tttjjj/elt_bench huggingface dataset:
pacf(1) was -0.481, and the pacf(2) was -0.2786. pacf (>2) were not significant.
I added two lines to generate the plot.
+1. Excellent suggestion. I have always found Gretl's GUI intuitive and to the point and the feedback it provides accurate and without too much frills that would put off some less "techy" students. Plus it is free, well-documented and has an R console if someone if incline to see something a bit "deeper".
I have very few data points. See my edits, the question should be clearer.
yeah $p_2=1-p_1$, and also $p_1 \\mu_1 + p_2 \\mu_2 = \\mu$. in excel i just put the formula and let the solver try.
@Peter, I'll expand a bit my point (and the well known fact). One facet of the difference b/w PCA and FA is that a component is the _error-free_ linear combination of all the variables, whereas a true factor is not. The regressionally computed factor (factor scores) is, but it is not true factor, only an approximation. Proof: correlation b/w f. scores - in contrast with c. scores - and a variable isn't exactly the loading, the true correlation. We can never compute _true_ f. scores - because we don't know uniqueness values on the case level.
Please don't ask questions in answers! While your output might be regarded as a partial answer to your question, your followup questions don't belong; they should go in your question or be posted as a new question. I will move them to the end of your question, but if you wish to post a new question (with a link to this one) you can delete them from there and post them as a new question.
It would be useful to have the reference if you are able to find it. Thanks.
@mbq: maybe this should be a separate question, but could you expand on your statement that Neural Networks are considered obsolete? (and by whom?)
As per my response to @dpott197 I am going to use R's fitdistr functionality to test my data against several distributions, one of which will be Gamma. Thank you for the tip about the Q-Q plot.
@Tomek I expanded my answer a little bit
Just as a reminder: the distribution of the LRT for variance components is a non-standard mixture of chi-square distributions with different degrees of freedom.
Look into Cohen's kappa.
They differ because they incorporate different variance components.  The mixed model has 2 variance parameters: one for subjects and one for residual error.  The fixed effects model only has one for residual error.
But $v\\sim\\text{Inverse-Gamma}$?  I have $$v^{-p/}=v^{-p/2+1-1}=v^{-(p/2-1)}-1$$
Accuracy and accuracy only.
I'm not familiar with Excel, but you want a [prediction interval](http://en.wikipedia.org/wiki/Prediction_interval) for an individual observation; not anything based on a standard error, which applies to uncertainty around the expected value.
"Sudden" peaks sounds like something that may not be predictable, period. If so, there is nothing a neural network will be able to do. The structure of the ANN is important, too; is this a [recurrent neural network](http://en.wikipedia.org/wiki/Recurrent_neural_network)? You may want to look into information about how time-series are modeled statistically (eg, ARMA) and forecasted to learn more about these topics.
I can certainly empathize -- I often do the same thing! :)
@snow_leopard I found a little gem and updated the answer. The most promising link is unfortunately broken, but here is the [website of mr wilson wong](http://wilsonwong.me/). Or [here](http://research.wilsonwong.me/), search for _Ontology learning from text using Web data for information exploration_. The example data does not seem to be available anymore, but if you contact him (or other researchers with promising papers) and ask politely he might help you out. In my experience, researchers react grateful if contacted because of their work (if they have time ;)).
Some links: (**1**) A. Owen (1988), [Empirical likelihood ratio confidence intervals for a single functional](http://www.jstor.org/stable/2336172), *Biometrika*, vol. 75, No. 2, pp. 237-249, (**2**) A. Owen (1990), [Empirical likelihood ratio confidence regions](http://projecteuclid.org/euclid.aos/1176347494), *Ann. Statist.*, vol. 18, no. 1, pp. 90-120 (*open access*), and (**3**) A. Owen (1991) [Empirical likelihood for linear models](http://projecteuclid.org/euclid.aos/1176348368), *Ann. Statist.*, vol. 19, no. 4, pp. 1725-1747 (*open access*).
(+1) Don't miss [ggobi](http://www.ggobi.org/) and `marginal.plot` from the [latticeExtra](http://latticeextra.r-forge.r-project.org/) package.
