tttjjj/elt_bench huggingface dataset:
@Silent: We would still need to guess what your problem really is. What is N? Number of sunflares in hundreds or the voltage you measure on some battery? It would suggest you plot your monthly means in a histogram. Fit this with a Gaussian an see if it fits and if you can justify a Gaussian fit from your model.
I am currently using `lme4:lmer()` for my linear modelling, as seen [here](http://nbviewer.ipython.org/urls/gist.github.com/TheChymera/7495934/raw/d32f49a6ebc0be9e66392ab26dc4d2bedc251a6a/texreg). Is that appropriate? Also, what about whenever I use t-tests and ANOVA - should I take means or input the raw data there? (supposeing I have a complete dataset)
+1 Reasonable and general advice (and I like your definition of political correctness).
An old topic, but a key point for clarification in the OP: when they say that they have "rain or not" data against which to compare the prediction, do they mean "at my house", or do they mean "within the prediction area"?
This appears to be related to multivariate outlier detection, e.g. http://stats.stackexchange.com/questions/213/what-is-the-best-way-to-identify-outliers-in-multivariate-data
Perhaps practical experience or knowledge of a situation in which the later or former is used for example would be beneficial to me.  Perhaps even what should go into the justification process.
Or if you wish to avoid introducing a package dependency, ```plogis(710)``` achieves the same result. (Indeed ```inv.logit``` is just an alias for ```plogis```.)
If you have two groups in your dependent variable, that's logistic regression plain and simple.
@whuber No disagreement there.  Plus the tag...  OK I withdraw my comment, but I'll leave it up as a potentially useful guide to the OP on what to fix.
@DilipSarwate, what you're saying is true. My point in using the terms "vertical" & "horizontal" is to make visually apparent the idea that the error is understood as *sampling error in $y$*, or *sampling error in $x$*. Should we plot $x$ on the vertical axis and regress $x$ onto $y$, the minimized *distances* will be vertical, but the minimized *error* will still be sampling error in $x$. It may be that my answer isn't clear enough; I may edit it, if I can think of a better way.
Hi Nick - welcome to CV.  Your question is very broad; you might have better luck getting good answers if you broke it up into smaller questions (and once you do, you may find that some of them have already been answered here).  At a minimum, though, you ought to mark your question as "community wiki".  That basically means that instead of the usual competing-answers format here, all of the answers as a whole will be considered The Answer.
@Karl Please [register your account](http://stats.stackexchange.com/users/login).
(+1) Note `lm` fails to estimate a coefficient for the quadratic term, & gives a warning about a singular design matrix - perhaps more directly illustrative of the problem than these plots.
(+1) ouch .....
Probably more informative to look at the impulse response function of the VAR.
@ayush - this is not the correct interpretation in your second last sentence.  Or at least you should add subscripts to "a" and "b", which makes it clear that it is these quantities which are varying over the 100 times.  Your current notation makes it seem like "a" and "b" are fixed quantities.
@MarcClaesen, well according to these papers, kernels in kernel methods are highly tailored for specific application which is not the case for these deep learning methods. Moreover they claim poorness is very general specially in handwriting recognition because of highly entangled and high curvature manifolds for digits. I suggest you to take a look at:
http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6472238&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6472238
To whomever downvoted this, it seems like a perfectly fine response to me, and deserves justification for why the downvote was given. @EpiGrad, I've never heard the colloquialism "close to sausage making", do you know where this saying comes from?
As I see [the table](http://www.pierre-marteau.com/editions/1693-mortality.html) and [the graph](http://www.pierre-marteau.com/editions/1693-mortality.html) (I don't know if it's the right one, but suppose that, it is linked from ) the data for age 84+ are insufficient (the graph line starts to bend). They cleary know why they cut it there. I think I wouldn't try to extrapolate in this case.
Usually one does the opposite: the application suggests likely distributions.  Not only that, it also determines how to check whether a distribution is a reasonable fit.  For example, in some cases it's important to get a good fit to the right tail (the largest values), whereas in others it's important to get a fit that doesn't deviate too much at any percentage point.  Thus, some amplification on your part concerning the application would be helpful.
