tttjjj/elt_bench huggingface dataset:
I'm just guessing here, but it seems to me that your original distribution is probably highly dispersed (and thus has little probability mass in the region where $r(x) < 1$), while the distribution you want to use to sample regions where $r(x) < 1$ with reasonable probability is the nearly singular one. If so, watch out! Importance sampling works best when the samples come from a distribution more dispersed than the target; in the opposite case, importance sampling estimates can have infinite variance.
The long answer is "yes" !  +1 and a LOL.
But why do you want to standardize your data, in the context of using the KS test?
Quite welcome! Sorry to say I share your confusion and can't help further. I think he *might* intend that $p_i$ is drawn from a different distribution for each cohort $j$. Meaning, each cohort might be analogous to a mint from which studies, or coins, are drawn. (I expect it would all be very clear if we heard the talk the slides are meant to support.) You might have some luck if you check and see if there are any code samples to support the book the slides mention. Model descriptions can be ambiguous; code cannot. Hope this helps!
The ACF and PACF suggest that there is no significant correlation to be captured by an ARMA model. The autocorrelations are within the 5% significance bands. You could test this with the test statistics in `Box.test`. You may be interested in [this post](http://stats.stackexchange.com/questions/106038/estimate-arma-coefficients-through-acf-and-pacf-inspection/).
Hi and thanks for your suggestions. SPSS doesn't do permutation testing, but, the GLM sounds like something that could work for me. My values are frequencies (Hz). I can run a generalized linear model but in SPSS I am a bit overwhelmed by settings. I have set it up so I am running a poisson loglinear model, the response (DV) is my frequency values, the predictor is what condition (1 2 3 or 4). But SPSS gives me a couple of other choices - one tab is labelled 'model' and another is labelled 'EM means' I don't know what I'm supposed to do here... Thanks again for any help, Roddy.
Do you want to first correct your code? Living has 10, Dead_Dist has 9 and Bay_Dist has 8 observations! They must have the same number of observation. You didn't define `mydata` as well.
Are you seeking a taxonomy of predictive modeling methods for univariate $Y$?
Thanks! Updated with the symbols and your answer.
I have heard good things about http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470073713.html, but I have not read it myself.
I was referring to Jaynes, *Probability Theory: The Logic of Science*, in which the repeated use of Bayes' theorem to update probability distributions as new data comes in is claimed to be a paradigm for the growth of scientific knowledge. I'm sure he deals with the problem of a prior that is too narrow, but I can't remember how, or how satisfactorily. And I'm going to change "general superiority" to "superiority on philosophical grounds", as that seems to better convey what I meant.
Attention to capitalisation and punctuation severely needed here. Look around you: the vast majority of questions don't look like texts to your lover, but make an effort at presentation. I may not be the only person who refuses to read this on principle.
The "shock" terminology normally refers to either the innovations or errors in a time series (though you do sometimes see it applied to the errors in a time series) rather than in a regression context.
@eric, you can compute the probability of one point for discrete distributions and discontinuous distributions (in some cases). For continuous, they're all going to be zeros, and only the intervals make a sense.
@gung I don't really get why "I don't think the right way". All I do is ask a question and ask for how I can answer it. I'm not suggesting any method. If you tell me the way to answer this question is to start by calculating autocorrelations etc... then ok, do you have any links to help me go through this analysis?
YES!! That's it!
Hint: this is the Pythagorean Theorem in disguise.
i dont have the truth file or labels. It is going to be used for evaluating the performance of my algorithm. So, I only have the data points that I have linked. The only thing I know is there are about 500 anomalous points.
if $X_1$ and and $X_2$ are given the obvious choice is non-linear least squares. What are the conditions on model errors? Depending on them better estimating technique can be used.
Sometimes I export the data and build the charts in Excel... this gives you enormous flexibility in the chart formatting and the chart is fully portable between Excel, Word, and Powerpoint.
It really *is* the same question.
But don't expect a happy result in this case, just a more accurate measure of how badly the model performs - it's already clear it's far too big.
have you looked at the image() function? Increasing the number of breaks increases resolution.
