tttjjj/elt_bench huggingface dataset:
So far this does not make sense because (a) you have not defined what a "vicinity" is nor have you quantified it and (b) you have not described any probability distribution for the vectors. Both these pieces of information are essential for investigating your question. If you have this information then please edit the question to include it.
Error bars representing what? Computed how?
Say you have 3 outer folds. This means you run an entire model building process 3 times, giving you three different models. You don't use any of those models in the end -- to get your final model, you run the entire model building process on all of your data (except for possibly an independent evaluate set). It seems like this would lead to overfitting, but if your model building strategy overfits, it should also overfit in the outer cross validation, leading to a appropriately higher error estimate.
sure, but contextually it's obvious I'm not looking for a link
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Is there no need to take into account the number of times a Move was made and therefore how accurate the winning probability is when comparing options?  Consider 999 wins:1 loss vs. 1 win:0 losses.
We appreciate your efforts but there's no need to post your material until you have actually finished writing it.  In its present form, the way it decays into sparse cryptic notes at the end will disappoint readers.
Yes, regardless of if it's called "correlation" or something else, X and Y are certainly not independent.
you could just draw the densities - you don't need simulated values. Try the following and check the various arguments (and examples, where relevant) -  `?dnorm`, `?curve`, `?lines`, `?segments`, `?abline`.
Thanks for the insight, it's much appreciated. In all of my statistics classes almost all of my professors have varied from R, Excel, Stata, so I don't think there is a standard one that they use. But thanks for the info about the different programs that do different functions!
Again, proof by induction. Base case is a window of width 1, i.e. the original points for a difference of zero. If you have a window width of N and add a point on each side for a window of width N+2, how much can those two points change your average? Well, calculate the greatest difference between any two points in the time series, let's call it D. Etc...
[Geometric series](http://en.wikipedia.org/wiki/Geometric_series). That's a result in mathematics, rather than a statistical one.
I think this question expands a lot on the one @steffen marked as a duplicate, so that one should be deleted or this one merged into that one or something.
Thank you. The slopes and intercepts have different values but the slope of two segmented lines are negative.
@susan: "Variables as columns" means that X should have 2000 columns and does *not* need to be transposed. Did you figure it out by now?
Both, depending on context. That's what I was trying to say
I might just be showing my ignorance here, but isn't the assumption behind ANOVA that the residuals are normal? In that case it doesn't really matter if the variable itself is non-normal, as long as the residuals fit the pattern.
Maybe this helps? http://stats.stackexchange.com/questions/24187/analyze-proportions
In other words, I guess my question had two parts: 1) how to deal with the hierarchical nature of the problem (I want forecasts at different slice granularities, so when making forecasts for slice X, should I care that I have data outside of slice X that is nonetheless related to it?) and 2) how to reconcile the fact that each individual time series slice has both time series components and non-time series components. It sounds like you're suggesting that for 2), the time series parts are less important than the non-time series parts, and for 1), I ignore the hierarchical/interrelated nature?
Actually between the variable and errors. But you can only observe the residuals (differences between the observations and the estimated function), while the errors are deviations between the observations and the "true" function, which is unknown. So, you solve the problem using the estimators of errors - the residuals.
p-value for what? Which null hypothesis?
Thanks, made the above edits.
I'm sorry - I specify assumptions about $Y$ and $Z$, and have observations of $X$. I think it does not derail your answer, though.
This same trick works much more generally and even in cases that might "appear" simpler to someone first encountering the subject. For example, consider $X$ and $1-X$ where $X$ is a Bernoulli random variable with probability of success being $1/2$.
@gung I think of dot plots as having a histogram-like component that is (or should be) mostly absent here. Judging by the responses here, that is probably not a widely shared view. I was hoping to point out that the artists just shy of 3,600 should be arrayed horizontally given their vocabulary size values, but their current position creates an illusion of a mass point that is unfortunate since this chart is not really a histogram.
