tttjjj/elt_bench huggingface dataset:
'variances equal' simply means that the population variance for one thing is the same as the population variance for some other thing or things. The distribution of the variance is restricted to the non-negative half of the real line - so variances can't be normal, except in a limiting sense (a variance is a kind of average, and the CLT will apply to it if the usual CLT conditions apply, so I think you'd need at least 4th moments to exist, for example)
You state that for the majority of problems need only one hidden layer. Perhaps it is better to say that NNs with more hidden layers are extremly hard to train (if you want to know how, check the publications of Hinton's group at Uof Toronto, "deep learning") and thus those problems that require more than a hidden layer are considered "non solvable" by neural networks.
This is one reason the concept of [measure](http://en.wikipedia.org/wiki/Measure_%28mathematics%29) had to be invented. Problems like this one show that probability is a number that is associated with certain kinds of *subsets* of a "population" rather than with individual members of the population. An important consequence of this generalization was the realization that in uncountably infinite populations, not every set can always have a probability associated with it (in a consistent way). In particular, probability generally is *not* a "ratio of the number of favorable cases to all cases."
Dear robin girard, I think your answer is fine as it stands. Thank you!
Thank you very much for the suggestion, I read the given link and a number of more books and articles, however couldn't find the answer that I am looking for. That is in cases where the overall percentage in classification tables for the test model is less than that of the constant only model, how to proceed. The objective of the analysis is to check if certain indepandant variables can individually predict an outcome when thet are acting together. There independant variables were found to be significantly associated with outcomes in univariant models.. Thank you
Can you provide us with examples of such questions? Or very briefly report what those particular constructs are and how they are assessed (is this a series of numerically scored questions that can be organized into different scales?).
I see it now. Because $S$ is symmetric then $a^TS = S^Ta^T = Sa^T$ same idea for $a^T(\\overline{X}-\\mu_0)$
Thanks.
@user4278 I also found some hits with Weka (e.g., [here](http://weka.sourceforge.net/doc/weka/datagenerators/BIRCHCluster.html)) but I didn't look further.
So I just don't know. I'll be sure to look to look at those 2 papers; I was sure I couldn't be the first to apply the idea but didn't find those. I'll think about writing something for _Significance_, since the articles I see look cool.
@Damien - but you said "standard deviation of the difference in means". Rather, the residual variance is the within-population variance. The correlation is not so meaningful for the binary x case, and so the formula with $(1-r^2)$ is not so meaningful for the comparison of the means of two populations.
@talischen Sorry: I have just realized that your question is how to estimate the mean of each population, not how to compare the two means. As said at the end of my post we can make a confidence interval for the ratio of the means if we assume equal variances (and log-normality). There probably are some known methods to make a confidence interval for the mean of a log-normal distribution. The profile likelihood method is easy to implement but it is not reliable for a small sample size, so is the bootstrap.
Thanks. Can you give me some examples with actual values plugged in?
If it is just a brownian motion, and not a general SDE,
you can multiply the sample you already have 
by the inverse of the Cholesky matrix:
this gives you a sample from N independent brownian motions.
You can then interpolate them separately 
(these are independent brownian bridges), 
and multiply the result by the Cholesky matrix.
Cheers! The thread behind this link is also a good source for understanding this :)
@baris_a I changed the title to better reflect the content of your question. I hope that's ok with you?
I have done a lot of number crunching, one website and few administrative scripts in R and they are working quite nice.
I liked your nice philosophical discourse of clustering. Regarding dimensionality reduction, I'd better used words "tecnique one should get reasons for" instead of `technique one would like to avoid`. Also, I think you ought to expand your notice about `Euclidean distance don't work well` since you touched that.
"Too big" would be a judgement that depends on circumstances and who is doing the judging. It's hard to say much without context but it's generally a case of "what would matter" vs "what really wouldn't matter".
Keeping in mind that seeing that your data looks "somewhat logarithmic" isn't particularly scientific, what do you mean by 'most scientifically correct', exactly?
