tttjjj/elt_bench huggingface dataset:
I know this seems unhelpful and kind of hostile, but they don't mention it because it is obvious.  Also, you want to be a little careful, here.  Usually, when you encounter a MSE in actual empirical work it is not $RSS$ divided by $N$ but $RSS$ divided by $N-K$ where $K$ is the number (including the intercept) of right-hand-side variables in some regression model.
You could also use other anecdotal evidence (e.g. amount of garbage generated compared to normal).
[The Essential Guide to Effect Sizes: Statistical Power, Meta-Analysis, and the Interpretation of Research Results](http://www.amazon.com/Essential-Guide-Effect-Sizes-Interpretation/dp/0521142466) by Ellis is a good introduction book. The first half introduces the idea of effect sizes and how to report them, the second half concerns its application in meta-analysis. It wouldn't make you ready to immediately work on advanced cases, but will get you reasonably literate in the subject to dive deeper.
How would the regression output change if you were, say, to add $10^6$ to each `pop` value and add $-0.0116584\\times 10^6$ to each `fuel` value? Intuitively, that shifts the data far from `pop=1029` without altering the regression line and therefore should result in a much wider prediction interval. That means you can focus your research on those elements of the output that change.  (Even if you don't have the actual data you can make some up and run both regressions to see what happens.)
Using `0` for unknown will really screw you. Because it is 'more' similar than if they had answered the exact opposite! The most central object will be the one that answered not a single question.
Your reasoning is correct, but there are also various tests for that. Regards, -A
This topic is pretty thoroughly covered at http://stats.stackexchange.com/questions/4220.
Having data for different years definitely makes a difference: You could then view your data as a sample from all possible years and there would be variation over time. Having multiple years gives you more data, lets you build more complex models.
I like this idea, but as it is now it doesn't fit the requirement that the new cluster sizes be close to the original. One way to achieve this would be to, instead of uniformly choosing an urn for a ball, assign each urn a probability proportional to the size of the original cluster and then use that categorical distribution when choosing which urn to put a ball into. This is intimately connected to the Dirichlet type process i described below, with the only disadvantage here is the lack of a parameter describing how 'close' the sample is to the original distribution on average.
@Didier Piau, @cardinal the book tells that the $Q$ is defined on $\\cup \\mathcal{F}_t$ which is algebra, and it has to be extended to $\\mathcal{F}_{\\infty}$, which presumably is $\\sigma(\\cup\\mathcal{F}_t)$. I will fix the text.
If the Weibull model is proportional hazards (which would be the usual case), then the estimate of that proportionality should be comparable.
@SihemSih Dimensionality reduction and variable selection are not exactly the same thing, as per my description. You can reduce dimensions by using techniques which transform the feature space, such as PCA or network trimming in neural networks. It is also possible to use ANNs for selection of features using the feature weights of the network. Which is your goal ... purely feature selection  or dimensionality reduction?
Alas there is more I'm not saying.  Each algorithm has a (different) number of calibration parameters so I want to use AIC to reflect the complexity of correctly choosing these.
I've just looked in a couple of mathematics textbooks. Neither seems to contain such a statement (there's no discernable hint of it in the index or contents, nor did I spot any from looking through the text). I think your claim that all mathematics textbooks say what you said is unlikely to be true. Can you cite an actual source, so the context (assumptions and so on) of the claim can be identified?
+1 Gung.  It is a good answer.  I mention Pearson correlation even though I realize that the number of points is a count variable.  Other correlation measures could be used.  I don't think it is really a regression problem though.  The OP is not looking to predict the radius based on points inside nor vice versa.  He just want do determine if they are positively related (tend to increase or decrease together).
"Further confusion surrounds the benchmarks suggested by Cohen (1969, pp. 278–280) to define small, medium, and large effects. As was explained earlier, these were based upon values of f that correspond to values of partial $\\eta^2$ of .0099, .0588, and .1379, respectively. ...
@LonelyBear Can you please register your account on SO and go back here? This way you will be able to take ownership of your question and be able to comment in its thread.
