tttjjj/elt_bench huggingface dataset:
I agree with David's response. Your data is not normal because it is discrete. If you want to blindly apply a normal curve, calculate the mean and variance and plot a normal curve over the histogram of your dataset.
There have been other questions I remember about SAS and the degrees of freedom in mixed models (see [Differences between PROC Mixed and lme / lmer in R - degrees of freedom](http://stats.stackexchange.com/q/29617/1036) and [Equivalent mixed models yielding different results in SAS](http://stats.stackexchange.com/q/26556/1036). Perhaps these will be useful. How do you know what the correct DoF are? You should include the code used to estimate your mixed model.
What exactly are you comparing between the two groups?  What is this "obvious difference" and how are you measuring it?  Also, please be careful with your terminology, because a "pair" and a "combination" and a "permutation" are all very different things. A pair literally is just two things; a combination is a subset of things; and a permutation is a re-ordering of all of them. Because you seem to have used these three terms as if they were equivalent, please consider editing this question to clear up that ambiguity.
Not at all, change away. You should insure that the question reflects what you want to know, so that you can get the info you need. Questions are often updated after initial posting to clarify what the OP is really after & to facilitate more appropriate answers. Also, it would make CV the appropriate place for the question IMO, should you want to keep it here.
@Theja: yes, the population distribution is 1-D, and $N_p$ is the number of values from the distribution. Here's the background: the shape of a manufactured part is deemed acceptable iff the maximal deviation $X_p$ from the desired shape, as measured over $10^9$-ish locations, is small enough. In fact, $X_p$ became the measure of the shape's fitness in the industry. It's infeasible to measure (manufactured - desired) at every of the $10^9$ location, so only a sample of $10^5$-ish points are measured. Thus the question: how to estimate $X_p$ given $X_s$ of the sample and the sample's momenta.
In response to your flag, I don't think there's much to say: your question looks fine, but there is often less activity during the weekend. However, you can edit your question by adding more details, if you like, or offer a small amount of your reputation (bounty) to draw attention on it.
What do you know about $B(t)$ and Gaussian processes that might be relevant (*e.g.*, what definitions are you using)? Have you developed any intuition for what this procedure is doing (stretching time by $e^{2\\alpha t}$ and rescaling the values by $e^{-\\alpha t}$)? If so, what approach would that suggest?  (Could you create a simulation of this new process or draw a picture of it?)
Great--thanks for the advice. I'll discuss this with my colleagues and see where we can take it from here. It's nice to see that the reviewer's harsh response wasn't completely correct!
Why do you call kNN nonparametric?
For those not already using *tm*, and wanting to play with *lda*, [JFreq](http://www.williamlowe.net/software/jfreq) also puts plain texts in LDA-C's preferred format.
I made a couple edits to my answer if you are reviewing it
A non-original quip: The learning curve is steep. If you put in a little effort, you learn a lot. (Otherwise put, it's vital to know which variable is on which axis.)
@whuber A valid suggestion! I'm new to CV & SO, and seem to err on the side of brevity. I've edited the answer to be more explicit. Thanks!
What is your question here? How to calculate confidence intervals? How to calculate confidence intervals in R? I made a small [reference page](http://rpubs.com/RomanL/7024) for myself on how to (calculate and) plot different intervals using `ggplot2` package. Feel free to browse.
If a pmf forms a geometric progression then it must be a shifted, rescaled, and/or truncated geometric distribution. If it forms a hypergeometric progression of degree (2,2) then a similar conclusion holds. There are distributions associated with *any* series that sums to a finite value, and so the hypergeometric distribution generalizes to many other distributions (by using different rational functions). Most of them do not have names. One exception is the [negative binomial distribution](http://en.wikipedia.org/wiki/Negative_binomial_distribution) whose pmf is hypergeometric of degree (1,1).
"these questions" link is wrong. Thanks for the info!
@Procrastinator Could you elaborate a bit on why in some contexts the likelihood is intractable. Given that you mention biology, genetics and ecology, I imagine that it is linked to the complex dependencies between parameters. I think this would be particularly useful for people not familiar with Bayesian analysis (of which I am), especially given that the wikipedia page on ABC you link to does not provide a lot of context. Thanks
Consider the chi-square test for independence.
