tttjjj/elt_bench huggingface dataset:
OK, not sure why you do that, but my answer still stands. You can use TF/IDFs for bigrams and trigrams, and there is no point in using a non-linear kernel instead of increasing the 192 limit of yours.
Hi, thanks for your feedback. I have edited, and hopefully improved the question. Let me know if there's anything else you would like to know.
In fact I don't have the underlying data and I am only given the CI + CL. I know that the underlying distributions will follow Normal Distribution. I assume that if I have CI I can compute compute minimal probability of getting 1 (by taking lower bounds) but I am not sure what happens to CL of my result.
Do you have a model for this variable? If not, according to the regression model you are presenting,  [calibration models](http://en.wikipedia.org/wiki/Calibration_%28statistics%29) might be of interest. Note also that from a classical point of view, you can obtain interval estimates of this coefficient, but a probability in terms of GDP as a variable can only be calculated from a Bayesian perspective.
Thanks for your reply. I am new to statistics so can you be more clear with that sum formula. i.e. what is the formula for ∑
c,s,r p(w|s,r)p(s|c)p(r|c)p(c); does it-> p(w|s,r)p(c)p(r|c)p(s|c)...
Suppose Dr. A bases her diagnosis on the presence of a runny nose and Dr. B bases his diagnosis on the basis of a low temperature.  Perhaps when they agree on a diagnosis that only means the patient has been outside in the cold a long time, resulting in a *decreased* chance that they are correct. Thus, in order to answer questions like this, more information needs to be supplied.  For an extended analysis of this kind of question, please see http://stats.stackexchange.com/questions/30842/what-is-the-probability-that-this-person-is-female.
But the question asks about the standard error of the coefficients, no?
Could you please give more context in your answer? Links are good, but we try to avoid answers that won't stand on their own -- links can disappear.
Isn't this almost a duplicate of http://stats.stackexchange.com/questions/24772/finding-the-bayesian-classifier-for-a-bivariate-gaussian-distribution ?
Exactly. This is also coherent with the inspection of the individual means. I update also a bar plot inside my question, in order to make this aspect clearer.
@thrope - right, but you either try to adjust the statistic or try to find the relevant null distribution.  My suggestion was to use the same statistic but try to do something like a permutation test.  Alternatively, if you have a reasonable model for the two series (particularly their autocorrelation), you could simulate under the null.
You need to *edit* this into your original question, @ShoaibAli, not post it as a comment here. In addition, you should use `set.seed(1)` at the beginning, since you are generating random data. Moreover, the answer, I believe, is still the same as what I put: `predict(..., newdata=data.frame(x=X.new),...)`.
@DJE There are even simpler yet rigorous solutions, such as comparing the mean of the more recent values to the mean of the earliest values. This overcomes (a) possible problems with autocorrelation (by leaving a suitable temporal gap between the early and recent values) and (b) problems with assuming linearity (because no such assumption is needed, although implicitly we assume there is no *appreciable* trend during the "early" and "recent" time periods). These solutions can be implemented with a t-test or Wilcoxon test (albeit preferably after a suitable re-expression of the data).
I am extremely sorry for my late response. Thanks a lot for your guidance and the paper change of measure was really informative. Thanks again.
Thank you for your answer. In this case, would it be enough to multiply a p-value with the number of quantiles tested, in this case 5 (for correction of multiplicity)?
Precisely. It uses the inverse distance between the pixels (as measured in pixels) to weight the measure of spatial autocorrelation. Note that I generated a grayscale image, but you could similarly apply this to a color image either treating the colors separately or taking some combined score.
Probably you are overfitting your data as you are using one classifier to aggregate the other classifiers (I dont know). But I suggest to use other fusion technique such as harmonic/geometric mean of the scores obtained by each classifier and then create a new score. Check out if this score is adequate for your requirements.
Whether the R^2 changes on average with sample size can't be answered without some assumptions about the process you're sampling. Since the X's are fixed in regression, this presents some difficulties in guessing what sampling circumstances you might mean. However, it's possible to specify reasonable circumstances in which the $R^2$ should approach a 'population' value.