So basically what you're saying is that your SVM classifier is classifying all testing data-set as 0. Is your data-set balanced (#of 1s is approximately equals to #of 0s)?
Have you looked at Fourier methods?
Thanks Peter, the intuitive reasoning does make sense. I should have phrased my question as, why is standardization of variables not done always? In my case, the magnitude of the parameters makes much more sense once the variables are standardized.
Gibbs sampling is usually *less* efficient than Metropolis-Hastings because it goes one dimension at a time...
Hmm, interesting Q... What's the distribution of the number of flips? Is it independent of $p$ ?
$\\epsilon$ is the random term for the linear regression model which assumed to be normally distributed with mean zero and fixed variance.
Good answer bnaui.  I was planning to say something similar.
The double use of $f(x)$ is confusing and should not have been used.  Do you have a link?
Yes it is odd that the cited reference is not in the bib. It appears to be the book "Experimental Designs Using ANOVA." I was trying to respond to the original request and provide references for the practice of substituting the mean for outliers. That paper was all I could find in a quick search and I hoped it could provide leads so that the OP could find a more complete answer.
you mean like some goodness of fit statistic (such as a Kolmogorov-Smirnov or Cramer-von Mises statistic)?
Have you considered a third option called item parcelling? [see here for discussion](http://jeromyanglim.blogspot.com.au/2009/09/item-parcelling-in-confirmatory-factor.html)
I don't quite understand what you mean by: 'Most likely it is minimizing the likelihood in the residual sums.' Are you referring to Least squares estimation? Why would this be reported as likelihood?
Please see question edit above. Thanks for the tip, this has at least allowed me to plot *something*...
@Henry The question makes sense for any real $n$, not just positive integers!
This is a good answer, although not my favored approach. However, when a user uses the tag "self-study", you'll want to give hints rather than complete answers.
@Mike, I have edited the answer in the light of your example. Part of the confusion was because you use "test" to mean the data (which makes sense in the context you now provide) and the test statistics computed on the basis on the test data. This has been clarified now. If you really, really don't care about "which test", then I believe that you really don't want to do multiple testing, but want to perform a data reduction upfront.
See ttnphns' comments.
We sort the test results in increasing order by their un-corrected original p-value, then, iterating over the list, calculate the FDR expected if we were to reject the null hypothesis for this and all tests prior in the list, using the B-H correction using an alpha equal to the observed, un-corrected p-value. We then take, as what we've been calling our "q-value", the maximum of the previously corrected value (FDR at iteration `i - 1`) or the current value (at `i`), to preserve monotonicity. Does this sound like the procedure you described in your second paragraph?
Welcome to this site! Could you please format your question (see our Help page for [editing post](http://stats.stackexchange.com/editing-help)) and provide reference to the work cited above?
It doesn't matter.  Take a=0.1.
Note that this is not a statistical model. It misses a stochastic component, or at least it is not clear (to me) what the  component is. What error structure do you assume/suspect? Is the error structure additive, homoscedastic, uncorrelated errors with means zero on the scale of $x_1\\log x_2$?
The premise of the model is that $E(y) = X\\beta$. But $E(y) = E(X\\beta + \\varepsilon) = X\\beta+E(\\varepsilon)$ (since $X\\beta$ is not random), so we can only have $E(y) = X\\beta$ if $E(\\varepsilon)=0$.
In a calibration context, "slope" typically refers to the relationship between the instrument's response and the known (or more accurately measured) value to which it is responding. Your code seems to interpret "slope" differently in terms of a change over time. To avoid possible misunderstandings, your answer should explain what the code is doing and why you think it is relevant to the question.
The fitted model does not contain enough information to simulate an entire distribution.  You might find it easier to simulate data from a known model, then fitting a quantile regression model to those data, repeatedly.
Another option that might keep the client happy would be to use the R plugin in SPSS.
Of possible interest: [Cluster Analysis followed by Discriminant Analysis](http://stats.stackexchange.com/q/3479/930).