If we should all be doing regression, why do books on Experimental Design, like David Cox's book, stress the importance of pairing or grouping in biological experiments? Pairing avoids the hidden assumption of linear dependence entailed in regression. But perhaps there are other reasons: anyone??
@macro: my observation is 21 and my variables are 5.my complete question is my previous question http://stats.stackexchange.com/questions/29612/minimum-number-of-observations-for-multiple-linear-regression
Welcome to the site, @ElioDruml. I can't tell if your main question is about how to estimate these parameters, or what the meaning of the warning message is. The former would be a good question for CV, but the latter is really a question for [Stack Overflow](http://stackoverflow.com/) (see our [FAQ](http://stats.stackexchange.com/faq)). Can you clarify what your primary question is? Would you prefer your Q stay here, or be migrated to SO? (If the latter, flag your Q & we'll migrate it for you, *please don't cross-post, though*.)
I am sorry for my complete lack of ability, I have been pretty much abandoned by my tutor in my efforts to managed my huge data set and don't really know who to ask.
@Macro: +1, nice answer!
A multivariate version of equation (3) of that paper is proven in the cited Kullback text on pages 27-28. The constant $1/2$ seems to have gone missing in the OP's question. :)
@mzuba I believe I am counting both ESS and TSS correctly, however for most of the cycles the R^2 is above 1, which I believe means there is an error. How can I understand this?
That is a good idea, thans for the insight. I Think it would then only be slightly strange to try comparing covariance values and other results (I will do Principal Component Analysis) that refer to differing time periods
At the moment question is not clear to me. You have two univariate Gaussian distributions. What do you want to infer then? If you minimize KL between two univariate Gaussian distributions you really get $p = q$ and $KL(q|p) = 0$. Or you want to state some connection between prior and posterior distribution? What is the question you want to answer?
Interesting quote from Berger's *Statistical decision theory and Bayesian analysis*: "we do not view credible sets as having a clear decision-theoretic role, and are therefore leery of 'optimality' approaches to selection of a credible set"
Please, [register](http://stats.stackexchange.com/users/login) your account so that you'll get notifications when new answers or comments come up, and consider using comments or updates to your question rather than posting new responses when replying.
@HarveyMotulsky There are others regulatory administrations/agencies (such as EMA) hence I'd prefer a "regulatory statistics" tag. Maybe this would be a good subject for meta.stats.stackexchange but my english is not sufficiently developed to open the discussion.
So the Variance of, say, $Z_1$, which is $\\Omega_{11}$ is $e^{X}$? I.e., the variance is a random variable here?
+1 for the links to the handbook, mentioning collinearity and IVF, and the specific solutions and even implementations in R. I am curious to hear your opinion about whether the data itself is not suited to regression analysis- I edited the question above to reflect that these are measurements of a network.
Essentially any book on ordinal modelling gives a very full answer. See e.g. http://www.amazon.com/Analysis-Ordinal-Categorical-Probability-Statistics/dp/0470082895
An alternative to the answer you have is by [reparameterization of the model into parameter and difference of the two](http://stats.stackexchange.com/questions/93524/testing-whether-two-regression-coefficients-are-significantly-different-in-r-id), by suppling the basline dummy and the sum of the two dummies. and a direct test of the coefficient for the difference. (In fact given the fact that being a dummy makes no difference to the approach, this Q is arguably a duplicate.)
I don't think you can: GLMSELECT only does linear models. If you are willing to use R or Matlab, there is the glmnet package.
Thanks @whuber!  That's really helpful and I'm going to try it out.
An example of the trade off for time/space is in the book, Making Maps (critical discussion and examples [given here](http://freegeographytools.com/2011/making-maps-a-visual-guide-to-map-design-for-gis-a-review-of-the-second-edition).
Right, $L(\\theta | data ) \\ne P( \\theta | data )$, the former is just notation for a likelihood.
In Stata, I wouldn't know a command to check that easily. When using implemented goodness of fit tests, you have to be aware you cannot compare the values across non-nested models in many cases, and definitely not across different frameworks.
