tttjjj/elt_bench huggingface dataset:
I found [this paper](http://web.ipac.caltech.edu/staff/fmasci/home/statistics_refs/CoskewnessAndCokurtosis.pdf) through Google. Is it not what you want?
Forgot to mention in my post that $X1,X2,X3$ all are independent
I am interested to know if (a) KS entropy = Shannon entropy (b) If entropy of a system increases then that means the information content is decreasing since for ex in case of noisy systems, noise increases the entropy. So, does this mean that the phase space volume of a dynamical system contracts? I am looking for links between phase space volume and entropy for dynamical system
Adjusted $R^2$ < $R^2$. If $R^2$ is negatively biased then adjusted $R^2$ must be more biased, not less. Figure 1 in the Zimmerman et al paper you linked to shows the bias of rank correlation.
Don't reweight the ACS -- it is a delicate, highly sophisticated product, and with all due respect I don't think you are as good a statistician as the Census Bureau collectively is. If you can get definitions of job consistent with your task in [ACS](https://usa.ipums.org/usa-action/variables/group/work) or [CPS](https://cps.ipums.org/cps-action/variables/group/work) for nationwide comparisons, then the apples-to-apples comparison would be to compute the expected number of "diversity" categories based on ACS for your business to act as reasonable diversity targets.
I do not have enough reputation to downvote this!
IMHO t-test may not be a good idea here
This is related to a past question: http://stats.stackexchange.com/q/2275/495
@CYB, there are still a lot of other distributions that you can use as well, don't limit yourself to just those 2.
As I am not getting any responses in this statistical forum, I am not sure if this is proper forum to post this question, or somebody  (suggest) migrate this question to stackoverflow
As noted by wolf.rauch, MCMCglmm can do multinomial with 3 levels of the dv via family = "multinomial3"
But, as I said earlier, just do the two sample proportions test instead, since it gives the direct comparison (86% vs 77%) you want; the fact that it's logically identical to the other three direct comparisons of proportions (in terms of which tables will be rejected) is of no consequence to that.
(Continued) What exactly are they averaging over? The best parameter? All parameters (I think that would only make sense in this specific example). Still, I think the charts in combination with the hint to Freedman's paradox is quite helpful. Maybe it helps some.
Sounds right to me.  But remember that this is basically a prior probability, because it is based on expectations (aka beliefs) about what will happen, rather than a description of what will actually happen to the price.  The price in reality is not random, because it will be set by the managers of the various companies.  Probability provides a way to describe the uncertainty due to not knowing what the other managers will actually do when setting their prices.
Can you fit the models on historical data (t=1..36) and then apply it to new accounts that only have t=1..3?
Mann-Whitney can be a good choice, but be aware that it makes some specific assumptions about the relationships among the two groups.  It is good when results appear reasonable, but that cannot be the sole reason to adopt a statistical test: that would be getting into a circular argument ("we chose this test because it gives reasonable answers; our answers are significant because this test says so").  At a minimum, make sure to graph all the data in a way that promotes visual comparison of the groups.
Added to the question.
Related: http://stats.stackexchange.com/questions/36176/why-does-overliney-hat-beta-0-hat-beta-1-overlinex-in-simple
Physicians \\neq physicists
I suppose she meant something like "best subset correlation"; select subsets of $k$ ($k=40$ in her example) data points out of your $N$ ($N=100$ in her example) and calculate the estimate of the correlation $\\rho(X,Y)$ (assuming that she meant to know a subset of points with the best *linear* correlation). However, this process seems computationally expensive for large $N$, because you have to calculate $\\binom{N}{k}$ times the coefficient.
+1 for your answer, but the answer of COOLSerdash is still right?
That's much better (+1). I don't see any "3D arrays," but I don't think that matters: you appear to be describing what we might term a "vector-valued time series" (or process) in which at each step iid Normal variates are added to the result of the previous step. The two processes differ in that for the "relaxed" case the vector is changed before moving on to the next step. The change amounts to adding some values and then averaging them all--but how are the added values determined? It's also not perfectly clear yet, but you seem to be asking about how the means and variances will evolve.