The text you cite defines white noise earlier: https://www.otexts.org/fpp/2/2 You just need to search in the same document.
That is as bad as it gets.
Stan, the role of modelling is to do exactly that so inference can be made and hypothesis tested.
Are the $z_i$ also independent complex Gaussian random variables?
Does it matter whether you take the reciprocal of the odds ratio? In other words, does it matter what the numerator or denominator is? Could we instead have $\\frac{e^{b_0}}{e^{b_{0}+b_{j}}}$ and $e^{b_{k}-b_{j}}$?
"Men are 30% significantly more likely" -- I don't know what this is intended to mean.
Did you read the vignette ? http://cran.r-project.org/web/packages/BradleyTerry2/vignettes/BradleyTerry.pdf
It's probably worth making your question more general by removing the direct reference to R - there's nothing special about R for this question, and the question and answer apply to using linear regression to estimate ARMA much more generally. Please consider editing your question.
@Anony-Mousse: It is a bit like set cover, yes. But the number of possible sets may be *huge*, so listing all of them will probably be infeasible. I guess vertex coloring might be the better analogy, with egdes for pairs if they are from the same day or too far apart. Yesterday I thought this modelling would break since the diameter of the convex hull need not equal the diameter of an enclosing circle, but today I'm not so sure, and this might in fact work out. Still thinking…
Yes, right. The sum is always > 0.
Ah, okay. You definitely can fit random/mixed-effects models with `proc mixed` in SAS (see, for example, [link](http://onlinelibrary.wiley.com/doi/10.1002/%28SICI%291097-0258%2819990215%2918:3%3C321::AID-SIM28%3E3.0.CO;2-P/abstract)). I suppose with the `weights` statement, you could add user-defined weights. Not sure about the details though.
The DF test always uses first differences as the outcome.
Also, some applications of logistic regression *are* (properly) survival analysis (i.e. discrete time logit hazard models), so can you edit your question to amplify on what you mean by "use logistic regression?"
Well if you don't care too much about a factor of two increase in computations, you can always just do $\\newcommand{\\m}{\\mathbf} \\m S = \\m X \\m  X^T$ and then $K(\\m x_i, \\m x_j ) = \\exp( - (S_{ii} + S_{jj} - 2 S_{ij})/s^2 )$ where, of course, $S_{ij}$ is the $(i,j)$th element of $\\m S$. This is probably *not* the most numerically stable, either, though.
Here are some links to related threads that should be helpful to read: for **linear** means: [What does linear stand for in linear regression?](http://stats.stackexchange.com/questions/8689/); for a simple example of a **non-linear regression**: [Linear regression best polynomial (or better approach to use)?](http://stats.stackexchange.com/questions/70153/); for what **parameters** are: [Is any quantitative property of the population a "parameter"?](http://stats.stackexchange.com/questions/63386/)
I see a genetic algorithm as a search over a parameter space. So even with a single (semi-)continuous parameter you could use a genetic algorithm as a continuous number can be represent as 24 bits (float) or 53 bits (double), which gives you plenty of genes to work with.
@COOLSerdash OK, but when you get down to sample sizes of 1 or 2, then the mean is identical to the median, and as such definitely no better. More generally, that's the limit as sample sizes diminish.
@heather Why do you call your DV as an estimate? If you call it as an estimate because you are taking the mean/sum of your likert scales then I do not see how that matters conceptually. As far as power is concerned, that would be dependent on the model/estimation specifics and I am unable to offer any suggestions on that issue. Perhaps, you can just email the authors for some suggestions or do a simulation to see how much sample size you need for desired power?
I have R and Stata
Not quite clear what you need. Kappa is a test for `k X k` frequency table with the same categories in both "dimensions" of the table (the two raters). The exist also multi-rater kappa, which is for `k X k X k...` multiway table.
@kjetilbhalvorsen Thanks :)
@farel:> if you click on the blue words, you will be directed to actual websites. The last document in particular contains working out examples (repeated in the edted version of my post).