@Rasmus: I guess that depends on exactly what you want to do with the information, but in general I'd say yes.
I haven't completely thought this through, so take my suggestion with a grain of salt. If you do come up with some further insights based on the usefulness of such an approach, I would love to hear about it.
@lilile Yes AUTOBOX . Available from Automatic Forecasting Systems .They have 30 day demo available at http://www.autobox.com/30day.exe .
(+1) Also to note, there is a paper by Andrew Gelman and Hal Stern that discusses this issue as well, [The diﬀerence between “signiﬁcant” and “not signiﬁcant” is not itself statistically signiﬁcant](http://www.stat.columbia.edu/~gelman/research/unpublished/signif3.pdf).
Hi Glen, I have added the model in the question now. Thanks!
I'm not watching a video for you, sorry. If you can transcribe the critical information into your question, perhaps I'll have a close look. But Gaussian distributions don't all have 0 mean. It's actually a family, with two parameters - the mean $\\mu$ and variance $\\sigma^2$.
I guess I would follow up with what are the main differences between GWR and WLS? I read more about WLS and they seem the same. I want to look at about 30 variables in the regression and there aren't really any clear breakpoints.
AUC (C-index) has the advantage of measuring the concordance probability as you stated, aside from cost/utility considerations.  To me the bottom line is the AUC should be used to describe discrimination of one model, not to compare 2 models.  For comparison we need to use the most powerful measure: deviance and those things derived from deviance: generalized $R^2$ and AIC.
What kind of statistical software do you use? Maybe there exist better source for you.
@Monica That's not a reference; that's an easy deduction.  I wouldn't even go so far as to say 80% is generally "acceptable,' only that I can imagine some situations where it would not raise any concerns.  Note that correlation depends as much on the spatial extent of the DEM as on anything else and therefore is a poor indicator of how well the DEMs match: see http://stats.stackexchange.com/q/13314.  *At a minimum* you should be using a an absolute measure of the differences instead, such as root mean square difference or median absolute difference or even maximum absolute difference.
Thanks for your suggestion on using an FDR approach for multiple testing correction.
@Aaron sorry, I only just saw your comment. In the end, I just ran separate random intercepts models for each year of data, using `glmer`. I did bootstrapping to compute confidence intervals for the random effects and these confidence overlapped to a very high degree from year to year, with no apparent trend, from which I concluded there was no change over the period. The fixed effects were also very stable from year to year.
@whuber, I think once I read your response to this indeed FAQ, but I have not found the thread :(
@MikeF: Can your tool overplot? That is, plot a line with small dots at each data point, then plot (on top of that) larger circles only at the above-threshold points, which will result in a sort of bullseye at points above the threshold. Avoids the whole color-blind issue and leaves everything at the same contrast.
Nice paper reference...hadn't come across that one before.
I have broaden my definition of 'explain' now.
Further, if negative fitted values don't make sense, why are you using a model that allows fitted values to be negative?
Thank you very much. You helped me very much! Voting as best answer
Thanks,I realize my questions were somewhat not clear, sorry. Pls consider that I'm relatively new to binary data. Regarding the points raised: I need to cluster variables, to check for their association (co-occurrence) in my dataset. I opted for the Jaccard (and the binary distance) for they do not consider joint non-occurrence. In my dataset, this is more suitable. About the Ward method, do you have any possible alternative, more appropriate for binary data?
About significance, I want to check the reliability of my clusters in consistently reflect an underlying association between variables.
What is your goal? Do you  really need Weibull, or any other parametric analysis? The `survival` package has loads of nonparametric methods.
The difference between fit1 and fit3 is sometimes referred to as Lord's paradox. See here for some discussion (on why the estimates don't change between the models) and a reference to a Paul Allison article, http://stats.stackexchange.com/a/15759/1036. Another reference is `Holland, Paul & Donald Rubin. 1983. On Lord’s Paradox. In Principles of modern psychological measurement: A festchrift for Frederic M. Lord edited by Wainer, Howard & Samuel Messick pgs:3-25. Lawrence Erlbaum Associates. Hillsdale, NJ.`
This is a near-duplicate of http://stats.stackexchange.com/questions/555/why-is-anova-taught-used-as-if-it-is-a-different-research-methodology-compared
Thanks for that - you are spot on with your reading of the problem, and what you say about error makes sense. As bill_080 says in the next comment, I guess it comes down to whether or not preserving the natural causal relationship is important or not. In other words, what's more important: reducing the error, or representing the causality?