@Alexis e.g. ["The binormal assumption on precision-recall curves" (ICPR '10)](http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&ved=0CEUQFjAE&url=http%3A%2F%2Fwww.ong-home.my%2Fpapers%2Fbrodersen10binormal.pdf&ei=gIrWU5XVFojB8QHd44G4AQ&usg=AFQjCNFaTYoP03zwx1QMtqOydEsY8AMU2w&sig2=U1POYjHLKrAvC4uVg_tBxg&bvm=bv.71778758,bs.1,d.b2U&cad=rja)
@ATMathew I understand that the specific values were your hypothetical choices.  I just meant should I interpret it to mean that y is on average 1.2 greater for mals than for females.
A combination of both works better. See http://www.otexts.org/fpp/9/4/
Hi Michelle, What I mean by the smallest interval is: there is an infinite set of intervals (each with its own alpha) some of which contain my new observation. I want to find the smallest of these. You are right that I can search from the answer by plugging in different values of alpha and checking if the new observation in in the interval but I was hoping for a more efficient approach since I'll have to run this calculation many times in a loop. Thank you.
nice! I like the approach, thanks for introducing me to this package.
Just a comment, not an answer: *Any* program that minimizes a sum of two terms, such as
$|w|^2 + C \\sum{ \\xi_i }, $ should (imho) tell you what the two terms are at the end,
so that you can see how they balance. (For help on computing the two SVM terms yourself,
try asking a separate question. Have you looked at a few of the worst-classified points ? Could you post a problem similar to yours ?)
From what I have been told, yes, permutation (monte-carlo). I have been trying to figure it out in R, but I am at the point where my eyes are melting.
@B_Miner I've updated my answer to address your question.
Any geostats text that covers change of support should explain this. One of the oldest (and still useful) is Journal & Huijbregts, *Mining Geostatistics*. Cressie obtains a general result for block averages in *Statistics for Spatial Data.*  The kernel convolution formulation of the concept of support appears in the introduction to Diggle & Ribeiro Jr., *Model-based Geostatistics.*
You also might find [this question](http://stats.stackexchange.com/questions/2910/how-to-efficiently-manage-a-statistical-analysis-project) interesting.
Doesn't multiple regression with $N$ observations require an $N$-dimensional TinkerToy set though?
Why are there 12 points? What is the underlying question of interest?
I presume you are using the GPML toolbox? Try plotting XTest vs m.
There's been some other discussions on similar topics -- see e.g. [Textbook deriving Metropolis-Hastings and Gibbs Sampling](http://stats.stackexchange.com/questions/33817/textbook-deriving-metropolis-hastings-and-gibbs-sampling)
You also need to coordinate between the RNG streams. Snow does that, multicore may now.
A standard example in signal-processing circles is a process consisting of a time-varying deterministic signal plus zero-mean weakly stationary noise.  This process is _not_ weakly stationary since the mean function of the process is the signal but it _is_ covariance stationary.  The examples in Karl Oskar's answer are of this type, with noise process being strictly stationary instead of only weakly stationary.
My very +1 for this instructive response (which nicely complements the other one you gave on SO, btw). For the OP @sridher who seems to wonder about understanding how Cluster Analysis works, there are a lot of clustering tutorials, including [this one](http://www.norusis.com/pdf/SPC_v13.pdf) or [this one](http://www-users.cs.umn.edu/~kumar/dmbook/ch8.pdf) (both in PDF).
@Xi'an
I use improper priors and the sample is quite small and maybe this might give some problems with properness of posterior. But another problem is that the general model is quite complicated (nonlinear hierarchica regression) and I do not know how to check integrability against the prior in this case. Maybe there exsist papers that might have guidance on such issue? 
I would really appreciate it.
@probabilityislogic, yes but in Bartlett test case this average is used to determine whether the variances are identical or not. If they are not identical there is no point in averaging them, since this average does not estimate any parameter.
@psychometriko, Well, It always is so with p. axis. With other methods, the ordering may depend on the software/package you use. What I recommend to do - to be sure that 1) ordering is from highest variance to lowest variance 2) variance is maximized for every preceding factor - do PCA of the _loading matrix_ after the extraction! (Do this PCA without centering/normalizing, of course.)