I think I tend to agree more with John Tukey -- "*Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.*"
Do you expect what happens under each condition to be independent of what happens under every other condition?
(+1) Interesting idea. I always think of coplots as a way to show trivariate relationships between numerical variables. Re-reading the help page, I see there are examples of use with factors.
I have to voice that the puppies on the cover of Doing Bayesian Data Analysis are respectably cute! And yes, it's a great text.
Hmm, no one? I´ve added a bounty...
@whuber, By true "p" I mean p's that are generated from a Mulivariate Logit Normal-Binomial Distribution and the estimated p's are those that are estimated using the same Bayesian model.
This material (about two tests) has been covered in two previous questions: http://stats.stackexchange.com/questions/11385/linear-regression-heteroscedasticity-whites-test-interpretation and http://stats.stackexchange.com/questions/8107/how-do-i-interpret-the-results-of-a-breuschpagan-test.
Great answers. I would like to stress that (as whuber already pointed out) comparing 95% confidence intervals is not the same as performing statistical tests at the significance level 0.05. There are of course papers dealing with this. If confidence intervals are the only statistics available [Payton et al](http://www.tandfonline.com/doi/abs/10.1080/00103620009370458) suggest to use 85% intervals for significance level 0.05 for Gaussian data. They follow up their work [here](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC524673/).
Whatever the method, you're going to have to properly define what is a peak and what is a plateau. Are two consecutive 'high' values a peak or a plateau? How about five? Some methods may not appear to need this information, but then this is hidden behind the scenes. As ever so often, it comes down to properly defining your problem, and the optimizing your parameters (and/or algorithm) for it.
Consider $Y_n = X_n/a$.
If you're comparing a continuous response variable between two groups, have you ruled out just transforming the variable to normality and fitting an ANCOVA?
could you post a graph of the distribution of the DV?  That would help me/us suggest the best test.
Thank you, that helps and is consistent to two seperate OLS-regressions
@IanStuart Hmm, unless I misread the `\\bar{}` over the $X_y$? If $\\vec{x}_i$ and $\\vec{x}_j$ are two row vectors from data matrix $X$, and $d_{ij}$ is the Mahalanobis distance between the two vectors, then $$d_{ij} = D(\\vec{x}_i,\\vec{x}_j) = \\sqrt{(\\vec{x}_i - \\vec{x}_j)^{\\mathrm{T}}S^{-1}(\\vec{x}_i - \\vec{x}_j)}$$ which is described on [Wikipedia](http://en.wikipedia.org/wiki/Mahalanobis_distance) that should workable. Is there an R function that you are aware of that already does this or do I need to write that too? (If the latter it will be inefficient R code.)
I used hindcast and senior management was asking whether this is the correct term.
Do you perhaps mean "I ran a multiple regression with Price as the *DV* and Age, Floor, Size, time_walk, and time_train as the *IVs*."  It seems that what you should mean, in any case.
Thanks. But some of the point is to present this data to "evryman". Managers at our customers can be everything from university professors to mechanics, and everything inbetween. So it needs to be easily understood.
@hudaKaeen I think you need to give us a lot more info before we can figure this out.
(+1) You might mention briefly the questions you have looked at, but that don't quite satisfy you. There are *lots* of questions on the bootstrap here. :)
Birth-death process attempts to analyze the throughput of the process (here, the parking garage clerk, or similar). I have a feeling that DavidD is looking for a method to predict the amount of cars that will try to check in the garage (not the queue, but the demand).
@AlecosPapadopoulos I've been thinking a little longer about your hint and have posted my attempt as an answer below. Could you please look at it? Thank you in advance :).
I am glad I could help.
If your purpose is to find the effect of a continuous variable on the dichotomous DV controlling for another continuous variable then maybe you should consider logistic regression.
I gather your response is binary (positive vs. negative). What is the status of your explanatory variables? Do you have any (eg, experimental condition vs. control condition)? Are there more than 2 groups tested? Do you want to control for, or assess the influence of, any other variables (eg, number of mitochondria in each cell)? The appropriate analysis will depend on these features.