Well, it is hard to beat [the explanation of vector autoregression by Rob J Hyndman](https://www.otexts.org/fpp/9/2) in general the book the link leads you to is a great (free!) resource!
@Deepend No problem, glad to help!
It's displaying it correctly, `16228 = 1622800%`, you'll have to normalize the data yourself as suggested.
In econometrics $\\beta$ refers to a coefficient, standardized or not.
@John: thanks for the comment. yes, i have, and the results are the same. however, i wanted to get a more conceptual explanation (also to know if there is a preferable way to express the SE), and also, the other two questions in my post are still open.
I see that you are getting all exponents around 6.92 and 6.93. I checked in mathematica and mathemtica is identical to your R output. Now I am worried about MATLAB, what the heck is going on? Thanks for posting though.
I will just silently remind that *IC <--> *CV correspondence from Shao paper works **only** for linear models, and BIC is equivalent only to k-fold CV with certain k.
I do understand that the problem is better suited for reinforcement learning, but my goal was to try to tackle the problem without "modeling" it too closely.   I figured in "real life" I wouldn't always understand the data exactly, but if there was a pattern, I should be able to predict it.  I chose tic tac toe so I could fully understand the model and evaluate where I went wrong, but I didn't want to build the a priori knowledge (eg, 3 in a row wins) into the model.  The "pattern" is just that there will be more samples where a certain (good) move wins than the bad moves.
Are the double subscripts in the displaymath deliberate? If so, what do they mean?
Your first sentence makes no sense as is. What is the null hypothesis?
Ok, this is out of my wheel house as I am not yet familiar with elastic net. I do notice your (\\theta) look to be pretty much all zero. Might be something work looking at.
I'm note sure this will necessarily be an ideal choice for what will likely be a very skewed distribution
Infinite variance happens when the integral (sum) defining the population variance increases beyond any finite bound as the limit is taken. Some discussion of examples [here](http://stats.stackexchange.com/questions/91512/how-can-a-distribution-have-infinite-mean-and-variance?rq=1)
What it means for a distribution to be normalized is not so simple (and it's usually not the distribution itself being normalized, but the random variable). For example, in the case of the uniform, some people may mean "linearly rescaled so as to get a standard uniform" (i.e. to get $a=0$ and $b=1$) ... while another person might mean "linearly rescaled so as to get mean 0 and sd 1". For the uniform, I'd normally assume the first, but as you see from an answer below, other people may take it to mean something else. The best option is to ask the person using the term to be less ambiguous.
I don't see how you can analyze survey data without that basic information. Are you just given the total number of surveys and the overall response frequencies?
Absolutely agreed on the version control.  I use it; as do a substantial proportion of the developers and statisticians.  (I'd like to see 100% adoption but that's another pipe-dream for now.)  The hard bit is getting non-techies to use it.  Any ideas appreciated.
I take it from the way you accentuate _some people_, you are not one of those people?
I think your error is in summing 'out' and dividing by the length - if you are using crossval to calculate MCR, there is no need to sum and divide and the output of crossval will be a the mean MCR across folds, though it is not clear to me exactly what 'perf_clsf' does but I asume it is a sub-function training and testing the SVM
Well I cannot answer my question yet! Anyway I found the answer if anyone is interested: dense labels and (maybe labels 1,-1 instead of 1,0)
I only have an implementation of the Bayesian LASSO for linear regression and the LASSO for logistic regression currently uploaded. Appologies.
Curious why you would model all of your effects as random? Are there no explicit comparisons of one level against another that you are interested in (fixed effect)?