@alex: I don't see why that should be a problem (at least with my limited knowledge).
I don't think it is really considered for other classifiers either.  For probabilistic classifiers, often the criterion $f(x) \\geq 0.5$ is used, but as far as I am aware this is merely a convention and makes little difference in practice.  Equivalently there would be no problem in assigning the pattern to the "positive" class if $f(x)=0$ for a support vector machine.
It seems to me this question on the normal-gamma conjugate has already been asked (and answered) many times on this forum...
Hi. The Gaussian linear model with a factor and a continuous predictor is commonly termed as "ANCOVA - a helpful keyword to search on the web
(+1) A great answer, which is surprisingly under-voted. I noticed a confusing typo: "excluded" should read "included". Apart from that: what would be an expected *practical* difference between treating school as random vs. fixed effect? I understand that treating as fixed would not allow predicting a performance of student from a new school, but what about the differences on available data? Let's say other fixed effects are students' gender, race, and weight (whatever). Does treating school as random/fixed influence the power of main effects or interactions of interest? Any other differences?
It would be great, to get some more advices. I don't know how to build this in R. The problem is, that I have problems to rebuild the predict() output and with it the CI for the predicted probabilities. Thanks a lot
Hi mpiktas, thank you for pointing me to the van der Vaart book. It actually helped: my original problem was to justify an asymptotic approximation $A\\approx B$ and, with the information in Asymptotic Statistics, I was able to do that (informally) with von Mises calculus. But I'm still very interested in learning how one would prove the assertion in my original post. I studied some variants of Glivenko-Cantelli and Donsker theorems but I'm still stuck. Thanks!
The first question is tough: one tends to think of [parametric bootstrapping](http://stats.stackexchange.com/questions/10727/how-to-get-standard-error-of-a-function-delta-method-vs-simulation/10729#10729) or the [delta method](http://en.wikipedia.org/wiki/Delta_method).  Are these the sorts of calculations that would be expected of you?  The second, in comparison, is [almost trivial](http://stats.stackexchange.com/q/9913), so consider addressing it first.
Much good advice here, but also some presumptions about the OP's background. Angrist and Pischke [NB] could be a useful book if you really are an economist and this is about your second time round with regression. http://www.amazon.com/Mostly-Harmless-Econometrics-Empiricists-Companion/dp/0691120358 gives more details. Andrew Gelman's review at http://www.stata-journal.com/sjpdf.html?articlenum=gn0046 gives a good perspective of their book from a modest distance.
I edited my answer to address your question.
For the word choice, start with its [etymology](http://www.etymonline.com/index.php?term=moment).
As you've written this, you *don't* need to include both $x_1$ & $x_2$ in the model - either one will do as it determines the other.  Are you sure that's what you meant?
I removed the Fisher test tag which is irrelevant here since you have correlated data arranged in a 2x4x10 array (or a design with two factors--10 trials and 2 groups--and a response variable like "number of attempts before success", or three factors--10 trials, 2 groups, and 3 replicates--with outcome=success/failure).
That was confusing, p is the number of parameters in the model, I now use $\\pi$ for the proportion. Thanks for pointing that out.
You've posed 2 problems: 1st your CF engine is biased learning. For the question in the title, the only way I see is by stratifying your image set into classes (e.g [0,0.5),[0.5,1]), crossing estimates and observed values in a confusion matrix and then computing precision and recall from it.
After learning the basics, it would be quite helpful if you use some tool i.e. Matlab, R, Excel to view your results in a more human understandable format.
Imagine you try to integrate the constant function $f(x) = 1$ on the interval $[0, 1.96]$. You will sample 1000 values $x_1, \\dots, x_n$ in this interval, compute the mean of the $f(x_i)$, which is 1. The value of the integral is 1.96! Do you see now what’s going on?
I'm not sure what "all statistical distributions" is supposed to include. I'm not aware that there is a fixed, finite list of possible distributions. Certainly there is a relatively small number of distributions that account for >99% of all analyses that are actually run, but even then, this doesn't make sense to me. Typically, people think about which distributions you might consider by thinking about what the data stand for and how they were gathered. That is, most of that work is a priori. Testing against a distribution is usually just a check to see that it's not too unreasonable.