This indeed answers a somewhat different question, but thank you nevertheless for reminding me about the useful concept!
+1 for badass base gfx skillz.
Here's a succinct answer accompanied by an illuminating comparative study of how not to do it: http://mchankins.wordpress.com/2013/04/21/still-not-significant-2/
In this particular case, I think it would be best to further clarify the R syntax and meaning of `summary` and `plot`, or to give external links that help to understand how to interpret LM output in R. Maybe John Maindonald or Peter Dalgaard's tutorials, or directly the CRAN contrib docs?
I should have given a little more detail.  These "sub-populations" are from an external validation data set from another institution.  No data-splitting of the modeling patients.  What I was thinking is if testing the model on multiple patient sub-populations from your external validation set raises problems of multiple comparisons (it performs well/worse on some population due to chance).  Something just doesn't quite seem right with training the model on a heterogeneous population and testing it on a small homogeneous sub-population of patients (again, from another institution).
Hmm. They really should try to come up with a different name for that conference.
On a different note, it seems to me that you have >1 observation per subject. However, this fact does not seem to be reflected in your analysis. You may want to look into mixed models & the `nlme` / `lme4` packages.
(ctd) i.e. consider this layout of group means:   $1 ---  (2,3,...,k-1) --- k \\quad$ -- where the first and last group are just far enough separated to make the WSD significant, while (probably) keeping the ANOVA not significant. That would be the first thing I'd try.
I believe you will be receiving   answers  suggesting accurate tetrachoric and related alternatives for ordinal DV. Just want to comment that often researchers avoid the nominal scale as their association measures may be missunderstood and/or because they may yield different alternative measures. Going into interval scales allows standard association estimations at the price of the akward implications of an interval scale (consecutive categories are equally spaced).
A search for ["gap"](http://stats.stackexchange.com/search?q=gap) reveals some promising techniques.
@lmorin: I understood you're proficient in MATLAB. Comparing languages is often of little value. If you experiment both, you'll see the advantages with your own eyes. Nonetheless, I *personally* dislike the entire R language, it's a mess. Furthermore, you mentioned image processing in the beginning, as far as I know, GNU Octave is better suited than R for such niche.
[This](http://stats.stackexchange.com/questions/59910/relation-between-omnibus-test-and-multiple-comparison/59919#59919) may also be of interest.
The same question was asked [here](http://stats.stackexchange.com/questions/69616/mixed-linear-models-with-exactly-the-same-aic). You should perhaps ask for your accounts to be merged.
Always doing corrections though, inflates your type II error rate. If you have all significant results before correction, you may lose them all after correction, not accounting for the low odds of getting all significant results.  This may depend on the cost of a type I or type II error in your context.
Thank you, excellent replication or Urlich et al (2007) method but using R! I slightly edited your answer to make it flow a bit better. Cheers mate!
@whuber actually the options you give (translational error, rotational error, intersection or not) may all appear at the same time (except for a rotation that makes the executed plane perpendicular to xz; in that case b = 0 and the method does not work). This complexity is why we are trying to assess the effectiveness of the guiding system by measuring the error represented by the random variable y. The guiding system is just helping the human operator, that's why we want to know which one has a better effect on the outcome. Thanks!
@whuber Apologies, I am referring to a scaled, recentered beta.  The points would specified exactly.  I had thought this might require numerical methods, but I wasn't sure and wanted to check if there might be an analytic solution.
Uniform random points on a gnomonic projection will not be uniform on the sphere, because the gnomonic is not equal area.  The projection proposed by Henry, $(\\lambda, \\phi)$ --> $(\\lambda, \\sin(\\phi))$ (from longitude-latitude to a rectangle in $\\mathbb{R}^2$), *is* equal-area.
I will give this one more shot. I don't see that the Friedman test has any real bearing on your interest in the most common category. Expectations for the frequency of the most common category must come from a model (generating process) for the data, and I see no model here, unless it is implicitly equal importance of categories. But look at Wilkinson, Leland. 2006. Revising the Pareto chart.  American Statistician 60(4): 332-334 for an indirect approach. You could bootstrap the sample proportions. What kind of sample you have seems a serious issue.