@Ocram Yes, please do.  Understanding what informative censoring is is the gist of my question.  In particular, how it relates to the question at hand.  I'll try to update the question once I extinguish the morning fires at work.
Are you dividing the data set into training and test data sets? I'm not sure if that could do this.
Colo[u]r coding a histogram isn't even decorative; it's an objectionable distraction. That detail apart, presumably you mean that the one variable being shown is the same. The common element is a moderately right-skewed distribution. Bimodality in #2 may be genuine but it's not marked. The rule of thumb always should be that details robust to variations in bin width and bin origin are likely to be genuine; details fragile to such are likely to be spurious or trivial.
Sorry, should have given more context. lm() is an R function that does a linear regression. The p-value is from a t-stat table, using the t-values calculated from the coefficient and standard deviation : t = [x̄ - μ ] / [ s /√ n]
Also it is worth to mention that building several random forests with the same algorithm parameters and then combining models into ensemble is equal to building one random forest but with increased number of trees.
How many fish species and anemone species do you have in total?
@Srikant: if we expand our search from linear transformations to analytic transformations (i.e., transformations that can be represented by their Taylor series), I think one could prove that all higher order terms need to vanish for the standard deviation to be unchanged. That is, the only analytic transformation that preserves sd would be adding or subtracting a constant to all values. Might be a nice exercise for statistics undergrads ;-)
Thank you so much for a detailed answer. I just realized I used wrong formula for last δ for output layer.  If it's not bothersome, can you answer to one more question. When I have trained weights, and want to use them to recognize letters , should I just go through feed-forward once and give result with 1s and 0s based on which neuron got highest value for prediction?  It all stays the same as during training when it comes to calculating output, right?
Thanks for the answer, I'm a little confused about the purpose of the Gamma and abline functions, when I try to run the same command on my data I get: "only using the first two of 130 regression coefficients". I should not that my model is more complicated than "dist~speed", there are 9 factors and I am currently using all 3 factor interactions. When I try to plot the abline function, I just get a vertical line at 0. I tried simplifying the model (and using the log link) and got a near horizontal line too, how do I interpret this data using the above method?
@dan as the 1s get more 'runny', so do the 0's; you can't really avoid measuring both. The total number of runs of 1s and 0s can differ by *at most 1* from double the number of runs of 1s.
Thank you very much fo ryour explanation Peter.  For you comment "There are situations where likelihoods simply don't work - no density exists in the model for example.",  I wonder if the hypothesis for uniform distribution on [a,b0] vs [a,b1] would be an example, since the likelihood ratio doesn't depend on sample Xi ?
`anova(glm1)` tests the hypothesis whether the whole group variable is significant or not whereas `summary(glm1)` provides Wald-tests for the single group levels (compared to the reference group level). For example: The p-value for group level 2 after `summary` is for the test of the difference between group level 1 (the reference) and the group level 2. See also my answer [here](http://stats.stackexchange.com/a/60821/21054) and [this post](http://stats.stackexchange.com/questions/31690/how-to-test-the-statistical-significance-for-categorical-variable-in-linear-regr).
Your answer doesn't address the OPs main issue, the use of time series data.
Dear Glen_b and Harvey, Your comments on my query is exactly what I looking for. And I'm absolutely happy with your response.I'm sorry to make You feel like. Thanking You.
Hadn't quite finished. I've done the t-test. My understanding is that t-test shows that A and B are different not how much A contributes to the overall figures. Is that right? Many thanks
not really an answer to your question, but have you encountered False Discovery Rates (FDR)? "Beyond Bonferroni" by Narum: http://www.springerlink.com/content/c5047h0084528056/
another good introductory reference is [Gelman and Hill, Data Analysis Using Regression and Multilevel/Hierarchical Models](http://www.stat.columbia.edu/~gelman/arm/)
Emulate the [Wikipedia example](http://en.wikipedia.org/wiki/Rao%E2%80%93Blackwell_theorem#Example).
