tttjjj/elt_bench huggingface dataset:
I hear or read similar sentiments to your first paragraph, but I tend to disagree. I don't usually see bootstrapping as necessarily useful in small samples. Its justification is asymptotic/large sample, and in many cases in practice its small sample performance is problematic; coverage of intervals, for example, is often quite different from the nominal rate. It's another useful tool but like many others that have been heralded over the years, it's not the panacea some people imagine it to be. I really don't think it's a solution to very small samples.
Where did you get those formulas?  The one for $t$ is not consistent with the one for $df$.
I don't really understand the question. Do you want an explanation *why* its corresponding feature space is infinite dimensional or an interpretation as to what the resulting hyperplane means?
@whuber @nico A zip file for XML can be found for example at http://www.stats.ox.ac.uk/pub/RWin/bin/windows/contrib/2.13/ (and similarly for some other versions).  There are other issues with it, but eventually it seems to work
As neither R nor any other language is a declared default on this site, it is a matter of courtesy as well as information always to explain the language being used. The second half of my question remains....
This output says that the estimated random effect variance is 0. One way of interpreting this result is that observations of `treat` with the same value for `farm` are uncorrelated. Does this result make sense in the context of the application? Some explanation of what the `treat` variable is would help clarify this. If it's a treatment variable, and treatment was randomly assigned within `farm`, then the population intraclass correlation would be zero, so we'd expect a small estimate.
It is a little more efficient to use the `matplot` function rather than looping through the columns.
Wow, until you asked and I looked, I'd have been sure that some package (like `car`, or one of the `*lab` packages) would have provided a function like yours. Sorry I can't help. I've read a bit about how k-way SVM works and it seems like it was more complicated than I'd have thought.
Be careful. It makes no sense to do this unless the time series are all stationary. See the work of Eamonn Keogh for some cautionary tales.
Welcome to the site, @ShichengGuo. Can you clarify your answer? For example, what does it mean that the OP needs to "take the parameters of the models. whether these parameter will influence your conclusion"? How should the OP try to do this?
The short answer is... because R just computes and doesn't babysit you for statistical correctness... much of the time.  If you're going to analyze days or hours you need to explicitly make them a predictor in your model and you need something much more complex than a t-test.
@Ivanov: it always answers "class a". You could have such predictions without even looking at the data, in that sense the classifier is useless.
Also, your document talks about comparing different populations, which is not the case of single predictor.
I don't know R syntax.  I almost need pseudo-code to get the gist.   I will google some of the concepts you used.  Thanks!
Ah that's helpful, ok, so from the model lm(value ~ factor1*factor2*participant, DFlong), how are the sums of squares actually calculated? i.e. what is anova() doing?
I'm curious even about the two-variable case.  What exactly is "shared variance" when the covariance is *negative*?
@whuber thank you for the input. The problem was in the model, not the Cholesky procedure. in the model I had some dependency, which turned up to crop up in some situations. Probably I should really need to completely re-write the question, but it would be different story. If anyone provide the answer such "start with analysing dependences in the model ..." I would be very happy to accept the answer, although thank you very much for what was already written.
@chi you could be right, its not easy to say without seeing the original data. My experience with pvclust is that it tends to throw error messages that are not very easy to interpret.
I would be very surprised if it could, absent other information that would be relevant to the ratings or to the collusion.
I think a distinction should be made between being Bayesian and using methods inspired by what a Bayesian would do under a particular prior and evaluating them via some non-Bayesian criteria like CV. Methods themselves aren't Bayesian or non-Bayesian, it is our analyses.
Have a look at the [VGAM](http://cran.r-project.org/web/packages/VGAM/index.html) package and the function `rgumbel`. Concerning the estimation of the parameters, you may find [this post](http://stats.stackexchange.com/questions/71197/usable-estimators-for-parameters-in-gumbel-distribution/71279#71279) interesting.
@adam I am in the EST time zone and am available for the next 7-8 hours .
I have an idea how to solve this using MCMC, but I would prefer something less computationally intensive.