Hi Dimitriy, for ln(y), is simply transform to ln(y+1) -- that deals with the ln(0)s. I will get back to you on the other question about the poisson.
@Glen_b, in your function, if you just want the interquartile range, you can get it directly via [?IQR](http://stat.ethz.ch/R-manual/R-patched/library/stats/html/IQR.html), instead of `diff(fivenum())`.
+1 nice. I would only have written assymptotic distribution for $1/\\sqrt{n}S_n$, to show clearly that CLT applies in the usual way. But that is only the matter of taste.
The problem is probably because you are estimating 2 different models and perhaps don't realize it, and almost certainly not due to differences in software. I'm not able to comment further without more detail on what you are trying to model.
Some clarification of your terms would help, because ordinarily PCA is used as an exploratory method and thus is neither a formal hypothesis test nor an estimator. If you consider it to be an estimator, clearly it is estimating the principal components and their eigenvalues: for which of these do you need "confidence" ellipses? Or are you referring to something else, such as a contour of the covariance restricted to the first two principal components? And is there a reason you use "estimate" rather than "calculate"?
It would be good to summarize some of the key points from these pointers. This would make this comment more like a sustainable answer to the question at hand.
thank you. Is there a sample-size limitation on cross-validation at all?
Thanks a lot. Sorry for the confusing. I'll try to make it clear. For the first question, I want to know researcher who conduct ELISA test will use optical density(amount of colors) or true antibodies density(calculate from optical density) to determine whether a person is positive or negative and find critical value(cut-off) between positive and negative. The second question, if they need to calculate antibodies density in serum, how will they calculate it?
Isn't Monte Carlo a random sampling method? Or isn't there relationship between them. I will check your link.
I'm sure it can. Machine learning really just refers to a method of solving problems - teaching a system to do something. I don't see why this would be restricted to multivariate data.
@whuber I don't know what I prefer. I just want the correct answer. Its not about personal preference. So can you please suggest the correct solution? Should I just omit the absolute values? Also, for gradient descent, is it better to derive wrt to one weight or the whole weight matrix?
Please tell us *how* a kernel was used to compute a covariance matrix.  Could you provide a link to the paper or at least a reference to it?  Please also explain the sense in which you conceive of a Gaussian kernel as a "distance function."
(1) I am aware that full models are preferred, but I have over 1k vars to choose from and I am required to build these smaller models due to industry-specific requirements. 

(2) That makes sense!

(3) Agreed! 

(4) True 

 (5) Interesting
Another reason for using simulations: you also get posterior simulations for any function $f(\\beta_0, \\beta_1, \\ldots, \\beta_p, \\sigma)$ of the parameters. For instance I use this possibility to get a credibility interval about the probability $\\Pr(Y > 10 \\mid x)$ for some value $x$ of the covariate. I don't know how to get a frequentist confidence interval about this probability.
That depends on many things, for example: Your exact definition of optimal or how strongly correlated the variables are. As a consequence, I don't think that there can be a general answer to that question.
Great! Thanks a lot. That got me going.
$x$ is the set of training examples. I meant to say $x$ is made up of 3 types of samples i.e. positive, negative and mixed.

//can you verify that they all have the same features (variables)?// - Yes, they do
I would not think there is a compelling reason for the Bayes factor to be close to one on average when generating from both models. It all depends on the prior distributions for both models.
@whuber: Thanks!
 Can you write down what $W$ is like after being standardized? I don't know how you standardize $W$, but $W$ is not sum, but absolute value of sum, so we cannot apply CLT here, can we?  If not, what theorem makes "standardized" $W$ has a normal distribution?
This is exactly what is done in random forests.  Have you looked at that literature?  http://www.statistik.uni-dortmund.de/useR-2008/slides/Strobl+Zeileis.pdf
I am talking about exchanginability for the distribution $p(X_1,\\ldots,X_n)$. They are i.i.d. conditioned on $\\theta$.
Great answer! It was precisely what I was looking for.
Also, I'll be sure to check out the references.
Thanks a million!