Soon I will be answering my own question, I enrolled myself in the Coursera class for Computing for Data Analysis. I will provide detailed steps taken here once complete.
"The latter", did you mean selecting variables manually is not recommended? Thanks.
@StasK if you search for any scientific paper on vanilla Google, then it will bring up a link to some of the Google scholar results at the top (IME)
Is this a case-control study? Or cohort study? Why is there an age difference (sampling scheme? pathomechanism?)? Is age age at diagnosis? Or is this a chronic disease and age is current age at taking tissue sample for gene expression analysis? Is age known to be related to the disease? Is the age effect on gene expression more the effect of time since birth or since diagnosis?  --- I would need the answers to these questions to see your question if "the classification analysis results are or are not influenced by age?" in proper perspective.
@vonjd I updated my answer. Most notably, I added the discussion on the condition that the distribution we typically observe is something close to the most probable distribution.
it would be preferable if someone could also provide links to those algorithms (sort of tutorials) which they are describing .
Alternatively, instead of marking this one as answered and asking a new one, you could edit your question here (fairly heavily), and mention to me you did so, and I'd need to edit my answer to write a new answer to a pretty different question. Personally, I'd prefer the first approach but I can work either way.
As I remember it, it's a good idea to standardize the predictors in order to understand what they're doing for the response. The interpretation of the parameter estimated will be clearer.

I thought they all standardized them by default, if it's wrong I'll edit my post.
Are the variables quantitative, qualitative?
Bootstrapping often does not work as expected with small datasets, anyway: it is valid only asymptotically (for larger amounts of data). But more to the point, either model is worthless, because it will produce an absolutely perfect fit and its parameters will not be identifiable (assuming the independent variables don't have hugely reduced rank).
@naught: That's not necessarily a problem, because it's likely $x$ and $y$ are restricted to a small interval.  But $1-\\cos(x-y)$ fails to be a metric because it violates the triangle inequality, no matter how small the range of $x$ and $y$ may be.  (Consider the triangle with vertices at $a$, $a+b$, and $a+2b$ for small $b$ and any $a$.)  For some clustering procedures that may be unimportant.
Standard tests for comparing medians (or means for that matter) are of little use here unless modified to match the dependence structure of time series.
Thanks that helps!. BTW people should know that all.equal does NOT return FALSE when false. So to do the comparison you need to wrap isTRUE around all.equal. A long way to go just to compare 2 numbers.
I did find this package after the posting. Do you happen to know if it handles time varying covariates (values change with time)?
"treating each [sample] as a single point estimate of $\\mu$" --- a draw from the posterior of the mean is not a point estimate of the mean. The sample mean of several such draws, however, is a point estimate of the mean.
Thank you very much. I think this will help. The High Frequency data that I am dealing with is much more varied than I had anticipated. So, yes, the temporal disaggregation will definitely help. Regards, simak
@ttnphns Ah yes, that is true. Also taken from your own post, you said " "covariance shows only the strength of a linear relationship" This is not true. Cov is sensitive to both strength of linearity *and* to magnitude of variation." Does this mean then, that by standardizing as per options (2) and (3), we are throwing away information relating to the _magnitude_ of variation, but keeping information relating to the _linearity_ measure?
I *never* seen "real" data that follows a Laplace distribution. Just curious, what kind of data is it? (I you can tell, that is...)
BTW Brian D. Ripley thinks it is a problem too: https://stat.ethz.ch/pipermail/r-help/2006-December/122353.html
One possibility is to choose all the parts of your model (such as say linear regression with student t errors) and write down the log-likelihood function and simply maximize that.
What about Dummy coding?
@shabbychef, if you set up a likelihood ratio test, then under both $H_0$ and $H_1$, you have a convex program to solve for $\\hat{\\mu}_i$. If you look at the KKT conditions, you might even be able to find an explicit solution. Maybe try "walking backward" from $i = n$, e.g., under $H_0$, it seems that if $|X_{n-1}| > \\gamma$, then $\\hat{\\mu}_{n-1}$ is likely equal to $\\mathrm{sgn}(X_{n-1}) \\gamma$. You might also look at the *fused lasso*, which has a "similar" (but not identical) form as your problem. I'm not sure that much is known about distributions of likelihood ratios in that setting.