I get the impression that the `gmeta` package ([tutorial PDF here](http://www.stat.rutgers.edu/home/gyang/researches/gmetaRpackage/gmeta.tutorial_2.2-3.pdf)) would help you estimate a population mean, but I can't tell whether it would work for estimating a population median...
You can't "make sure" of this, you can only set the probability that, for a given effect size and alpha value, you will get significant results.

Also, it isn't clear if this is what you are doing, but you should do power analysis only *before* collecting data, search 'post hoc power analysis' for more on this.

Finally, this whole topic has been discussed a lot here; please see, e.g. [this](http://stats.stackexchange.com/questions/21237/calculating-statistical-power)
@ whuber: not with respect to the unit root process
I made the corrections.
In the context of maximum likelihood estimator, it is obvious that any constant is irrelevant. My question is not closed in the MLE estimation, but in the more general Bayesian framework. Due to my innocent/stupid previous understanding I did not noticed that you really start with likelihood, and after you enrich the model with the Bayesian equation you simply switch the fixed/reference point (you switch from fixed parameter to fixed data) to estimate parameters. In the book the switch was already assumed, and in this context the likelihood is not a pdf anymore.
I don't see this as an unusual application of factor analysis -- I've seen tons of these (and by the way, putting factor scores into regression as predictors leads to [measurement error attenuation bias](http://ideas.repec.org/a/spr/psycho/v66y2001i4p563-575.html)), but as Maarten Buis pointed out in another thread, these variables look more like a formative/causal than reflective/effect indicators of the manager experience.
Could you please reformat your answer (add some paragraphs)? It is quite hard to read.
Ha, yes when in doubt check to see if you understand the definition. As you mentioned I was thinking more in terms of convergence in probability (which now that I think about it we haven't quite shown). The answer is clear to me now. Thanks!
I think you should ask the moderators to move this question to stats.SE.
"For instance, why do you think your independent variables are correlated? Is it that $X_1$ might have an effect on $X_2$ and this has an effect on $y$?" This is an important issue to address. If, in your observed data, $X_1$ and $X_2$ are correlated, you may not be able to disentangle the effects of $X_i$ on $y$ from each other. With just the information in your example, it is possible that $X_2$ has a causal effect on $X_1$ and $y$, and it wouldn't be feasible to vary $X_2$ while holding $X_1$ constant.
I take it back, thanks, I think the question has been answered as you suggested.
@EamonnJohnKeogh Welcome to this site. If you have time and inclination, other users of this site would certainly benefit from your full reply on this thread.
Thanks for the insightful response Maarten. I get the impression the field of statistics is fracturing into many subfields which don't communicate with each other.
Thank you Peter, you confirmed what I was thinking!
Hmm, "drosophilla" is, well, when you put a simple experiment and get knowledge which is valid for much much more complex problems.. Are chip design or robotics simple? I dont't know! :)
GREAT anwser! I've read now about caret. Not 100% sure about the relationship between caret and glmnet package, so I did an update to my question to clarify the 'merge' of these to packages or either the switch from glmnet to caret.
Welcome to the site, @user23658. Would you mind fleshing out your question a little? I'm not sure if it is answerable in its present form.
I presume you can already work out $P(\\text{rnd} \\leq x)$ for any $x$. Just rearrange the expression like so: $P(\\text{pattack} \\geq \\text{cdefense} + \\text{rnd}) $ $=$ $ P(\\text{rnd} \\leq \\text{pattack} - \\text{cdefense})$.
The Excel function TDIST takes in a t ratio (and df and #tails) and reports a probability. TINV takes in a two-tailed probability (and df) and reports a t ratio.

From the Excel help:

TINV returns that value t, such that P(|X| > t) = probability where X is a random variable that follows the t-distribution and P(|X| > t) = P(X < -t or X > t).

A one-tailed t-value can be returned by replacing probability with 2*probability.
+1 I've used the Box-Cox transformation with success. In R,  http://stat.ethz.ch/R-manual/R-patched/library/MASS/html/boxcox.html
@chl - thanks for the clarification.  I feel much better about my ignorance, seeing as I know virtually nothing about genetics, I can't even spell the actual word for DNA (its "deoxy-narglyic-acid" right? lol).