If I understand correctly, you want a GAM for your whole dataset. You can just plot the individual patient data. Also, seems like your data is multilevel, so you're going to want fixed or random effects, depending on your goals
The Chi-Squared test does look somewhat like what I'm looking for, but http://en.wikipedia.org/wiki/Chi-squared_test"seems to suggest that it tests for variance, whereas I just want to determine whether the difference in proportion of a binary variable between two groups is statistically significant.

What I would really like is a formula that I can give n1(sample group 1) p1 (proportion of successes in sample group 1) and n2 p2 which will output the p-value
I'm getting a different confidence interval from the one you wrote there. On the log scale, the confidence interval is $ \\log(.806) \\pm 1.96 \\cdot .061 = (-.335, -.096)$. Exponentiate that and you have $(.715, .908)$. As I said, since on the log scale the lower bound must be smaller than the point estimate, and $\\exp$ is a monotone function, it's impossible for the sample odds ratio to be less than the lower bound of the confidence interval.
Brownian motion at time $t$ has the normail $N(0,t)$ distribution, and this distribution not have the memoryless property (only the exponential distribution does). The connection between the exponential distribution and Levy processes is that the holding times of a compound Poisson process are independent and have exponential distribution.
It seems the issue is not related to the Matlab/GPML implementation, so the question should perhaps be retitled.
I would say you don't want regressors ($y$ in this case) to be correlated with the error term $v$ since both contain the $u$ term: $v=\\frac{u}{-\\beta_{2}}$. You certainly want your regressand and regressor to be correlated.
Welcome to the site, @jimmy. Your answer here doesn't make complete sense to me. Would you mind elaborating on your ideas? Since you're new here, you might want to read our [FAQ](http://stats.stackexchange.com/faq), which has guidelines for answering questions on CV.
This is essentially the correct answer, but the fact is that tomtom does not have any probabilities at all but just observed frequencies, which are just an estimate of the underlying probability.
I am not sure that $W$ is unknown -- isn't it the case that $W$ can be chosen arbitrarily by the researcher? Unless you're referring to the $W$ that produces the most efficient GMM estimator. If that's what you meant, then the estimator in my question is not necessarily the efficient one.
At this point, you've observed the elements of the vector, so you're in likelihood-land, not PDF-land.  However, perhaps more to the point, I think perhaps you are confusing the big-X = random variable, little-x = observation terminology with the big-X = vector, little-x = element of vector terminology (just guessing, really.)  If I have a vector $X$ of length 10, and each element of that vector $\\sim N(0,1)$, then the vector is $\\sim MVN(0,I)$, a multivariate normal with mean vector 0 and covariance matrix equal to the identity matrix.  Both vector and elements have distributions.
@dafeda Hah, thanks!
Correct. See the edit I just made to my initial answer.
If it was only two groups I think the [BK plot](http://andrewgelman.com/2014/04/08/understanding-simpsons-paradox-using-graph/) would be a good illustration - one point for the original and one point for the final. It isn't obvious how to extend that type of plot to 3 groups though.
You might want to also check out some of the other questions with the tag network, http://stats.stackexchange.com/questions/tagged/networks . They will have suggested graphics and tools to do those graphics as well.
Be sure also to talk about hypothesis testing (Neyman-Pearson tests) and not significance testing (Fisher tests). These approaches are commonly mixed even if there is no notion of error in the second one, and proper usages should be different because they lead to different kinds of conclusion.
Pick any $n$ and any multiplicative value (2 fold, 10 fold?), I can give you a probability model for which maximum likelihood has that value as relative efficiency to the bootstrap.
Have you tried cross-correlation?
Thank you, I can see the difference now. Now, I am wondering whether a discriminant analysis (such as ML discriminant rule i.e. Bayesian discr. for priors 1/2 and 1/2) is an acceptable way of doing model selection when we are comparing two models from which we inferred posterior information about some parameter/hyperparameter via Bayes' theorem. I.e. although we assume that the data are generated by one model, if you do discriminant analysis, won't the percentage of the mixture reveal the model that the Bayesians' describe as 'more likely'?