Thanks!! Re point 2, up sampling did not help me train flour the high precision region, since performance in the un balanced data stol suffers in the pr curve.
The origin is effectively arbitrary. Smaller BIC (further left on the number line) is better by the criterion.
Be clearer about what you need help with. What does gamma or gaussian have to do with it? And that formula appears to imply more than 5 parameters.
Sometimes Pearl uses the term [Collider Bias](http://ftp.cs.ucla.edu/pub/stat_ser/r332.pdf) to refer to the example you give, but I'm not sure if that fits your bill.
Please expand upon this recommendation. Either why you feel it is appropriate or why is is better than some of the other recommendations.
Added references/links
Bill, thanks for your thoughtful answer. It has been a while since I needed this, but I still appreciate it.
Awesome, I was able to verify this, well actually: $V_2 = \\frac{N-1}{N}V_1 + (\\bar{X} - \\hat{X})^2$.  When I use the edited/corrected version of $V_2$.
Perhaps you can provide a link to the particular reference you are using. Do you know what a [sufficient statistic](http://en.wikipedia.org/wiki/Sufficient_statistic) is in general? What does the letter $i$ index?
The code in the question is incorrect, because it implements the model $\\log(E(y_i))=\\beta_0 + \\beta_1 \\text{exp}_1 + \\beta_2 \\text{exp}_2.$ Note the two distinct differences: $\\beta_0$ is not $B_1$ and, more importantly, the variables are not the ones intended.
The way the cognitive map and the graphical model in the paper has been developed follows a recurrent neural network and perceptron where each concept is actually a neuron. So, it is related to artificial intelligence. These models are used in natural language processing (http://www.google.com/patents/US8190422) and machine learning techniques are used to learn the map. Hence, I thought that maybe semantics, natural language processing and machine learning experts in this site may be familiar with the terms & will be able to help.
+1, a more complete illustration than mine. (In fact, I knew there was something in the `TeachingDemos` package but was too lazy to search for it.)
Is it a balanced design?
Great!  Do you, by chance, have any idea of what approach I might take to resolve my second question?  I know from Gleser and Olkin that the covariance between $d_{g_1 - g_2}$ and $d_{g_1 - g_3}$ is $1/n_{g_1} + (d_{g_1 - g_2} * d_{g_1 - g_3}) / (2 * (n_{g_1} + n_{g_2} + n_{g_3}))$, but it's not clear to me how to use this information to obtain the covariance between the two effect sizes for $d_{diff}$.
@cardinal: Ah. I get it. Edited. I think the important thing is that in the general case there's no constraint on how far off the "bad" 5% of CI's can be so no reason to believe that the particular CI you have calculated is even close to a credible interval. (Unless there are other constraints on the problem/data that would constrain the CI's.)
Sequential imputation is one technique used in Bayesian inference with missing data. But like @Dapz says, it depends on why the data was missing(e.g. can you assume that all entries were equally likely to have come up missing? or, does your measuring instrument tend to fail when numbers are too large?)
Thanks Whuber! you are right, those far locations are rural and they are far away from everything. In this case, the distance is between patients and the only service provider. so the only alternative is not getting treated.
@Max, why not turn that into an answer?
Hi RCP. As it stands your question could really only be answered with 'it depends'. More context/detail is needed if this question is to stay open.
Covariance is not necessarily interchangeable with correlation - the former is very unit dependent. Correlation is a number between -1 and 1 a unit-less scalar representing the 'strength' of the covariance IMO and that's not clear from your answer
I think you can use factor analysis or principle component analysis for the selection of variables.
Then I guess you've also probably seen this line on the wikipedia page: "In the case of a simple null hypothesis α is the probability of a type I error. If the null hypothesis is composite, α is the maximum (supremum) of the possible probabilities of a type I error."
There is too little information for you to get a good answer. For starters, why do you look for an alternative and ẃhat is the setup and goal of whatever you have in mind?