Wow, I love the word "aleatory".
I wonder if there is confusion somewhere with the related concept that p-values are uniformly distributed under the null hypothesis..
Remove all occurrences of "first" from the problem.
@Kaspar: that's the case of an "outer independent test set" cbeleites refers to (though 100 observations would be too few to get a precise estimate of performance).
I think [this](http://stats.stackexchange.com/questions/55501/test-a-significant-difference-between-two-slope-values) is gonna help you. An maybe [this](http://stats.stackexchange.com/questions/59327/how-to-compare-two-regression-slopes-for-one-predictor-on-two-different-outcomes/59331#59331) too.
I suggest to change "real values" in the question header to "scores" or "confidences", since "real values" is a rather arbitrary term (as explained in my response).
Yeah $w_t$ and $x_t$ have same variance. But the mean is different. So we can only say that the variance is equal not the distribution of $x_t$ and $w_t$ itself. So how can we write $p(x_t|x_{t-1})= f_w$
This was very very insightful and validated some of my thoughts and gave me something to think about.  i really do appreciate your thorough input.
Hm, interesting, so far I only found your variant of expressing it...
@B_M How does that work?  Perhaps you are thinking of medians?
Surely one of the applets at http://statpages.org/#Power will solve your problem.
From a long career of setting questions I can say that it's largely a student myth that teachers set trick questions designed to catch students out. Why would they do that? If grades are lousy, the teachers suffer too. It should always be true that questions are designed to test understanding at the level being taught and expected, but that's different. It is often true that questions are easy once you see the kind of question being asked and difficult to impossible otherwise, but that's different.
At first I thought this reply did not address the question, but then I realized it's pointing out that a t-test is probably inappropriate because the evidence is that the data are (a) few in number and (b) highly skewed. (Normality isn't really an issue with t-tests; normality of the *sampling distribution of the mean* is what matters.) Interestingly, a permutation test of the mean for these data gives a one-sided p-value of 0.00038 (n=100,000), suggesting a two-sided p-value around 0.0008, which is exactly what a Wilcoxon test produces. The t-test lacks a little power, but seems ok here.
I am not sure I understand. Unless you are talking about multilevel models, all the variables on the right side of the equation are treated the same.  Please elaborate
I'm not sure this question deserves *so many downvotes*. Although it lacks some information, some clarifications are given as comments, upon request -- @yO2gO, maybe you could now update your question and just add a rough definition of what you think of or expect from such a *confidence score*?
Indeed, it makes more sense.
http://wikidoc.org/index.php/Cross-validation : "The K results from the folds then can be averaged (or otherwise combined) to produce a single estimation"
Can you provide some more information about your data. How many points might there be for "A", "B", etc? Are the values in the second column presumably continuous?
@flameiguana: the link works for me, maybe it was just a temporary problem
Thanks, this is an interesting paper. I will try both the MSE and one of these loss functions and see what I get.
I'd say differently: it is optimal whenever you want to maximize the accuracy. Otherwise is suboptimal. See http://en.wikipedia.org/wiki/Sensitivity_and_specificity and http://en.wikipedia.org/wiki/Receiver_operating_characteristic for performance measurements of classifiers.
I find such rubrics less than satisfactory. One is that they have no direct connection with the principles behind the plot: they have to be memorized separately (and can be completely confused by a faulty memory). Another (in this case) is that it's too complicated to be reliably useful. Yet another is that a lack of standardization in how such plots are drawn can make this method incorrect when applied to a qq plot made by a different procedure. But qq plots are easy to interpret: see my attempt at an explanation halfway down http://www.quantdec.com/envstats/notes/class_03/probability.htm.
Classical hierarchical clustering methods _can take in_ nothing but symmetrical matrix: a distance from A to B = from B to A. Special other methods exist to deal with asymmetrical (you may google). As for triangular inequality - it is not necessary condition for the methods you mention. (However, common wisdom thinks of "distance" as smth with the inequality, so it is worth considering to impose it if it's missing. To do it, iteratively add small constant to the distances and check. And if you continue to add upon reaching it then you will soon arrive at euclidean distances)
one approach you could take is to draw it out using a [probability tree diagram](http://www.mathsisfun.com/data/probability-tree-diagrams.html).