+1 A sweet puppy dies each time you do feature selection with genetic algorithms.
@JG I just edited the post. I meant to write that we minimize the squared skewness of the transformed data because the best possible skewness is zero. For more information on skewness, see the [wikipedia article](http://en.wikipedia.org/wiki/Skewness).
0. Plot your series and think about it.
From your comment above and as you've tagged this with `propensity-scores`, I believe 'common support' means the same as 'overlap in the distributions of covariates' as discussed by [Rubin 2008](http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.1640v1.pdf). My reading is that this paper says lack of such overlap *is* a problem. I'm no expert on propensity score analysis, but I understand Rubin to be saying that this is a problem for estimating causal effects from observational data whether or not you use propensity scores, but using propensity scores make it more obvious.
What matters is *the effect on your inference*. The only form of inference such a tiny effect would be of any impact at all would be with a prediction interval... and even there, I'd likely use it with little compunction, unless I needed a prediction interval far into the tail (say 99% or more). Of more concern would be issues like dependence and bias and mis-specification of the model for the mean or variance.
Are you familiar w/ mixed-effects (aka, multilevel or HLM) models? Your situation sounds similar (structurally) to studies in psycholinguistics where there are participants & words, both of which are treated as random factors sampled from a larger population. This thread might be a place to start reading: [Example reports for mixed-model analysis using lmer in biology, psychology and medicine](http://stats.stackexchange.com/questions/26855/).
@BR whats the bottle neck here? Basically what's taking time in `Rprof`.
Are you able to measure or find the actual sunrise/sunset times with some degree of accuracy after they have occurred to test the predictions against some known/true values?  Also, is there a general agreed upon definition of sunset/sunrise that would disallow disagreeing estimates?  I'm not an expert in the field, but I would expect that the estimates are based off a mathematical model with little variance other than your physical viewing location.
Hi, Michael, welcome to the site. I think you make a good point here, but I wonder if it might be helpful for the OP if you provided a little more information. Can you say what a ROC curve is & why it might be better; perhaps even provide a link to some internet resources that will allow the OP to begin exploring further?
+1, nice information here.  Your point about value and how the colors will render after conversion to black and white is particularly good.  The link to the Few paper is helpful as well.  One note: it's best not to refer to other answers as "above", use @so-and-so instead; the answers move around based on how many votes they get.
The link doesn't give us the full paper and so we can't look at Section 2.2. Can you give us the relevant part of the section that gives the derivation?
Should this be 1 - (1-F(x))^n?
It's always good to try special cases, like, say, $X = 1$ with probability one (conclusion?) or, $X \\sim \\mathrm{Ber}(p)$. Even more qualitatively, note that a random variable can have a second moment without its moment generating function being finite, which is already enough to disprove such a result in full generality, without even having to exhibit explicit counterexamples.
Added the result, still not sure how to interpret it! Please advise.
You are following me perfectly. 
Thank you for your view on weighting the regression identically. It is the approach that I am taking for the same reason that you suggest.
Yes currencies are a zero sum game when look at the cross rates, that is, USDZAR or EURPLN or whatever (the entire matrix). But, I have used PCA to create currency indices so that we isolate the movement due entirely to the currency itself. I then take the first principal component of the 28 indices as the market beta, and I observe that we DO have some currencies which are low or high beta. Empirically this my experience.
Did you intend to write this as a comment beneath Dapz's reply? Also, I've merged your two accounts but you will need to register this one to to benefit from all the advantages of the Stack Exchange community.
thank you F.Tusell, Is there any code example that you can share?
For the second proposal, what is the form of this posterior?  Another Dirichlet?  It makes sense that the Dirichlet would be conjugate here, just like if we were using a multinomial.  But we're not using a multinomial.  So what is the pdf of the distribution you propose?  (It's a multivariate bernoulli that has been conditioned on observing n successes, right?)