I guess I am inclined to turn the question around and ask you whether you have references which say that such a prerequisite exists. I am confused why you think it should. Nowhere in the definition of a cross-level interaction is the idea of random slopes ever invoked, or random effects at all for that matter; we can even have cross-level interactions in mixed-model ANOVA, as in the traditional analysis of "split-plot" experiments.
It just covers a country canada
Are you asking how to compute the likelihood or are you asking whether it's sensible to select the bucket with the highest likelihood?
Thank-you, this is very helpful
thank you for the inputs, specially for the references, but I wrongly refered to Factor Analysis: I was actually  thinking about Principal Components in order to reduce my variables set to a sub-group of independent variables. my mistake
It *precomputes* a set of campaigns for the user, so the output is a (ranked) list.
Great! This is very helpful, thank you so much.
You may find helpful those related posts http://stats.stackexchange.com/questions/6856/aggregating-results-from-linear-model-runs-r http://stats.stackexchange.com/questions/1812/fa-choosing-rotation-matrix-based-on-simple-structure-criteria
AdamO - I would like to know how the three groups differ in there responses for the two continua. More specifically I would like to know if the duration (cont2) of the vowel (cont1) affects responses as a function of group.
depends completely on the journal (and the field of research).
We don't "e-mail" here. The point is that the answers can be re-used by the people which have a similar question.
Write the function for corr with the parameters hardcoded. From a programmatic view you probably want to do it as a partial application. From a statistics view you lose the ability to specify upper and lower bounds of theta, which would require a rewrite.
Sorry for the late response. I am going to edit my answer above within 24 hours to include an example that will illustrate your concerns. For now, I don't think there is a universal answer yes/no that applies. As far as I know, in real life problems, models have measurement errors integrated into the *before* doing statistical tests. This is because you know you're making a measurement error since you're not able to measure the thing you want to measure. E.g. in animal studies, you may not be able to measure because it would either kill the animal or require you to remove it from its habitat
@ronaf: That's the right idea.  If one uses signed side lengths and also considers the angle as a real value (rather than its value modulo $2\\pi$), there is no inconsistency with normality in either case.  Your point about the inequality possibly being wrong is excellent.  All I can do in response is to claim that the equation is an excellent approximation under the assumptions made because the chance of X or Y being negative is negligible.
@Mark, I'm sorry but I don't quite understand your issue. I explicitly excluded the intercept (`-1`) therefore all levels *should* be included. the first regression output above features all 3 variables (but no intercept). or didn't I get your point right?
That it admits a lot of "run of the mill" examples is why I thought there might be a name for it. The structure does have some inferential implications. And, indeed, $Y$ is not generally going to be in the exponential family marginally - if it was, I would just use the exponential family representation and be happy :)
Well your answer helped a lot. Thanks for the link too. By the way how did you plotted the using `predictor` and `predicted` variables?
A negative predicted price is not necessarily an error.  We have no basis to expect perfect predictions. Although such a model should give one pause--clearly it does not fully or correctly capture the relationship between prices and the explanatory variables--it could still have great predictive value.  (Nevertheless, I have to agree with @Glen_b's answer suggesting that you consider using a more realistic model.)
To my way of thinking 11 events out of 171 cases is not very rare.  It is greater than 0.005. If the analysis is exploratory and has nothing to do with your main hypotheses I see no reason to put a limit on the number of tests to look at.  Also multiple comparisons is not an issue because you wouldn't try to interpret p-values in an exploratory analysis.  In your case if you can enroll 10,000 patients (not uncommon in clinical trials especially for pharmaceuticals) you can have reasonably powerful tests for this level of rarity.
@Largh, Arguably, this question falls under the category of "collecting data," which is specifically on topic according to our FAQ.
It is easy to implement the density (and therefore the likelihood) in R using numerical integration, but a major concern here would be parameter identifiability. I tried to approximate the MLE in this way but I found (empirically) this issue.