If I understand you correctly, you can compare values before and after fixation (whatever that is), which means a paired test. Your difficulty is scientific as well as statistical, in disentangling how far differences reflect the result of fixation and how far they reflect differences in what tissue has been outlined. The question is how far everyone in your field must have the same difficulty.
This can all be implemented in Max/MSP/Jitter with the [peak] and [trough] objects for the first example and with [jit.3m] for the second example.
+1 Thank you for the clarification.  I took the liberty of putting it directly in the question so that all readers are aware of what you are trying to cope with.  It would be good to know more about why so many ties might arise.  Are you able to tell us what those observations represent?  If you can, please go ahead and edit the question itself.
What do you mean by "merging" CDF's?  This is probably straightforward if you specify what operation you are performing on the N random variables with those N CDF's and how those random variables are related to each other.
Quotas /choke :)
@Pat I'm doing some kind of outliers detection for text, like inverse spam problem or in another words detecting important texts. I may remove up to 90% points from the set in such way that in new set proportion of the important texts would be higher. I'm running knn and leaving only texts which are classified by it as "important" which gives me concentration of really important texts among them to be around 20-30% which is not enough for my task. I need concentration to be >50%.
@Joel, i didn't get it when you said "Ultimately, you find the best c & g, and **you can train the final model on all your data**." I've have divided my data into 5-fold,then obtained the best values for c and g based on the average accuracy.What do you mean by train the final model on the data?
@Candace White I think you will need to be more specific than "isn't clear" if you would like a focused answer to your comment.
And I believe the specific justification for saying it's nested is that you can create 1 from 2 by restricting parameters: Fix 2's `a=0` and you get 1.
First of all, I wouldn't place much trust in the K-S test with samples <25 or >300.  But otherwise, interesting:  how to quantify on a unidimensional, 0-to-1 scale?  On the one hand, it's not hard to imagine that when a distribution shows a perfect fit to the hypothesized one, the effect size would be 1.  But what about radically poor fits--how would one distinguish between the poor fits to the normal of, say, a U-shaped distribution, a uniform, or some multi-humped polynomial one?  Also, there's a question of scale:  it seems *Z* would have to be infinite for the effect size to be 0.
I added some code using JAGS where I seem to be getting a different answer. Where is my mistake? Is this happening because of the priors?
I'd divide by n-1 instead of n, no?
CW? No, it certainly has a potential single best answer.
There is no much use of Mahalanobis distance in cluster analysis, typically, because covarince matrices can be different for different clusters, and you don't know clusters in advance. If your variables strongly correlate but your clustering method "prefers" uncorrelated features, do PCA first to ortogonalize them. If you still think you need a SPSS function to compute a matrix of Mahalanobis distance between cases (pairwisely) - I have written one. (Unfortunately, my web-site is currently offline, so you can't take it, then leave me your email and I'll send.)
No the whole point of matching is to reduce the bias that results from lack of randomization. Throwing out treatment cases loses information but so does throwing out controls in the opposite situation. It could be that the set of treatment cases that you wind up with can differ from the original sample.  But that is done deliberately to make the treatment and control cases balanced in the characteristic that could confound the treatment effect. Reduced bias and confounding due to matching will probably more than compensate for bias that comes from the lost treatment cases.
Thank you. My data contained mixed types of variables, binary, nominal, ordinal and scale, all. So, I went for CATPCA first. The scree plot suggested me a 4 factor solution. But as CATPCA can not rotate the factors, so I used the optimally scaled variables in Analyze > Factor Analysis > Method(Principal Component) > Rotation(Varimax). I have tried different rotations too to get more clear factors. But not getting a better result! Now, as I mentioned, I want to use the two linear combinations and some other variables individually in a further regression. Will that be valid?
"Significant p-value": you mean that the p-value is small and so the null of independence is rejected?
why did the dose need to be reduced? if it was reduced based on data from prior time points, this is obviously an issue that isn't easily addressed
@user20650 It makes sense; but whether it is the best choice is another matter.
In most cases the needs of the follow-on application will determine the goodness of any solution.  Perhaps, to give us some guidance, you could say more about that.
+1 for the explanation of mixed norms. I never understood them myself.