I'm not sure if multicollinearity could be interesting. Say you had some outcome `O`, and your predictors are `Income` and `Father's Income`. The fact that `Income` is correlated with `Father's Income` is intrinsically interesting, but that fact would be true no matter the value of `O`. That is, you could establish that `O`'s predictors are all collinear without ever collecting your outcome data, or even knowing what the outcome is! Those facts shouldn't get especially more interesting once you know that `O` is really `Education`.
+1--very clear answer.  Welcome to our site!
Also, ideally, your loss function is as personal and subjective as your prior is.
Do you know what k1 and k2 are, and can you calculate them? If so, then no problem! Any svm library would work!
I think the question is a little unclear. "Data is good enough" is not clear. I didn't downvote your answer, I'm just wondering whether it is what lovekesh wants to know.
I provided links to step-by-step guides to SPSS MIXED procedure in http://stats.stackexchange.com/questions/24662/how-to-organize-the-data-for-this-repeated-measure-within-subject-setup/24686#24686 There is also some relevant material at http://www.floppybunny.org/robin/web/virtualclassroom/stats/course2.html (week 6)
(1) $g$ and $L$ are two different names for the same thing in the two different notations. (2) Yep.
Colin, I tried to figure out how to expand the Wikipedia formulae to non-equal m_i's, but didn't have any success. Can you please help me with this? (sorry)
Thanks; and based on the answer by @tharen and comment by G Jay Kerns, "relative margin of error" is the terminology we now use.
I am uneasy about some aspects of this procedure; my example just points out one of the reasons why.  The $L_i$ are strongly interdependent, so it's unclear which "multiple hypothesis testing procedure" would be applicable.  Moreover, the $L_i$ will depend on the density estimator--as you point out--so that opens up a whole battery of questions about how best to estimate the densities for this purpose.  These are problems even with parametric univariate outlier detection procedures, so I don't expect them to be any easier to solve in the multivariate case.
I would not recommend binning into groups.  Group boundaries are arbitrary and the resulting predicted values will have higher mean squared error due to taking more degrees of freedom while having worse fit (it assumes piecewise flatness).
Gee Frank You could have plugged my book too! But I gave you a +1 anyway!
@JakeWestfall  Thanks for your comment. From the Residuals VS Fitted values plot. I suppose it should be randomly around 0. Besides, the bottom-left and the top-right part of the data are randomly distributed if you look at them individually.
Thanks for the note.  I think that $D_{xy}$ and $C$ are not bad for describing the predictive discrimination of a single pre-specified model.  But as you said, they lack power for doing more than that.
ya, i wish people would sign up there faster - it will be awesome!
It's not clear to me what you mean by "specify the parameters"; aren't they part of the fitted model already?  Can you be more clear about why `simulate` isn't what you need?  (PS.  You might also look at `sim` in the `arm` package which simulates the uncertainty in the fitted model as well.)
@AdamO yes I was refering to that work. I couldn't find the technique name here, does it have a different name? : http://en.wikipedia.org/wiki/List_of_machine_learning_algorithms 

Also when you said "(there were 100s)", did you mean there were 100s of people who used that technique in the competition? Or 100s of winners who achieved the same results with different algorithms?
Thanks, @Jonathan. The first answer isn't really what I was looking for... perhaps I need to rephrase the question. The list of faux pas was quite useful, however!
Does each of your datasets contain the same number of samples?
I'm not sure who "they" are, or what they mean. The ordinal logistic regression model estimates a single set of betas, and then a set of l-1 thresholds or cutpoints (where you have l levels). If you have 0, or sufficiently few observations in a level, the cutpoint cannot be calculated. That would be my best guess at what they meant, but I don't really know.