You should be able to edit the title (I did a similar thing myself earlier).
Since the business thinks along "frequency" ie Claim Count / Exposure, to keep the output here in a similar manner. You are correct "Observed Claims", is the count of Claims occuring in that exposure period.
Once you get to $1$, think of $11$ and $12$ as absorbing states.
Sedimentologists have been cooking up ad hoc equivalents of moment measures for decades, e.g. Inman, D.L. 1952.  Measures for Describing the Size Distribution of Sediments. _Journal of Sedimentary Petrology_ 22: 125-145 but most of these measures predate widespread availability of calculators, let alone computers. For a more systematic alternative, consider L-moments e.g. 
http://en.wikipedia.org/wiki/L-moment
Can the beta distribution handle the zeros?
"*how can I make inferences over the population?*" - if I follow what you're saying, it sounds like you want mixed effects models, where participant has a random effect.
I am sure that whatever was published at the time of the Johnson and Kotz book would be covered in there.
agreed, the MOA toolbox would be a good place to start
+1, this answer makes this question worth keeping.
I'm not aware of any standard conventions on this. My opinion is that the way you've presented it is fine. I clearly understood what was being shown. Also, conditional probability highlights the difference in filament replacement trend between company C vs A or B more readily any reasonable alternative method I can think of. But, as said, that's all just my opinion - I don't have anything to back it up with beyond gut feeling. If anyone else answers with a more concrete justification you should probably listen to them.
It is one intervention that has three components to it. Each component requires implementing a handful of items to be compliant. So the overall construct is compliance with an intervention, which is represented by 15 specific items that can be grouped into 3 categories. Does that answer your question?
@Scortchi - you would think that after all these years I would reflexively write "Jeffreys'" instead of "Jeffrey's", thanks for covering up my embarrassing mistake!  And my mother was a professor of English!
The key question to me is: *when is separation meaningful*? IMHO, separation can help finding meaningful clusters, but if you only optimize for separation, it by no means the results are meaningful; they are just some mathematical optimum that may be completely detached from reality.
Now if you only have Mahalanobis distances, it's hard to say how well clusters are separated and how much they overlap, as this distance value is center to center, and not cluster border to cluster border.
0,0,1,1,1,1,3 is a counter-example to the common assertion that mean, median and mode coinciding implies a symmetric distribution, although a binomial such as ${10 \\choose k} 0.1^k 0.9^{10-k}, k = 0, \\dots, 10$ is likely to seem a better one.
Thank you! I think I will have to read up on some of the concepts you mentioned.
Side note: "validation" has different meanings in different fields. Some authors use it to indicate a kind of testing that is used to select models (I'd suggest that optimization test set would be more intuitive), whereas in other fields validation means demonstrating that the *final* model is fit for its purpose.
Thanks.  From first glance the paper seems quite interesting and practical.  Will start reading it.
I don't understand this reasoning.  It seems that if you have a bad fit, then you could get the causal association completely wrong.  [Hormesis](http://en.wikipedia.org/wiki/Hormesis) is a good example that should be important to epidemiology: if you fit a linear dose-response curve to a hormetic effect, you not only wind up overlooking the hormesis, but you draw entirely the wrong conclusions about low-level doses.  How, then, can one justify overlooking this possibility by not checking goodness of fit?  Am I misunderstanding your claims?
Wonderful link to that blogger - thank you aix !
This may provide some interesting points: http://en.wikipedia.org/wiki/Credible_interval
Peter, I have tried to clarify my question. Re: Q#2. I can re-derive the 3 formulas from my data set. For example modelG uses 4 variables and I can derive a newModelG from my own data set with those 4 variables, but the coefficients are different. So the new formulas are not identical with the old formulas.
+1 Good catch. There is nothing in the theory of regression that says when you randomize the *weights* that the p-value should average 5%! In fact, because the *data* remain the same during this simulation, we would expect the average p-value (or correspondingly some average t-value) to reflect whatever significance inheres in the data, regardless of the weights. In short, this simulation seems to be just an enormously inefficient way of doing unweighted linear regression.