Taster relationship and gender can be ignored - This is a variable used for other analysis within the experiment. It would be easiest to make the taste location the independent variable, and treat the five different flavours as separate analyses. I'm trying to see if older participants are more likely to taste the flavour in one particular part of their tongue, or if it stays seemingly random across all ages.
Note that cluster analysis does *not* predict. So it will not get you very far alone. It may however improve the result of the others *sometimes*.
try to use a graph database. the bit vector solution seems to bee reasonable but not for a large amount of data in a relational database, a simple query execution time could jump up to seconds...
Perhaps "infinity" should read "one"?
Did abhinavkulkarni answer your question?  If so, please mark that answer as accepted.  Otherwise, please clarify your question.
An intervention doesn't necessarily need to be a planned event. For example, the effects of natural disasters (i.e., hurricane) on oil or gas prices could be modeled as an intervention. May be we should call it an event instead of an intervention but the modeling procedures are the same.
Epi, it's all specified in the `pump` function: $a$ and $b$ are hyperparameters for $\\theta$ (themselves with Gamma priors) and $\\theta$ is a parameter for a Poisson model for the probability of failure (as a function of time).
Alternatively, look at asymptotic p-value the one based on tau values. If p<0.05, then the null of unit root is rejected at 5 percent level. Here p<0.01 so null of unit root is rejected at 1% level. So, it is stationary at 1 % level.
In the work cited above, the authors test three types of filtering, by effect size (average inter-group fold-change), by value or signal (mean across all samples), or by variance (across all samples). With both simulated and real gene expression data, the effect size filter improved the power but also introduced FDR bias. The signal and variance filters, which were independent of inter-group differences, did not introduce significant FDR bias.
@xiaoyao, yes I assumed $t$ indexed time and $i$ indexed the features in your feature vector. If your feature vector consists of $n$ binary random variables, then in general you will need $2^n-1$ parameters to represent the conditional joint distribution $p(x_t\\mid s_t)$. This is exactly the same as what you're already doing when converting the binary vector into an integer, and as you noticed, will get unwieldy very quickly. One way to deal with this problem is to assume the features are conditionally independent given the state, in which case one would only need $n$ parameters.
Is the sum of two independently Bernoulli distributed random variables a Bernoulli random variable? Nope. So the original question needs to be rephrased as something about independent and suitably scaled random variables.
Welcome to CV, @AjayShankarBidyarthy. [Your question](http://stackoverflow.com/q/23495597/1217536) was too broad on SO; unfortunately, it isn't any less broad here.
I have improved your formatting. As you see, you can put $\\LaTeX$ straight into your post (even down to having the underline be green as in your original), so there's no need to use images for a little mathematics.
Actually, few bookmakers would make money if they had to depend on forecasts. Sure, they want to maximize gain, but at any given time they constrain this objective by making sure that *no matter what the outcome,* they will end up paying out less than they have *already* taken in.  In this fashion they do not have to forecast anything, nor do they even care whether the odds they are offering are "correct."
could i do chi-squared, by combining male and female "yes"s and male and female "no"s and then fill in the contingency table with combined yes, and combined no, as my rows; and for columns use survey version?
Should be community wiki.
@MichaelChernick : I don't believe that is correct. Suppose for instance we have three uniform distributions on $[0,1]$. Then, if I'm not mistaken, $P( X_1 < \\max_j X_j ) = 2/3$, whereas $P(X_1 < X_2) = P(X_1 < X_3) = 1/2$. I do not know if you meant to write $P( X_i > \\max_j X_j )$, but then the same example shows that it still isn't valid.
Can you clarify why you want to use a generalized linear model? If it would be possible to use a t-test, then your response variable is presumably continuous & normal enough. Why not use a regular mixed effects model or a multiple regression? Of course, these are special cases of GLiMs, but we don't usually refer to them as generalized LMs, we typically reserve those terms for cases where the response variable is not continuous (eg, binary or a count, etc).
I guess I should start running :)
+1.  This is called a [beta distribution](http://stats.stackexchange.com/search?q=beta+distribution+prior).