Thanks for this answer and for the references (+1) and for confirming my suspicion that I'll have to "make my own" to handle this problem. I agree that barriers like lakes - where crimes literally cannot happen - may be sensibly removed from the "space". Regarding your sidebar - obviously there are issues of interpretation but in a continuous space model like this (which I have good reasons for needing to do in this project), you have the practical consideration of needing to represent covariates continuously, so... Aside from that, there is literature regarding how alcohol outlet _density_,
@rolando2 I got stuck on 2, as I'm normally only worried about individual cells when I'm data cleaning, like I am doing today, and then I just do automated searching and recoding based on cell contents, not cell vector position. :) 8 hours of string cleaning and counting... /sigh
I don't follow your argument at all.  Isn't the question whether or not when n$_1$>n$_2$ P{X$_1$<=k)<P{X$_2$<=k} for each k<=n$_2$?  I don't even think this is true.  It could depend on p.
@BenBolker thanks -- every now and then I arise from the depths of Unix and have to watch my Caps key.
A couple of small notes about the scales of measurement that you list: (1) Only the scale of the response variable is of primary importance; (2) The concept of measurement scales is largely overrated, IMHO; (3) I wouldn't call a count variable (i.e., your #5) a ratio scale variable--it's sort of true, but not really the right way to think about it.
(if you take more than five minutes to write a comment ...). What I wanted to write is that you can think of the averaging as a matrix multiplication. The rows in the middle will have 1/30*[1 1 1 ...] before the diagonal. The question is, how do you deal with points at the borders of your vector in order to make the matrix invertible. You can do this by assuming that they are a result of averaging over less elements or you think about other constraints. Note that while a matrix inversion is an easy way to understand it, it is not the most efficient. You probably want to use an FFT to do that.
Actually the default arguments to the `svd` function ensure this already. See output from `args(svd)`. If you inspect the code for `prcomp` you will see it calls `svd` with `nu` set to `0` and the default for `nv`
@whuber what do you mean by substracting the min from the max? I thought when doing a chi squared test I should calculate the  expected range by the formula of the chi squared test the relative frequencies: $e_i=n*p_i$ and the absolute frequencies.
@Procrastinator Thanks. Note that the two examples you offer are both special cases of the general definition I have supplied: the central symmetry generates a two-element group of isometries and the spherical symmetries are also a subgroup of all isometries. The "elliptical symmetry" in the link is a spherical symmetry after an affine transformation, and so exemplifies the phenomenon I pointed to with the lognormal example. The "angular symmetries" again form a group of isometries. The "half-space symmetry" [sic] is not a symmetry, but allows for discrete departures therefrom: that's new.
$x_1$ is the number of k12-teacher-librarian answers you've got doing the surveys.
$Y_i$ is a different variable. What I mean is that the variable that dictates your sampling probability (usually disease status in a case control) is not the same as the outcome variable - think secondary analysis of a data set. For example, say the sample was generated by systematically sampling drug users and an additional (frequency matched, w.r.t. certain covariates) set of non drug users but the outcome variable you are studying is some other behavioral measurement. In this case the sampling scheme is a nuisance. Thanks, btw!
"most practical" will depend on how important precision is; and everything will depend on the stability of the process.  Can you give any more context?
Calling this "censoring" implies you believe that some proportion of those reporting not being sick actually were sick but that some mechanism prevented the true positive values from appearing and replaced them with zeros. Usually it also means you know *which* observations were censored in this manner.  Is this what's really going on, or are you using "censored" merely to mean there is a natural lower bound of zero to the values and you would like the KDE to respect it? If that's the case, your question has been answered at http://stats.stackexchange.com/questions/65866.
Have you tried to use `tryCatch` or simply `try` to handle errors?
What do you mean by "make it"? Does that mean "estimate the parameters"?
Can't you use the same MLE routine to compute a point estimate and s.e. for $p$ directly?
Thanks all.

The behavior that lead to the accuracy and time measures was very controlled. I'm looking at the results from an exploratory perspective, while trying to ask why the inaccuracies occurred.

I'm unsure about "Each participant provides 6 values, therefore it is not unbalanced"? When subjects are correct, I have a different number of time measures between the levels, e.g. subject A got 23 correct in level 1, 16 in level 2, 10 in level 3. If I take the mean correct per level per subject can I just ignore the number of correct answers & the difference in the number of correct answers?
@PeterFlom I've added the tag. It's not homework but part of my exam-preparation.