Thanks for pointing out the difference so clearly. I sort of knew it but could not express it properly.
I don't think a correlation coefficient is a particularly useful measure of dependence for binary data. Does your measure have to be bounded between $-1$ and $1$? If not, I'd say it would be better to use something like an [odds ratio](http://en.wikipedia.org/wiki/Odds_ratio) to quantify the dependence.
@miura, One of the *leitmotifs* of that chapter in Mosteller & Tukey is that when the $x_i$ are correlated, the partials $x_{i\\cdot j}$ have low variances; because their variances appear in the *denominator* of a formula for the estimation variance of their coefficients, this implies the corresponding coefficients will have relatively uncertain estimates. That's a fact of the data, M&T say, and you need to recognize that. It makes no difference whether you start the regression with $x_1$ or $x_2$: compare `y.21` to `y.12` in my code.
Are you asking whether you should put men or women on the bottom of a stacked bar plot? I'm not sure that "politically correct" has much statistical content.
If your organization simply needs commercial support, as opposed to say, believing that commercial software is inherently better than open source, then you should consider that R and Python both have nice commercial distributions. See Revolution Analytics for R. For Python, see Enthought, Rogue Wave Software, and ActiveState.
(+1) It seems the important point for addressing the OP's concern may be to emphasize the necessity of observing $(X,Y)$ *pairs*. Observing *only* marginal counts tells you next to nothing about the (empirical) mutual information.
(+1) Nice references. (About `gllamm`, viewed another way--from the perspective of a psychometrician used to IRT models: it's just horribly slow :-)
This question in its current form appears to be unanswerable.  Could you tell us *what* detection algorithm is proposed and--more importantly--exactly what your challenger might mean by "just doing some statistics"?
it would be easier to judge if you insert a plot of your data. For adf-test you have an option to test the trend stationarity, also consider alternative tests KPSS, PP. It may happen that you have some deterministic parts. You may use HP and more general Kalman Smoothing for trend extraction, loess do the same locally, so it bares in mind only a window of data, by default, I think, it fits linear trend. So loess for seasonal smoothing HP, Kalman not for seasonal but cyclical smoothing. Baxter-King though could do both. Looking for the data screening though to add more.
Thanks for the suggestion! I will check out those services.
That's an interesting page and good illustrations, but I find them more confusing then helpful because (a) the "bias" and "variance" discussed in the context of regression do not appear to be the bias and variance as defined at the beginning of that page and (b) it's not at all clear that the statements being made (about how bias and variance change with number of parameters) are correct.
Do you have the original data still, or are you able to calculate standard deviation?
Haha, my wife and I chose it when we got married. :)
Welcome to CV. I edited your post so it is readable. For computer output and such, put 4 spaces before each line and it will then format it one line at a time. Also, please look at your posting yourself and make sure people can read and understand it.
1) For a related discussion, see http://stats.stackexchange.com/questions/7912/mahalanobis-distance-between-two-bivariate-distributions-with-different-covarian?rq=1

2) I don't think you can use two different transformations and then make sense of the results.  You might consider whether using the pooled covariance would meet your needs.
It is hard to understand what you are asking.  What is your research question?  Could you formulate things in terms of dependent and independent variables?  How does time come in?
This was awesome. Thank you so much for this response. You've given me a great jumping off point. Any books you recommend since you seem to "get" where I'm at.
Thanks very much for your answer.  I will look into cleaning/deseasonalizing as you suggest.  I am trying to learn about this stuff.
(-1) It's not true that the student $t$ can be depended upon to *deal with the outliers*. See the example [here](http://stats.stackexchange.com/a/86447/603) or chapter 2 of [this](http://onlinelibrary.wiley.com/book/10.1002/0470010940) textbook for more explanations.