As your Wikipedia link states, the polychoric correlation assumes that the manifest ordinal variables come from categorizing latent normal variables; Kendall's tau & Spearman's correlation do not assume this. Other than that, the differences are covered in [Kendall tau or Spearman's rho?](http://stats.stackexchange.com/questions/3943/) If there is anything left that isn't already covered, please edit to clarify.
Thank you @PeterFlom! The time nature of the data isn't particularly important, so I'd be willing to ignore it.
@Spencer The norm in your case is capped; the vectors (4,4,4,4...) and (1,1,1,1...) are as far apart as possible. You could calculate the highest norm possible and subtract the actual norm from that if you want a similarity measure.
A question is too broad. How do you know that $A$ is the cause of $B$?
(+1) Nice presentation, as usual. :)
Many undergraduate textbooks on _probability_ theory mention all the above results; but perhaps _statistics_ texts do not cover these ideas?  In any case, a $N(0,\\sigma^2)$ random variable $Y_i$ is just $\\sigma X_i$ where $X_i$ is a standard normal random variable, and so (for iid variables) $\\sum_i Y_i^2 = \\sigma^2 \\sum_i X_i^2$ is simply a _scaled_ $\\chi^2$ random variable is not surprising to those who have studied probability theory.
I think the key thing to clarify is whether you want to predict if objects of category C will be absent in the actual finite collection of group G (as your question is currently worded); or if you want an estimate of the probability that objects of category C are at the site, even after group G has been collected and no category C objects were found.  McBride and Johnstone's approach is appropriate in the latter case but not in the former (and as you have currently worded your question).
Could you please be more specific about your data? Explain all your variables and hypothesis, and if possible, add raw data (or at least FULL output from R).
It certainly can, if the model is not the same, any comparison is even more difficult.
Boxplots, histograms and density plots are all useful for examining the distribution of data. It often is useful to plot data more than one way. I meant to try box plots in addition to rather than instead of the other ways suggested. The outliers will still be a problem. Have the outliers been checked for reasonableness? I have seen cases where the outliers turned out to be copying errors or other erroneous data.
I should also mention that the covariates in the multivarite analyses are likely to differ across studies to be included in the meta-analysis.
A correlation coefficient is something always standardized. When standardized, a "part" can become bigger than a "whole". It can even change sign! See [here](http://stats.stackexchange.com/questions/44279/example-where-a-simple-correlation-coefficient-has-a-sign-opposite-to-that-of-th)
@steffen Yours is a very *similar* question, but it's not an **exact** duplicate.  You had several specific requirements unrelated to this question (e.g. that it uses Java).
One way is to generate the data in wide format, so each row is a subject and you have 30 columns for the repeated measures. In this format you can specify the correlations between columns to satisfy the sphericity requirement and then reshape to long format. See an example of using the [`rmvnorm` function here](http://stats.stackexchange.com/a/24271/1036).
@Macro: Yes, it's in the `lme4` package.
Thank you. I will edit the question so that it mentions raking, and also to clarify. You are right about the general idea. However, I asked specifically about multilevel raking/fitting/... algorithms and methods; the single level case has been chewed through already. -- I'll take a look at the `survey` package.
@rolando The -1 is unfair, because Adhesh is asking this question *specifically* to put an end to the repetitive series of correlation-based questions.  See comments at http://stats.stackexchange.com/questions/15598/significance-of-correlation .
Properly interpreted, the result is true even for zero density. :-)
not sure how this addresses the questions, which centers on validating a model.
I think that's a problem
Generally speaking, yes. ANOVA or ANCOVA "worsen" as groups become more unbalanced. This is because main effects get entangled and and they also get entangled with interactions terms. Different SS types (I, II, III) try to untangle them in different but not optimal ways.
that's an excellent answer. The only problem is that in the software as it currently is, I can merely approximate spectral data in the first place. I'll have to dig a bit deeper to see the necessary conversions. Thank you for all the extra information. That will be very useful.