Straightforwardly, for each unit change in the reciprocal of GDP, employment changes by $\\beta_2$ units (the units are whatever you're measuring GDP & employment in).
The DieHard test requires almost no statistical experience to apply: it is fully automatic. It does require a little bit of *computing* experience, because it needs an 11 MB file containing a long binary sequence of 31 or 32 bit values from your random number generator. The documentation is clear and even the source code is available (in several languages) if you have any questions.
I can second pretty much all of this. Two points that I want to add: A) what you seem to do is some kind of *overfitting*. By systematically evaluating measures, weights and methods, there is a high risk that the parameters you end up with are highly specific for your current data, and may be useless on other data or even later data. B) what good is it to know the similarity of the dendrograms. Consider what you want to do with them afterwards, and then try evaluating at the end result. Evaluating interim results may be misleading.
I have no idea if this title makes any sense. If someone can title this better, feel free.
One way is to [look at the objective function](http://stats.stackexchange.com/questions/7308/can-the-empirical-hessian-of-an-m-estimator-be-indefinite/7629#7629) (which is usually a negative log likelihood or a measure of goodness of fit).
Please provide more info about this data.
"*The number .05 is arbitrary and based on an example Ronald Fisher used ~80 years ago*" -- it is arbitrary, but there's a [little more](http://stats.stackexchange.com/questions/55691/regarding-p-values-why-1-and-5-why-not-6-or-10/55693#55693) behind its widespread use than 'an example'
I would be cautious of trying to use any colour model to map three different variables -- there's just too much interaction in the perceived value of the colour.  (E.g., at low saturation or extremes of value hue becomes indistinguishable).  That said, you can probably successfully map *two* variables to colour, either using two dimensions of hue, fully saturated (like the [YCbCr colour plane at Y=0.5](http://en.wikipedia.org/wiki/YCbCr)), or using one dimension of hue between two primary colours and one dimension of brightness.
Welcome to the site, @Candide. This looks like a helpful contribution (+1), we hope we'll see more in the future. Note that we prefer you don't sign your posts or add other, peripheral / conversational comments. Your flair, with your username and a link to your user page are automatically added to all your posts.
One additional point. In the case where the data is created with a $b_3$ different from $b_1 b_2$ the AIC difference would be much larger and hopefully the F-test would be significant.
No, it is not unfair. That's what ROC analysis is for. ROC compares the ranking capabilities of classifiers. The way they rank is irrelevant (e.g. the actual score values). It's perfectly valid to use ROC analysis to compare, say, logistic regression with SVM.
I've added a little to the end of my answer
My point is that often times you want to do MCMC to approximate the entire posterior (e.g., to get the predictive) but it's intractable, so people go with just trying to find the MAP parameters, which is usually formatted as an optimization problem. However, if you look at most papers in NIPS or other related venues, usually the authors choose to do a variational approximation and then apply EM, rather than treating the full posterior as an optimization problem that requires a global search operator. I'm wondering if there is a reason or if it's just a bias in the machine learning community.
+1 You can see why I did the multiple regression case for this... thanks for going to the extra effort of doing the simple-regression case.
You are missing an adequate number of hidden variables to do decent approximation.
Thanks for mentioning this Mike.
Are you the same person as [this user](http://stats.stackexchange.com/users/44135/kate)? If so, please register & merge your accounts. (You can find information on how to do that [here](http://stats.stackexchange.com/help/merging-accounts).) This offers you advantages: you will be able to keep track of your questions & will be notified about what happens to them (eg, new answers). You will be able to comment on your questions, & will earn privileges as well.
@Aniko, I am looking at those places where there is exon-skipping event in either 1 or both time points. Therefore, I am interested in finding out, if there are exon-skipping events that are present in 1 time point but not in the other. I guess my null hypothesis (for each junction I test) would be: Given this occurrence of normal events for each time point, there is no difference in the occurrence of exon-skipping events between the two time points.
Looks ok to me, thanks.