@PeterEllis I've edited the question a bit to make it easier to read the key points. I've edited again in response to your comment. Does that make it clearer?
But when I switched to a logistic regression setting, I realized that I wasn't really sure how to transfer my methodology. Hence this submission.
I was not able to immediately get my hands on kolen and brennan, however I found vonDavier "Statistical Models for Test Equating, Scaling, and Linking" also by Springer.  From what I have read so far, it looks like a valuable read for me.
Check out the likert tag questions for some suggestions.
F(x) is a CDF of X, correct.... and that *is* the marginal distribution ... it's not just equal to it in the sense of having the same value, it's actually the object that we're talking about. If you'd like to write an answer, please do so. I'll do so if you really don't want to, but you might as well have the reputation.
Thank you for your reply. I did what you suggest and now I think that, perhaps, svdvar is correct but I am calculating the "wrong" values.
Take the example above, which I took from the Wikipedia page:

 http://en.wikipedia.org/wiki/Ordinary_least_squares


Although it is written how to calcute the standard errors of the coefficients \\beta, h and h^2, I cannot arrive at those values.

Can someone please show me an example about how to calculate the standard errors of the OLS coefficients?

Thank you.
In that case you can calculate the relevant population parameters directly so I don't see the need for statistical inference. But, if you did carry out the "usual" statistical inference then you'd need to define exactly what your target population is, since it must be something above-and-beyond the population you have a census of (otherwise, why are you doing any statistics at all?). One possibility is that you're envisioning this as a sample from a hypothetical infinite population but, again, you'd need to specify exactly what that target population is for your results to be interpretable.
@Maddy & I also misspoke (miswrote) about lasso reducing the bias. It tries to reduce *variance* due to estimating $\\beta$s for all covariates at expense of a bit of _increased_ bias in the remaining $\\beta_{\\mathrm{lasso}}$. If the reduction in variance exceeds the increase in bias, then MSE will be reduced. That's what the Lasso aims to get at.
Whether any suggested solution is appropriate will depend on two things, which I hope you can clarify in an edit to your question: (1) Do you hope to exploit the evident *ordering* from non-smoking to smoker to daily smoker?  (2) Will this variable be used as an independent variable or dependent (response) variable in the model?
Thank you, somehow this just was not clicking for me.
One thing to bear in mind, @Michael, is that comments are read by everyone, not just to whom they may be addressed. However, when it seems necessary to provide a definition or clarification, it's usually better to *edit the original reply* (or question) than to bury that information in a comment. Had Emre done that (hint, hint), I think this discussion would have been more productive. In general, people interacting on this site try to avoid personal comments, attacks or criticisms: they are focusing on the *ideas.* This should help guide your default interpretation of any remark.
This article may be of interest, http://dx.doi.org/10.1093/esr/jcp006 , apparently comparing effects between Logistic models is considerably more complicated than in the OLS case!
@Rob Hyndman yes that is what it is mean to be
Why run two regressions when you can run one with a dummy variable for weekends and just test its significance?
I appreciate the response, but I work with R due to money limitations. Thanks.
I can't read Diggle's mind, but I would say it's closer to unbiasedness.
This looks like homework... if you have a book or class notes it should be fairly clear from their definitions and examples of main effects and interaction effects which is which in this particular case.  If you lack references just search for "anova interaction effect"
The very definition of a volatility depends on a defined time interval. One might argue--I don't know how successfully--that government intervention cannot overcome market forces over the "longer" term. Thus, although *daily* volatilities are clearly affected, it is possible that weekly or monthly volatilities are much less strongly affected. Perhaps these thoughts will point you in a fruitful direction for further investigation...
@spore234 Indeed, I have updated my answer in order to account for this.
This is a great starting point.  I'll have to commit some time to go through the whole thing.  Good link - thanks.