I once heard that proportional will not affect sampling at all, and that's why it is frequently used in Bayesian statistics. How to understand that? Thanks.
Gallamine, I don't really know anything about intervals for weighted binomial distributions. However, I would be surprised if a weighting made the normal approximation any more reliable.
A good question that would be even better if you told more about your data.  E.g., how many variables are measured per user?  Are there repeated measures?  If so, how many observations per variable per user?
Oh yes this makes sense, thanks!
There's nothing in binomial or negative binomial regression than needs to be normal. If it's the response they transform, that may well be highly counterproductive; it will screw up the GLM.
Answer can be checked from most textbooks / google.
This imposes an impossible standard (If they never did, "did they ever?" means we'd have to know *everything they ever said* - how is anyone to do that?). There's no reason to think they did, or would, endorse anything of the kind; the onus would be on anyone saying they did support such a thing to show it. But in any case the general way they (Fisher vs Neyman&Pearson) looked at hypothesis testing isn't hard to find.
Hi David - calculator is fine - but the idea is to not have too many numbers (Since they all need to be written on the board)
Rotation is not limited to FA models: You can use it on any loadings or pattern matrix, provided it makes sense. In fact, there is a `promax()` function in base R which takes as input the loadings matrix, and other oblique rotations methods can be found in the [GPArotation](http://cran.r-project.org/web/packages/GPArotation/index.html) package. This is basically what `principal()` from the [psych](http://cran.r-project.org/web/packages/psych/index.html) package uses.
By "unbiased," you mean unbiased predictions, correct?
Actually I am working with SAS (proc nlmixed). R does seem to be attractive to work with for this kind of data, I will take a look at it.
Thank you for your answer!
The p-value from the chi-square test does not tell you the likelihood that they are different. The p-value tells you what the probability is of the observed difference in the percentages or an even more extreme difference under the assumption that there really is no difference in the true percentages. That is something very different than the probability that the true percentages are different.
For what it's worth, as a PhD student in machine learning, every machine learning paper and textbook I've encountered has used precision and recall.
Thanks Peter for your answer.When nobody was answering, I was started thinking that I asked a wrong question :).I was also wondering if LASSO or LARS method can be used in discriminant analysis. I read about them as good variable choosing method in the book "The elements of statistical learning: data mining, inference, and prediction", but don't know how to use it in my present framework.
Brownian motion is a random function, for instance.
@singelton this results from the formula $\\Pr(X_1 \\in A_1, \\ldots, X_n \\in A_n)=E[\\Pr(X_1 \\in A_1, \\ldots, X_n \\in A_n\\mid \\Theta)]$.
@Curious `pt()`
This question covers about half of an introductory statistics book for social scientists based on SPSS. Besides, there is no sign here of any prior research. A moment's Googling would have shown you that there are many tools other than SPSS.
@mpiktas I have the house numbers. Actually, what I need is to simulate/forecast the probability for a house in a region to be vacant...
Are 'widget A' and 'product A' the same thing or different things? When you say 'tested together with' what do you mean?
I think this is a much better *introductory* text than Gelman.
...as [here](http://stats.stackexchange.com/questions/15361/what-type-of-error-correction-do-i-have-to-use-after-wilcoxon-matched-pairs-test) @John advised me to *"report the standard confidence intervals of the effects in question"*.  
Jeromy, I have a counter-question: the term *within (and/or between)-subject design* is more general than, for instance, ANOVA or RM ANOVA and so on, isn't it?
Of course, the independence is a too strong hypothesis.
+1 That's right.  But (to head off possible confusion) the problem isn't just that $Y$ can equal $0$: it's that it can equal $0$ *with positive probability.*  (For instance, a quotient of normals does have a distribution even though the denominator can equal $0$.)  Thus, $X/Y$ is undefined with positive probability, making its mean (and any other moment) undefined as well.
For starters, when you are comparing mixed-effects models use `ML` instead of `REML` for your fitting. Use anova or AIC (I would go for AIC), you are testing for fixed effects anyway. Standard methodology workds fine. In general step-wise regression is not a very good way to go, just try to define a set of sensible models and pick the best one from that set.