Thank you for the elaborated response. Actually, these are 3 dependent variables.  I have never used R before. Will SPSS be more complex to conduct the MANOVA, as compared to R? Another question is that if I conduct an ANOVA 3 times, will that be more prone to Type I Error, in comparison to conducting a MANOVA? Many Thanks
+1.  $\\mathbb{E} X$ and $\\mathbb{E} Y$ are harder
(+1) Great answer. I don't know if this is relevant, but the UMVUE for the arithmetic can also be calculated using the [$_0F_1$ Hypergeometric function](http://reference.wolfram.com/mathematica/ref/Hypergeometric0F1.html). Namely $m(x)=\\exp{(\\bar{y})}_0F_1\\left(;\\frac{(n-1)}{2};\\frac{(n - 1)^{2}s_{y}^{2}}{4n}\\right)$. I mention this because the Hypergeometric function may be implemented already (e.g. in R in the `hypergeo` package) eliminating the need to program Finney's G yourself.
I could reply that even more observations would fall within $10 \\sigma$ of the mean, giving a better estimate $\\hat\\sigma=\\frac{R}{10}$. I shan't because it's nonsense. Any number over $1.13$ will be a rough estimate for *some* value of $n$.
added a link...
I agree with you, I had not explained it well
Regarding the counter-intuitive sign, i wonder if it is because our intuition is interpretting the wrong covariate - like a main effect as if it was nested or interaction effect.
Exponential smoothing is not a variation of garch and its parameter can't even be estimated.
Not sure what you mean by the "between estimator". Do you mean you  have two groups?
Before proceeding you would need to have justification for there being a discontinuity in the system.  I.e., does a discrete external event happen at the supposed change point?  If this is not the case, then it may be more reasonable to estimate the smooth relationship between time and the effect of $X$.  This can be done using time-dependent covariables (e.g. a spline function in time interacting with $X$).  You could start with a smooth scaled Schoenfeld residual plot in the context of the Cox proportional hazards model.
*Residuals* are not independent in logistic regression or even in linear regression. Why would you test something you already know the answer to?
Along the same lines, one could say that if you are using stepwise regression why are you interested in inference at all?
@Cagdas Ozgenc Maybe [this paper](http://docs.edhec-risk.com/mrk/000000/Press/EDHEC_Publication_Optimal_HF_Allocation.pdf) of EDHEC contains more info for what you are looking for.
I think time series analysis is a little more complex than the usual "test for different samples". This is because there may be some underlying time-dependant structure on your data, and therefore distributional assumptions are hardly met in time series.

Given that as a fact, the first approach that comes to my mind would be to fit one of the various kind of time series models (see, e.g., http://www.stat.pitt.edu/stoffer/tsa2/R_time_series_quick_fix.htm for a quick tutorial in R) along with a straight line and see if the slope of that line is significant or not.
Sara, please don't just repeat the same question if you are not satisfied with the previous answer ([see previous question here](http://stats.stackexchange.com/questions/111824/pca-which-original-variables-are-used-to-construct-a-new-variable)). Let's continue the discussion in the previous question, which you can edit to make clarifications.
You have n X variables. Are you saying how to correlate any particular one w/ color (eg, cor(color, x_1)) or the combination of all of them? In addition, your categorical variable is understood to have >2 levels, right? (Note you have 2 'reds'.)
@nico That's a fair point. But, this is not a reason not to use efficient graphical summary. A schematic illustration of what a boxplot actually does might help the reader.
Thanks.  Very pretty.
I agress with G.Jay that tricky question is who "the magician" actually is. I think this is less a statistical than a philosophical question ;).
What do you mean by power? What type of analysis are you even using?
@jbowman the part i was given is only the simple monte carlo, but i read that it's not the best method to estimate the expected value. For myself, i want to do the other two methods, in order to reduce the variance of my estimator as much as i can.
(+1) (I have worked with Scott Ferson and enjoyed many stimulating conversations with him about this subject.) It is worth understanding that the bounds given in the literature you cite are *extreme*: they correspond to arbitrary *worst* distributions. If you have any expectations about the underlying distribution at all, even something as mild as (say) having a continuous PDF and no more than three modes, you can always obtain better bounds with [standard semi-parametric](http://stats.stackexchange.com/a/68238/919) or Bayesian techniques.