Your binomial problem is essentially the same one as the hypergeometric one with $m_i=Np_i$, as $Hyp(k|N,Np_i,n)\\to Bin(k|n,p_i)$ as $N\\to\\infty$
Gelman discusses Pearl's *Causality*, in addition to SL Morgan and C Winship's *Counterfactuals and Causal Models* and A Sloman's *Causal Models* in a 2011 [review essay](http://www.stat.columbia.edu/~gelman/research/published/causalreview4.pdf) in the Am. J. of Sociology. He is generally very supportive of Pearl's contributions, especially Pearl's formalization of causal models in terms of interventions (do-calculus). However, he remains concerned that state-of-the-art causal theory may still invite oversimplified causal models and subsequently false causal inferences from observational data.
Is your binary categorical variable _O_ your dependent variable? Could you tell us what your model looks like now?
Highly likely that you *don't* want to do this. `summary()` is showing the results of $t$ tests that the difference between the state level and the reference level. That one is not significantly different doesn't mean that that category is not different from some of the others. If you want to get rid of the category, you need to throw out those data and then you are cherry picking and possibly will also render some other categories "non-significant" due to the reduced degrees of freedom.
The left hand side, if it is to be a log likelihood, must be a *number*.  What does that tell you about the right hand side?
Aaactually, this will work. I just realized I made an error in my question. D'oh! (I really meant $f(x; a, b, c, d) = f(1- x; d, c, b, a)$). I will amend the question. Thanks!
Both are used by applied economists. In practice, the average marginal effects and predictions from the two are often quite similar, so the choice usually does not matter very much, except in cases where a lot of observations have probabilities near zero or one.
Ah, I see the regression idea was stupid now... not very appropriate for one-step-foreward prediction algorithms 8-/
+1, but just to make sure that everything is clear: LDA will find the discriminant axis (single axis in case of only two classes) that maximizes the ratio of between-class and within-class variances. This will be true for any dataset whatsoever. In case the classes are Gaussian *with identical covariance*, LDA solution will be optimal for classification. If these two assumptions are not true, then such optimality is not guaranteed.
@ZafarS If this question and the previous one are any indication, and assuming you're accurately reproducing what your teacher is covering, your teacher *needs* a textbook. Here's a section on hypothesis testing [from one](http://ipsur.org/IPSUR.html#cha-Hypothesis-Testing), and [another](http://onlinestatbook.com/2/logic_of_hypothesis_testing/logic_hypothesis.html). Also see [this](http://en.wikipedia.org/wiki/Statistical_hypothesis_testing)
Look up for "response surface plot" on Google; e.g., if you're willing to use R, [Surface Plots in the `rsm` Package](http://cran.r-project.org/web/packages/rsm/vignettes/rsm-plots.pdf).
@AlecosPapadopoulos I don't think the $\\lim_{N \\to \\infty}$ case for distributions with unbounded support is interesting, since $\\lim_{N \\to \\infty} \\mathbb{E}[\\max S] = \\infty$; it's the asymptotic results that matter. I suppose you can just do that for the different cases of the extreme value distribution.
Do you understand the concept of double/nested cross validation?
I'm asking here to get feedback on the general problem. Such as, in machine learning sensitivity is measured via such-and-such, but in a classical Frequentist setting it is measured with blah-blah and in a Bayesian setting it's measured via blah... hopefully with references. Also, this is issue is quite old now and I have moved on from the position where the original project happened. I'm still very interested in this issue though ... just not connected to a specific problem instance anymore.
Thanks for your reply. I have added an edit the original question. I hope that is OK. Any further advice would be most welcome.
"the probability that X attains some value within an infinite set, such as an interval, cannot be found by naively adding the probabilities for individual values." While this statement is true for the special case of intervals (as well as for measurable sets containing an uncountably infinite number of points), it is not true for _countably_ infinite sets where adding the probabilities _does_ in fact work. Countable sums of numbers can be defined in terms of limits (when they exist) and the "naive" method of adding probabilities breaks down because uncountable sums are not defined.
Please define which specific z- and chi-square tests you mean, and if possible show us what was actually said about the chi-square. I believe there are generally distributional assumptions for most chi-square tests (having derived a number of them as exercises).
In similar problems, the setup is usually $Y\\sim\\mathrm{Pois}\\left(\\theta\\right)$ and $Z|Y\\sim\\mathrm{Binom}\\left(n=Y,p\\right)$. Are you sure the problem has been copied correctly?