You've asked a number of obviously related questions http://stats.stackexchange.com/questions/21727/guidelines-for-calculating-sample-size, http://stats.stackexchange.com/questions/21658/is-it-necessary-for-a-sample-to-broadly-reflect-the-target-population-distributi, http://stats.stackexchange.com/questions/21595/what-is-a-representative-sample.  It would definitely be worth your while studying some basic texts on sampling and weighting and if possible taking a course or getting specialist assistance.  As Michelle says in an answer to another question, this is a highly specialized area.
Ignore that...thought I was on a different site >.<
It would be helpful to explain the statistical principles on which this method is based, if there are any.
See my comments on the math stack page version of this.
Also very closely related is http://stats.stackexchange.com/questions/175/.  Many potential outlier detection methods are described in answers at http://stats.stackexchange.com/questions/213.  But more to the point would be some *context*: what are you doing with this scatterplot? What conclusions are you trying to draw from it? Some conclusions will depend little on what you do with outliers, whereas others might depend on them critically. This indicates that the methods you use to identify and treat outliers must depend on the intended analysis.
kNN is not a clustering algorithm. It's classification. And k-means won't work with such metrics, as it minimizes variances (and needs means, which isn't well defined for non-numeric attributes)
What would it mean for the $R^2$ to be "higher than it should be"?
If the sample size is big enough, sequential and non-sequential estimates should be close enough, since non-sequential procedure produces consistent estimates. The sequential procedure has its advantages, since even if the exact structure of error variance is not known, you will get consistent estimates of the parameters $\\beta$. If the model for the error turns out not to be AR(1), using maximum likelihood might in turn produce worse estimates than sequential procedure.
Right, relatively speaking.  See http://stats.stackexchange.com/questions/1576/what-are-the-differences-between-factor-analysis-and-principal-component-analysi
This is a good answer but, given the increasingly common use of tools like generalized additive models, the comment *"if you add a variable to a regression model as a quantitative variable you assume the effect of that variable to be linear"* is not quite true. But, given that the OP was most likely talking about _linear_ logistic regression, I think it's a good point to make. +1!
More a comment than an answer: KPCA is very similar to Spectral Clustering -- in some settings it is even the same. (see e.g. http://www.cirano.qc.ca/pdf/publication/2003s-19.pdf).
But what if you are estimating a translog production function? By definition, all the variables must be in logs, including dummy variables Dan
I think N26 is suggesting a thought experiment. I.e., if when designing a study you have a choice between two scales, should you prefer, prima facie, the one with the greater variance. Also, having two predictors that represent the same construct, but are measured differently does not violate the assumption of independence of observations.
This sounds like straight coursework. Can you explain the context in which it arises please? The parameters you supply to rlnorm are NOT the log of the mean and variance of the lognormal (see [here](http://en.wikipedia.org/wiki/Log-normal_distribution) for an explanation of the usual parameterization), but in any case, to plot a density, you just use `dlnorm` rather than generate  a random sample and smooth it.
you seem to be posting the same question using different variable names, see [here](http://stats.stackexchange.com/questions/12960/error-message-when-estimating-group-level-interactions-lmer) and [here](http://stats.stackexchange.com/questions/13161/testing-group-level-interactions-using-lmer).
@Sepehr I disagree with roland2 about the appropriateness of your question here.  I think it relates to experimental desing is sues and hence is appropriate for CV.  Regarding the efficiency issue that I brought up my implicit assumption is that the two populations have the same variances (or at least the variances are close to being equal).  In that case an estimate of mean difference based on a fixed total sample size n will less accurate when the sample sizes are unequal and it gets worse as the imbalance increases.
My very big +1 because it is really a lot of good advices. In the same vein, I like to show to students that it is really pointless to summarize data gathered from surveys (or votes) as % with a lot of decimals without considering sample size (which impacts standard error).
Two more comments: 1) Is the 4th step in your algorithm simply to check for convergence? 2) You should be looking at the sum of squared distance not the average distances.
A paired t-test will help you decide if there was a change in mean.  It will not help you decide if there was a change in variance.