I think it depends on how you define "population". By "population", if you mean a collection of observations that can never be sampled again (representing the universe of obs in its entirity), then yes you could use a finite population correction factor to shrink the stnd error on sample estimates as n approaches N. However if your "population" can be considered a random sample from a much larger theoretical population of observations, then inferential statistics still apply without an fpc.
By the way, what Peter is getting at is that, by default with binomial data labeled as `0`s and `1`s, `R` will model the probability of a "1" response while SAS will model the probability of a "0" response. To make SAS model the probability of "1" you need to write your response variable as `use(event='1')`. Of course, even without doing this I believe we should still expect the same estimates of the random effect variances, as well as the same fixed effect estimates albeit with their signs reversed.
Interesting distinction. I thought model selection was central to machine learning, in almost all meanings of the term.
I completely agree with @Glen_b: with your more than 11,000 values, you can precisely characterize almost anything you like concerning the last 30 years. The big unknown is the extent to which the future might or might not behave like the past. I suspect that component of uncertainty dwarfs any other aspect of this problem. If you have a good climatological forecasting model, you might consider exploiting that in your work, using it to create stochastic simulations of future daily rainfall. In all other respects, the calculations would be identical.
The answers to this question could be broad and complex, because issues of coordinate systems, datums, and projections can arise, as well as considerations of how latitude ultimately is related to the other variables of interest. Note, however, that a truly international standard for *representing* latitudes is the "decimal degree" which simply converts your base-60 numbers into base 10. For instance, in base 10, "39° 37' 39" is written "39.6275." For more about this [search the GIS site](http://gis.stackexchange.com/search?q=decimal+degree).
This question appears to be off-topic because it is only about software. If a *reproducible* example were provided it likely would be welcome on SO.
@user26409 It seems you've lost your account information. Please follow the instructions on our [help page](http://stats.stackexchange.com/help/user-merge) to merge your user profiles.
I've made substantial edits to your formulas. Please check I didn't get any of them wrong. On my previous comment (sorry about the improperly formatted link there) - also see the precautionary comment under the answer [here](http://stats.stackexchange.com/questions/57715/expected-value-and-variance-of-loga/)
Also, thank you for the detailed answer!  You clarified most of my other questions.
This question appears to be off-topic because it is about searching for software package recommendations.
You sure you don't want to try your luck in Stack Overflow with this question? It seems more like a SymPy question than a Stats question. (I wouldn't mind to be proven wrong, but I am saying this so you get an answer sooner.)
Do you want to model your degree of belief in the "generally accepted to be more accurate" and "may have some accuracy problems" statements?  If so you may want to look at Bayesean techniques.  When I've seen other people do this kind of calibration activity (I recall a paper with different models of radiosondes) the relations have been non-linear, so you may want to look at a non-linear model.
Take care in interpretation. It's conceivable, for example, that the "choice of [any] single student" is not at all random and should not be described by a multinomial distribution. (Some students might hate bananas, for instance.) What a distribution can describe is a process for *selecting* the $n$ students from a population. For the multinomial distribution to apply, that process has to be analogous to picking slips of paper--one per student--out of a well-mixed bowl of a great many such slips.
Is it some jealousy going on here? Why would anyone vote down a valid answer? Moreover, an answer that was actually related to the question? Curious...
(+1) For showing what you tried and your thought process.
There is a good answer [here](http://stats.stackexchange.com/questions/8104/why-is-a-p-sigma2-sim-textig0-001-0-001-prior-on-variance-considered-w) about the use of an IG(0.001,0.001) on variance parameters.
I have a dataset of 1000 instances. What if I would split that in three folds, and perform a cross-validation (training+validating) no 66% and testing on 33%, and do that 3 times?
Hi Chet, I would imagine that if there was only one such algorithm, everyone would simply use that.  I suspect that the reason that many different algorithms are still in practice would be because  different algorithms will performance differently on different settings of the problem/datasets.  Hence, I am not sure anyone can help you choose the "best" algorithm for your problem with the information you've provided so far.  Cheers, Tal
I don't know where to move this question: it properly belongs on a cognitive neuroscience or futurism site.