I agree - if this is what you are saying - that my approach is equivalent to a single regression on the whole dataset using numerous indicator variables.  Taking maternal age as an example, a potential problem with any model that treats it as a continuous variable is that it requires an assumption on functional form (a relation between maternal age and later obesity might be curvilinear). By contrast, a model using a set of indicator variables for maternal age bands needs no such assumption and in that respect is more general.
It is surprising to hear that the Rabiner tutorial did not help.
How does it help to suggest that this is an "undergrad" question?  Is that relevant to the answer?  Does it suggest ways to search for an answer on the Web?  I hope this remark wasn't intended to belittle the questioner.
Hi thankyou for your reply, but I did not record individual ID for each of the students so that is why i am in a bit of a dilemma as there is no way of knowing the students that completed both questionnaires or not.
I also find that sometimes is difficult to determine when an effect must be considered as fixed or as random effect. Althought there are some recommendations about this fact, not always is easy to take the right decision.
How *could* they be different if they are numerically equivalent?
@user11852 All of my grid samples have measurements at the same spaces at all times. I can edit in some further information about my data if you would like.
If there is such violation, I dont think bootstrapping cures it. Instead why not try to transform (log) the data to get closer to normality and use a robust standard error such as from the sandwich package in R?
Also, if I was trying to find the $cov(z_t, z_{t-2})$, does this seem correct: $cov(z_t, z_{t-2}) = \\phi^2 var(z_{t-2}) + \\phi cov(a_{t-1}, z_{t-2}) + cov(a_t, z_{t-2}) = \\phi^2 (\\frac{\\sigma^2}{1-\\phi^2})$ ?
@raegtin - I don't think probability theory is separate from statistics, rather it is the theory.  "Statistics" is the application of probability theory to inferential problems (i.e. the practice).
I don't quite follow your situation. Are the "discrete paragraphs" of the title the "descriptions" in your spreadsheet? IE, do you already have the list of words for each case identified, & you just want to know which ones are related to inclusion? Or, do you need to figure out how to get the words from the descriptions (?) in the 1st place, & then will need to assess which are related after?
+1 I supposed something like this may exist.
Zhubarb, I'm trying to determine which features are redundant, in the sense that I'm trying to find features that are roughly linear combinations of other features. In other words, I'm trying to find features that can be computed with little error by some function of the other features (preferrably, a linear function). 

As I understand it, LDA is basically a classifier; it tries to find categorical class labels as linear combinations of continuous features. 

I guess that what i'm looking for is more similar to [Factor analysis](http://en.wikipedia.org/wiki/Factor_analysis) or ANOVA.
ARIMA tools for R: http://stat.ethz.ch/R-manual/R-patched/library/stats/html/arima.html
Yeah well, so you are suggesting I use the analytical expression for computations? furthermore that's only the cdf.
@Glen_b you are correct that it is an article the article is Functional responses, seasonal variation and threshiolds in behavioural responses of moose to road density, Beyer et al 2013. Journal of Applied Ecology.
Effect sizes aren't, but the accuracy of inferential estimates thereof is. Low power probably means a large confidence interval for your d.
Welcome to CV. Is this a [self-study](http://stats.stackexchange.com/tags/self-study/info) question? Please add the `self-study` tag if appropriate.
You can certainly calculate sd, interquartile range and range. CI are trickier. What will you do with the information?
RD requires other assumptions. First, individuals cannot manipulate the assignment variable. So there's no moving across the border for the better tax rate. More importantly, the other variables need to be smooth functions of the assignment variable conditional on treatment, i.e., the only reason the outcome variable should jump at the cutoff is due to the discontinuity in the level of treatment. That is not likely if the unit of observation is a county. It maybe reasonable if the units are people.
thanks, i'll try to use MLE!
No. Assuming by ROC you mean area under the ROC curve (AUC), it is much more informative than misclassification rate.