This isn't exactly what I was looking for but it provides good general information that might be helpful to others. And seeing as it is the only response, I'll take it. Thanks.
Chapter 13 of Maxwell & Delaney (2004) "Designing Experiments and Analyzing Data" provides an in-depth treatment of exactly the answers you are looking for in your first two bullet points.
@FrankHarrell As much as I dislike the business strategy of SPSS, I have to frankly say that it's relatively learner-friendly: interface is simple and functions are well categorized. Plus some lecturers/teachers specify the software to go with their class, it does not have to be Lauren's own decision to pick up SPSS.
Note that `glm(y ~ x)` does not give you a logistic regression, You have to set `family=binomial(link="logit")`. Note the output says `Dispersion parameter for gaussian family`, not `binomial family`. If you do it right, `fitted(glm.mod)` actually returns the estimated probabilities, not the logits. You get the logits with `predict(glm.mod, type="link")`.
This all looks fine.  The histogram is the null distribution of differences in deviance between the full and reduced model.  Because you have a large (40) number of levels in your smallest random effect, the likelihood ratio test is accurate -- the p-values based on parametric bootstrapping and on the LRT match almost exactly.  You can also use `PBmodcomp` from the `pbkrtest` package to run these sorts of comparisons, or `KRmodcomp` (same package) to get a better (than the LRT) approximation of the p-value.
This is what lead John Myles White to comment that "[p-values measure effort, not truth](http://www.johnmyleswhite.com/notebook/2012/07/17/criticism-5-of-nhst-p-values-measure-effort-not-truth/)".
+1 to @Emer's suggestion that you think of panel (longitudinal) data modelling. There are variants of PCA that cope with this kind of data structure, but they aren't prominent in many statistical environments. Dependence in time is no barrier to PCA; otherwise it would hardly be routine in meteorology and oceanography. But the biggest puzzle is why you think PCA sounds "ideal"; for study of what influences what you are better off with some predictive model.
So if I have nothing but the t-table on paper, how do I know which p-value to use?
(1) The residuals will be awful because the $(x,y)$ data trace out a step function (having only five levels). (2) The narrow range of y-values (varying less than $\\pm 6\\%$ from their middle) indicates there is little difference between fitting $(x,y)$ or fitting $(x,\\log(y))$. (3) One would guess the $y$ values are either counts or rounded decimals that have been converted (via some kind of calibration information) to absorbance values. A maximum likelihood estimate suitable for *the raw data* ought to converge and do a good job of estimating $b$.
Okay, I deleted the other one. They said it was off topic anyway.
Hint: what are the implications of the characteristic roots being non-negative? Try to find a way to utilize that $y'\\Sigma y=y'E(X-\\mu)(X-\\mu)'y=Var(y'(X-\\mu))$.
Given that the scores are categorical, making a polynomial out of them isn't a good idea.  If you have categories (1,2,3), squaring them gives (1,4,9), but they are still categories, so there's no extra information there.
Thank you, that was helpful. I would still love to see some benchmarks though.
You can (now) get [robust standard errors from plain vanilla SPSS](http://www-304.ibm.com/support/docview.wss?uid=swg21477323).
I added a link to Wikipedia on CTT. Hope you don't mind - I didn't know it was a thing so it might be useful to others.
I found plotting the function quite interesting, since at the macro scale it is approximately linear, offering no improvement of the base error rate.  Only when $P$ is quite small does the voting actually start to really help.
+1 This answer has a lot of good advice for working with statistical functions on *any* platform.
Even if you have the whole population, we typically think of those as a sample of a larger *hypothetical* population. Eg, imagine studying a rare disease where you have access to every person alive w/ the disease. It's still possible that some different people will have the disease in the future.
I also assumed that the prohibition was never taken seriously in practice, so I was surprised to read this from Gelman:- " I certainly don’t want to return to the circa-1990 status quo in Bayesian statistics, in which it was considered virtually illegal to check your model’s fit to data."
@ttnphns Testing and estimation are different concepts: parameters can be estimated without any test being performed (*e.g.*, many opinion polls provide only parameter estimates and no tests) and not all hypothesis tests require anything to be estimated (*e.g.*, what is the Kolmogorov-Smirnov test estimating?).