This [answer](http://stats.stackexchange.com/a/64988/27403) describes how this can be done using a Cholesky decomposition of the covariance matrix. Of course, you could use `mvrnorm` from [MASS](http://stat.ethz.ch/R-manual/R-patched/library/MASS/html/mvrnorm.html) but it is less fun.
+1 Many good points here.  Regarding specific algorithms, I'd add that I've encountered uncertainty regarding C4.5 and C5.0.  I don't use either of them, but I remember encountering (many years ago) people who had concerns about whether they could re-implement the algorithms.
@ssde That's right (reading your "$\\mu_0$" as "$\\mu$", which is the only symbol involved in the concrete case): that's a classic one-tailed test, assuming that the alternative hypothesis is $\\mu\\in(c,\\infty)$.
No problem, I vaguely remember something similar to Q2 in a paper by Kohavi.
Thanks so much! That was really enlightening!
Thank you for clearing things up!
(+1) laughed out loud at "Giving a preposterous number of digits (males gained 3.102019 pounds more than females)".
@Cam.Davidson.Pilon Sure, but in this case, the likelihood surface will be almost entirely flat and the prior will dominate almost entirely.
This sounds like a transformation of the measurement.  My understanding is that first you prove stability in your measure (whatever it is) then you compute control limits.  The limit computation, like Levey-Jennings, is textbook.  The dial you can change is the measure itself.  It sounds like you are looking for the logarithm base-2 of a proportion.  

Could you supply sample (or synthetic) data here to allow a guy to show an approach on what you consider reasonable data?
Agreed. As an addendum I'd like to ask in the case where the goal is a medical application, which do you think is most important - training time, or accuracy of results?
One.  One cluster is always "reasonable" (a somewhat subjective criterion...) and takes only O(1) time, effort, and RAM to compute :-).  Lest this seem facetious or non-constructive, my point is that this question really needs some clarification and additional information to be answerable: what are you clustering; why are you doing so; what really does "reasonable" mean, and exactly what would constitute an "optimal" number in this situation?
How far have you gotten with building and training your RBM?
Tossing a coin so as to land the predicted way isn't all that hard, it just takes practice. (I've heard of kids tossing coins to determine the start of a soccer match - instead of calling heads/tails, they'd call 'odds/evens' (meaning different side, same side) because everyone could toss the coin predictably. A dice roll is much less predictable than a coin toss, so I'd say no, it's not possible. But given that magicians regularly do things that I'd say were impossible, maybe. It depends on what mechanisms they are allowed to use.
@rolando Which [comments](http://stats.stackexchange.com/search?q=user%3A4253+%2Bspline&submit=search) did you have in mind?  None of the ones I can find seem to relate to this question, but maybe I'm not searching for the right keys.  Even if you do make a good spline fit, how do you go from the coefficients to estimating the locations of the regions (which is not the same as getting the spline coefficients)?
Your assertion that 'the test is not working properly' is mistaken. When you *add* an observation to a sample, you totally change the conditions; it doesn't matter where you add it, you'll change the p-value in some way, and with such tiny samples, it can change a lot. I showed you that when you *move* an observation instead, then *as long as it was already outside the range of rest of the combined sample*, the K-W doesn't respond to it at all as you move it further from the data. The K-W seems to be behaving just as it should.
FA extracts but "fixed" number of factors. `Eigen values more than 1` and other similar rules only can orientate toward a likely approximate number.
I think you were using "frequency" in the scientific sense (inverse of the period), whereas in time series "frequency" is usually a synonym of period. So my suggestion of dividing by $q_{0.5}$ will have the effect you describe.
I notice that this answer hasn't received any upvotes yet. While it seems that it doesn't answer the OP's question directly ("under which conditions the quantiles of the boostrap samples of $\\hat{\\theta}$ provide a valid confidence interval about $\\theta$?"), it seems like you provide a useful and highly relevant example. I think that the answer would benefit from better formatting though - it would be easier to read if you added some blank space and used $\\LaTeX$ for equations and Greek symbols. You could add an Amazon link to the book as well (these help pay for the Stackexchange sites!).