A large fluctuation affecting many close sensors is indeed important, but a fluctuation affecting a lonely sensor is important as well (as I can't tell how local it is).
Thank you for the answer PsycStats .  Unfortunately @whuber is correct in that my answer is referring to understanding the error in the area underneath each curve.  So, I am not sure that the answer you gave is directly applicable, but perhaps it may help someone if they happen to stumble upon this.

The problem I have is unfortunately (*I think*) fundamentally different in that the measured data will not change appreciably with extra measurements.  So essentially I am looking for how certain I am that the fit I have made is the *correct* fit.
An you need 96 observations just to estimate the intercept (that will yield a margin of error of 0.1 in estimating the overall probability).
@BerkUstun  The capital G is a typo for a small that I will fix promptly.  X/Y is just a generic ratio of random variables. IIRC all this is explained in Liu's Monte Carlo book (something with scientific in the title.)
If you have paired data, the Wilcoxon test may a good one.   But you were asking why the inconsistency between parametric confidence intervals and the nonparametric test.  I think I answered that.  If you want a confidence interval that is consistent with the test (which is desirable) then go with the example above.  This confidence interval can be thought of as the set of pseudomedians (median of all possible pairwise means) that if hypothesized to be the population pseudomedian would not be rejected at the $1 - \\alpha$ level.
A better example would do a lot to improve the question.
From what I can understand, their approach was to consider both teams in each observation separately and individually rather than as an interaction. So instead of one Result variable they had two dependent variables Points1 and Points2 denoting the number of goals scored by each team. They then ran a Poisson regression on Points1 using only variables related to the home team and on Points2 using only variables related to the away team and assumed that the two teams do not interact. They then adjusted the home advantage/attack/defence ratings until their regressions were consistent.
In linear regression I would create two additional variables of the moderator, + and - 1 standard deviation, create interaction terms with the focal predictor and +/-1SD, running two additional regressions, and interpreting the focal predictor coefficient in those two additional regressions. Is this the same for a multilevel model and a within-level interaction?
As a note GeoDa and SatScan aren't open source, they are freeware (not that it makes much difference to me though!)
To expand slightly, the decision boundary will depend upon the relative losses of misclassifying an $X$ and a $Y$ as well as upon the parameters; given that, you can easily determine that you will always pick either $X$ or $Y$.
Here's some discussion that might help you: http://www.statmodel.com/discussion/messages/12/6845.html?1385336235
What package/function do you use to fit the GEE in `R`?
$2^{-10}$ is small but not absurd for $C$, and yes, if your feature values are small then $C$ will also be smaller. If your fit isn't good you could try a nonlinear kernel....
+1 for offering a classic and for the remark on brevity!
@nkormanik, re: "Why complicate the matter??" - if there are non-linear effects, including polynomial terms effectively gives a higher order approximation to the true regression function $f(x_1, x_2)$, similarly to how including more terms in a taylor series expansion improves the approximation.
I don't think this is an appropriate Q for this context.  Without knowing what you are trying to demonstrate, and to whom, and what the stakes are, we have little basis for answering your "Do I have to?" question.  If you want to learn about survey reliability and validity, there's a world of literature out there.
@ils, once you have a table, you can coerce it to a data.frame (`as.data.frame(table(your.object))`). Try it and see if the output is what you are after.
@kwak: Have I misinterpreted that last statement?  The eigenvalues of a 3 x 3 correlation matrix, for instance, are determined by three correlation coefficients (a,b,c).  For (a,b,c) = (-0.9, 0.5, -0.1), the ev's are (2.07415, 0.91532, 0.0105346).  Changing c from -0.1 to -0.01 changes the ev's to (2.03383, 0.99151, -0.0253402).  Thus, a relatively small *decrease* in absolute value of a single coefficient can destroy the positive definiteness of the matrix.
@MarcClaesen. Instead of doing cross validation on part of the data separated from the training set, I want to provide a separate validation set
1) Don't confuse the ANOVA procedure with the ANOVA table; you can have ANOVA tables in more places than that. 2) ANOVA is simply a special case of regression in any case.