Wow, this is a great explanation.  Thank you so very much!
Explain what is 2D?
I would like to learn about multiple imputation and was looking for an online learning material. Could you suggest some learning material for MI?
@Rabnir You just minimize ∑ |e$_i$|= |Y$_1$-β$_1$-β$_2$|+|Y$_2-$2β$_1$|+|Y$_3$-β$_1$+β$_2$|. Other robust approach are possible also.
+1. However, given that there are only about two years of history, I wouldn't worry too much about leap years - any error introduced by using a 365 day period instead of a 365.25 days one is probably swamped by the noise in the series.
Totally off topic, can you recommend some bibliography on Edwin Jaynes and "probability as extended logic" ? Greetings!
Surely it depends on your question?  For instance, if I was interested in the answer to the question because I was allocating my marketing budget: "is about 50% of the population of the USA female", a census and a sample would give indistinguishable results.  But if you're a lottery company and you want to know if anyone holds the winning ticket to your lottery, I'd rather a census of the ticket holders than a sample of the ticket holders.
"Still the nullity of parameters" was a typo that I fixed in the text. Sorry about that :-)
How many percentiles are included in your real data? I hope it's more than in your example!
@John As I wrote, error bars are a visual *clue* to help make ad hoc assessments while investigating the plot; actual testing needs some hypothesis to be tested, thus obviously should happen in the text.
James -- if everyone gets the treatments in the same order, how do you separate any potential order effects from treatment effects?
$B_0=0$ is on the log odds scale. Try converting it into a probability & see if it ends up equaling 0.
Same here, which is why I ended up using the mean of the segments to test against.  In my specific application I can assume that the majority of segments will be valid and only a minority are artifact.  Therefore, the mean of the segments will generally reflect a valid waveform.  Hence comparing each against the mean will find those that have similar distribution and can be considered valid.
Are you just looking for the `dbinom` function?
Nikita: Where in the accepted post do you see an answer to your question, that is, if I read you correctly, a function $f$ defining the UMVE of $\\beta$? If there is one, I might have entirely misunderstood the question, in which case please explain what your question is, really...
You can find more ideas and code in "Separating Two Populations in a Sample," http://stats.stackexchange.com/questions/899/separating-two-populations-from-the-sample.  (Is there perhaps some better way of cross-referencing threads than I've done here?)
@DPY would you like me to edit my answer to reflect what 
ttnphns's comment suggested?
Thanks! That is what I thought! Is there a easy way of doing this in r? I'm using rugarch for the forecast!
Rather than necessarily focus on polynomials *per se*, there's a wide literature on approaches that don't try to identify a specific functional form but focus on assuming smooth relationships. Both spline-regression (including penalized-splines) and local-linear/local-polynomial (i.e. kernel-based) smoothing are motivated by this sort of desire. See, for example, chapters 5 and 6 of [*Elements of Statistical Learning* 2ed](http://statweb.stanford.edu/~tibs/ElemStatLearn/) Hastie, Tibshirani, & Friedman (a pdf is available at the book website there - you can see the link by scrolling down).
@JamesStanley I fixed the typo. The questions still stand
I think you can explore these packages for your case: hglm or HGLMMM.
Bayesian methods are quite difficult in the details. The overall picture is easy: *Return a distribution of the parameter in question, given the data and prior*, but the small details like: *how to sample*, *what to do with samples*, *what do I need to calculate* and so on can be intimidating. It took me three straight days staring at a computer screen to finally break through ahha
In light of my analysis at http://stats.stackexchange.com/a/50583, this reasoning appears to be incorrect.
You don't need to do either. You can compute the expected return on your bet given the bookmaker's odds (which determines the payout), under your probability model. If the expected return is high enough (at least positive, presumably, though if you're risk averse it would need to be more), you should bet.
I think the question of how to compare two bimodal distributions depends on what you are interested in comparing, but I would go for graphical methods here. Overlaid density plots, quantile-quantile plots, perhaps parallel box-plots.