$Xb^{ols} = Y_i -\\hat u$
I see curvature and heteroskedasticity in y vs x4 and y vs x5 which suggests an issue, but it also looks like something else is going on.
@PiotrMigdal Yes, I'm aware of that difference. Could you please explain why is it important? Please, take into account that I'm not a statistician...
@user1203297  Live and learn, we all do, check out the link I gave above as it's an easy way to impute missing values.  Just switch the `mean` in the code for `median`
@PeterFlom, edited, please advise
@RobertF - sounds like a fun study. I guess you need to decide: are you looking at a time period where your studying both patients and non-patients or are you only looking at those that have had an admission to identify predictors for readmissions. It seems like a very interesting question, identify "frequent flyer" risk factors - let me know if you publish. I've had some trouble implementing time varying coefficients, but that was mostly due to difficulties in explaining complex interactions - I ended up splitting my dataset into two periods, one early and one late period.
If you have one missing value at one of the variables then this case is entirely out for this analysis (listwise deleted), and the power of the result is decreasing. If you believe that you can replace one missing value with some other reasonable number (an option would be to find the mean difference for the other subjects between altitudes and calculate the analogous score for the subject with the missing value) then do that. However, if you have many missing values this is not a right thing to do and you may restrict your analysis to the variables with no missing values.
Interesting. I will try to find other functions or software that will give me p values for the effect as a whole.  Since I am interested in hypothesis-testing, not prediction, I don't care about the odds ratios, only p-values.  Thank-you for the hint!
It probably is so highly application and data dependant that we cannot answer this question.
Well, I do not know how to fit the K-Means, which assumes the observations to be a d-dimensional real vector, to a co-occurance data. Also, since we're talking probabilities here, random initialization can be a bit of a pain, even tough I did end up using it. But doing some table testing with a dataset of just 5 observations did clear things up for me. Other than that, good general advices.
Thanks Russ. Your answer has helped me.
As you said, here the crucial point is whether the 20 items define an unidimensional scale (which is doubtful, but let's go for it!).
It would be much faster and more accurate just to rasterize the polygon and estimate its area by counting the cells it contains.
@Chase Re: "why we have to treat V3 as a factor" `scale_linetype_discrete` expects a variable with discrete values (factor or character, from `plyr::is.discrete`), check out the src code on Github, http://j.mp/ejaRRT. Nice response (+1).
Standardizing can be useful, but it does not get rid of units, it makes the unit a standard deviation. And it does not get rid of the "problem" of combining in your first paragraph, but there really is no problem. A regression equation does not "create" the dependent variable from the independent variable. It relates the DV to the IVs, and no sensible physicist would complain.

With standardized data, the unit is the standard deviation, which is still measured. The sd of height is measured in cm, etc.
So you are telling I can just use either odds or probability and no need of using odds ratio(OR). I don't know STATA. I'm using SPSS. Is it possible to calculate OR for rxc(not only 2x2) tables? For this I can do it manually but if know in SPSS please answer me. Thank u very much.
Using Holt-Winters with frequency of 144 is a bad idea. Use a more parsimonious model such as tbats() from the forecast package.
sorry, this is beyond my knowledge. couldn't you solve it analytically? probably this would be better placed at: [http://programmers.stackexchange.com/](http://programmers.stackexchange.com/)
Also relevant: [1](http://stats.stackexchange.com/questions/44475/is-there-a-statistical-test-to-compare-two-samples-of-size-1-and-3) [2](http://stats.stackexchange.com/questions/21473/minimum-sample-size-for-unpaired-t-test/21474)
I agree on the main effects. I don't have a formal math/stat argument for it, but it "feels right" - for what that is worth. When considering a Victor Lo approach, it is more concrete to include main effects, but I will be using this feature selection process as a pre-screen rough guide for features to include in next modeling phases - where I tend to use machine learning and a probability decomposition approach : support.sas.com/resources/papers/proceedings12/108-2012.pdf