May I suggest an alternate interpretation? Standardized coefficient should be unitless because its formula is $\\beta_1' = \\beta_1 \\times SD_x / SD_y$, the unit of $\\beta_1$ is **unit in y/ unit in x** while the unit of the SDs are their corresponding **unit of x** and **unit of y**. $y/x \\times x/y = 1$ and hence there is no unit.
Isn't http://en.wikipedia.org/wiki/Multiple_correlation good enough?
On further research it would appear that the fourier() function would be applical here, but I'm not sure on to apply it to my example.
This is too broad of a question to be answerable. Do you want some references for DSGE models?
How do you get this without knowing the st dev? Unless I use the .098 or something...
@Nick The question does ask for "other methods," which this answer addresses. Many people find a link to a downloadable text to be useful, perhaps even more so than just a reference. To an anonymous flagger: providing a link to one's own work is not spam. We welcome researchers and other innovators here and would not want to limit their abilities to help us by requiring that they never cite their own contributions!
Have you tried tracing the bibliography sections of the paper backward? After a few generation backward you should be able to see something older. The terms might have changed along time so directly nailing down a pre-1990 paper maybe a bit challenging.
yeah that's true but if the MSE is high it means the variables are less correlated isn't it? So there is some kind of relationship between correlation and MSE
For reference you might want to add the line y=x, not a linear fit.  This is more relevant to the need to demonstrate the two datasets differ.
Your diagram is helpful, although I'd like to know for sure what "aggregated 5 item scale" means.
I've edited your English quite heavily. Please check that the meaning remains what you intended.
@AntoineVernet yes, you're right. But I couldn't find any other version
It would be nice to know what kind of data you have and what you mean by a "pattern" so that we can decipher what it means to "average" an interval.
I copied the results from MsSnowy's related question
Did you really maximize the *negative* log likelihood?
I don't quite see how linear regression could help you estimate $\\alpha, b, \\beta$. I suppose least squares could help you to set of a moment-based estimating equation if you know the moments of this distribution as a function of $\\alpha, b, \\beta$, but I'd tend to go with maximum likelihood as the default choice. You have the CDF there, so you can get the log-likelihood easily and optimize it. Is there some reason you don't want to do that?
Excellent point, I haven't considered this before. Is there a workaround to the GLM methodology in cases where the distribution is not of the exponential family?
Both models seem to have a problem - there are some fitted values that are much higher than all the others, and there are some outliers. 
Can you tell us what you are trying to do? What is the DV and the IVs?
You have access to [R](http://cran.r-project.org/) :)
thanks for the clarification about the normality testing and sample size.  About applying t-tests or anova to non-normal samples, it makes sense , (and i had this somewhere in the back of my mind when I wrote the question) when you perform t-tests or anova you have to look at the distributions of those groups, which should look normal, not at the whole sample,  which brings me to my next question: if these groups fail to look normal then should you be worried about applying t-tests or ANOVA? Checking the residuals for normality is something i did not know you can do for t-tests or anova.
Excellent. Thank You for taking effort in answering my question. I do have both the forecasting books in Hard copy that you recommended. I personally still favor the Makridakis et al a classic, simply because of exceptional writing style. I also like the latest Hyndman et al because of thr R codes accompanying the book.
Then, I confirm my suggestion. You may use DTW on your data by using a polar transformation $r = \\sqrt{x^2+y^2}$ for example, or you can calculate the centroid of each trajectory and calculate the distance of that trajectory to its corresponding centroid using afterwards that distance vector for the alignment.
@Horst, such a procedure would not be repeated measures ANOVA. Mixed models can fit models with missing data (and that has been published and peer reviewed).  However those are not repeated measures ANOVA. I think your comment only serves to cloud the issue.