have understood that xcorr and xcov should be very related.
Although I wrote that a general solution could be complicated, a solution specific to your data might be obtainable from the formulas here. All that matters is whether the particular $T_i$ you are interested in has any tied values. If not, the same formulas apply, because there will never be any question as to whether it is the $3$rd ranked value in the second group. If it does have ties, you can sum over the possible ways in which $T_i$ can be tied for third.  Because this can get tricky, I recommend checking any such solutions with simulations of small datasets.
Also, I am not wedded to this idea -- I just thought it might be more powerful than K-S or Chi-squared at low sample size. Forming the CDF of 5 samples strikes me as a bit ham-fisted. My boss wants me to perform a test of this sort and I just want the best tool for the job, and I don't care if it's my idea or something totally unrelated.
I think that the argument at the end of your answer is problematic. You're not just throwing out small differences with broad categorizations of the test, you're potentially throwing out the pattern of the relationship between the test and the effect score (or whatever the questioner uses). There could be a curvilinear pattern that is quite dependent upon all those individual points to reveal adequately. I only used linear as an example. There are so many good options for dealing with non-linear these days that breaking it into categories is never a good idea.
In infectious diseases epidemiology the infection path usually has two parameters: virulence and contact rate. Virulence is how likely a person will get infected upon a single contact, and contact rate is frequency of contacts. Your 30% is currently unclear... if it's virulence, holding contact at 1 person/day, then there should be 200*0.3, if it's contact rate is 30% of the people with a virulence of 100%... then I guess the town is going to be over pretty soon.
@chl Not yet; but thanks for reminder.
EDIT: actually, you are interested in the evaluation of `Uniform(..)`, so I would code it as `sigma=  Uniform("sigma", 0, 50); precision = sigma**(-2)` and use precision in the observation variable.
@Remi.b I think some of the confusion results from the way you use the term “effect size”. It is more a concept (the strength of the effect, e.g. of one variable on another) than a single value. Consequently, there are several effect size measures and it's not clear what “computing *the* effect size” would mean. Even the raw difference in means between two conditions is a perfectly reasonable (unstandardized) effect size measure. If I understood you correctly, you are specifically interested in Cohen's $f$ to carry out a power analysis? Is that right?