@amoeba: Thank you for the clarification, I guess I didn't read your answer carefully enough. Yet, I'm still troubled about an optimistic bias of this approach (both procedures). By measuring accuracy while trying different CV splits, you estimate the variability that is caused by the arbitrary splitting. Yet, you ignore the fact your entire data is a random sample of larger population of observations (that you didn't collect). If you have a small dataset that by chance achieves perfect performance (regardless of CV splits), your confidence interval is zero and this is incorrect.
LMs and GLMs don't make *any* assumptions, statistical or otherwise, about the relationships among predictors. This is fortunate because pretty much the only time they'll be all neat and uncorrelated is for balanced experimental data.
Thank You very much :)
Thank you so much for these excellent suggestions! With regard to the Gini index, is it reasonable to use with so few observations (5)? Will it be at all meaningful?
For intuition about the CLT, please see http://stats.stackexchange.com/questions/3734.  The short answer (given by [laws of large numbers](http://stats.stackexchange.com/questions/22804/what-theories-should-every-statistician-know)) is no: $\\hat x$ converges to the common expectation of the $X_i$.
It's the same except for the whitening part.
This comment doesn't impact on your answer as an answer to the question, but your link doesn't show *all* possible charts... for example boxplots, mosaic plots, biplots just for starters are all missing.  If you want a comprehensive view of all charts it's probably better to think in terms of principles rather than enumerating them all - the "grammar of graphics" is a good start.
+1, however, the phrasing is somewhat ambiguous: being 'linear' means *linear in the parameters* which is unaffected by the existence of polynomial terms. I know you understand this, but the latter half of your first sentence might confuse people who don't on that issue. Would you mind tweaking the phrasing a little?
I'm reluctant to convert this question to CW because it looks like you already did some consulting and are asking for thorough comments and advices (like one of the reply you got already) that might lead to an acceptable answer.
@Brandon -- Iterator put the smiley in there and you *still* got whooshed!
@MichaelGreen changed my answer entirely. Do you feel you can implement it?
That really depends on the underlying model R code and whether the formula or non-formula interface is used there, so it is hard to say
(+1) I figured this information could be all effectively put on a single graph without too much clutter. Thanks for spending the time to demonstrate how it can be done!
@Emre, by level of dependence you mean what?
@csgillespie: thank you for retagging it :)
I think it would help to tell people what fit1 and fit2 are
Glad I could help. Next time you ask for something in relation to a software package, try to state the version you use also (`Help` > `About Gretl`); it will save you hassle in the long run.
yes I'm also thinking that VSM is an improved version of bag-of-words.
The point is that while $E[(\\hat{p}-p)^2]=\\frac{p(1-p)}{N}$ you also have to consider the relationship between $\\frac{p(1-p)}{N}$ and $E[\\frac{\\hat{p}(1-\\hat{p})}{N}]$
@Madeline, I think you ought not to feel knocked out. Remember that rotation is an arbitrary tool that only aids interpretation, it doesn't change relative positions of the items. What I think I'd do in your situation: either (a) base myself on the 5-factor solution, plus maybe discard those 2 questions that split away from the rest and redo then 4-factor model; or (b) conclude that some of the items are worded unhappily to be multi-meaning, and reword them to make them less so.
what is a 'mean correlation coefficient'?
Hi Maarten, thanks for your comment. I edited the question to better reflecft what I want, as I was talking about the marginal effect of X, which in this case i not b_3, but b_1 + b_3*Z. Does it get clearer? Thanks again
Are you interested in conditional distribution of $X$ given $N$ or unconditional distribution? Try to write your question properly so we can help.
Ok, that's great answer does what I asked and a bit more. I suspect I will award you the loot, but I'll just wait a few hours to see if anyone else surpasses this (I doubt it).
I updated my post again (I kept the y for simplicity)
If your goal is to quantify parameter dependencies have you considered a sensitivity analysis? This [report](http://www.nrel.gov/docs/fy08osti/41958.pdf) may be of use to you.