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Tags
list
7347
2
null
7330
1
null
Yes, arbitrary rotations in an $n$ dimensional space can be written as the compositions of Givens rotations. The other question (and I think what you're aiming at) is > Or perhaps a better question is: if a prior distribution is invariant when rotated about 2 arbitrary dimensions, is it invariant when rotated ab...
null
CC BY-SA 2.5
null
2011-02-17T22:00:09.717
2011-02-17T22:00:09.717
null
null
30
null
7348
1
7349
null
35
24598
I find R can take a long time to generate plots when millions of points are present - unsurprising given that points are plotted individually. Furthermore, such plots are often too cluttered and dense to be useful. Many of the points overlap and form a black mass and a lot of time is spent plotting more points into tha...
Statistical methods to more efficiently plot data when millions of points are present?
CC BY-SA 4.0
null
2011-02-17T22:29:30.310
2019-11-14T10:45:29.190
2018-06-27T21:45:14.067
8013
2726
[ "r", "data-visualization" ]
7349
2
null
7348
14
null
This is a hard task with no ready solutions (this is of course because density plot is so a tempting fallback than no one really cares). So, what can you do? If they really overlap (i.e. have exactly the same X & Y coordinates) and you are not using alpha, the best idea would be just to reduce the overlap using `unique...
null
CC BY-SA 2.5
null
2011-02-17T23:32:55.593
2011-02-17T23:32:55.593
null
null
null
null
7350
2
null
7
1
null
[http://www.ckan.net](http://www.ckan.net) has a number of datasets too. [http://www.biotorrents.net/browse.php](http://www.biotorrents.net/browse.php) is also starting to have quite a large amount of BIG datasets.
null
CC BY-SA 2.5
null
2011-02-18T00:06:24.633
2011-02-18T00:06:24.633
null
null
3291
null
7351
1
7352
null
48
7976
I am trying to get upto speed in Bayesian Statistics. I have a little bit of stats background (STAT 101) but not too much - I think I can understand prior, posterior, and likelihood :D. I don't want to read a Bayesian textbook just yet. I'd prefer to read from a source (website preferred) that will ramp me up quickly....
Bayesian statistics tutorial
CC BY-SA 2.5
null
2011-02-18T00:35:17.267
2022-07-16T16:57:20.707
2012-10-16T16:16:40.557
null
3301
[ "bayesian", "references" ]
7352
2
null
7351
19
null
Here's a place to start: [ftp://selab.janelia.org/pub/publications/Eddy-ATG3/Eddy-ATG3-reprint.pdf](ftp://selab.janelia.org/pub/publications/Eddy-ATG3/Eddy-ATG3-reprint.pdf) [http://blog.oscarbonilla.com/2009/05/visualizing-bayes-theorem/](http://blog.oscarbonilla.com/2009/05/visualizing-bayes-theorem/) [http://yudkows...
null
CC BY-SA 3.0
null
2011-02-18T01:04:21.207
2011-06-23T20:29:50.033
2011-06-23T20:29:50.033
2775
2775
null
7353
2
null
7348
17
null
I must admit that I do not fully understand your last paragraph: > "I am not looking for a density plot (although those are often useful), I would want the same output as a simple plot call but much faster than millions of overplots if possible." It is also unclear what type of plot (function) you are lookin...
null
CC BY-SA 3.0
null
2011-02-18T01:13:27.283
2016-01-13T18:52:38.197
2016-01-13T18:52:38.197
36419
307
null
7354
2
null
7208
4
null
I find caracal's answer convincing, but I also believe Cohen's Kappa can only account for part of what constitutes interrater reliability. The simple % of ratings in agreement accounts for another part, and the correlation between ratings, a third. It takes all three methods to gain a complete picture. For details p...
null
CC BY-SA 2.5
null
2011-02-18T01:26:44.263
2011-02-18T01:26:44.263
null
null
2669
null
7355
2
null
7351
5
null
Some more depth: - http://math.tut.fi/~piche/bayes/notes01.pdf covers Bayes' theorem - https://ccrma.stanford.edu/~jos/bayes/bayes.pdf and - http://www-personal.une.edu.au/~jvanderw/Introduction_to_Bayesian_Statistics1.pdf are more about statistical applications
null
CC BY-SA 2.5
null
2011-02-18T01:33:51.137
2011-02-18T01:33:51.137
null
null
2958
null
7356
2
null
7348
45
null
Look at the [hexbin](http://cran.r-project.org/package=hexbin) package which implements paper/method by Dan Carr. The [pdf vignette](http://cran.r-project.org/web/packages/hexbin/vignettes/hexagon_binning.pdf) has more details which I quote below: > 1 Overview Hexagon binning is a form of bivariate histogram useful ...
null
CC BY-SA 2.5
null
2011-02-18T02:02:39.183
2011-02-18T02:02:39.183
null
null
334
null
7357
1
7359
null
44
21328
I know this is a fairly specific `R` question, but I may be thinking about proportion variance explained, $R^2$, incorrectly. Here goes. I'm trying to use the `R` package `randomForest`. I have some training data and testing data. When I fit a random forest model, the `randomForest` function allows you to input new tes...
Manually calculated $R^2$ doesn't match up with randomForest() $R^2$ for testing new data
CC BY-SA 3.0
null
2011-02-18T02:32:48.823
2018-01-09T09:06:16.900
2018-01-09T09:06:16.900
128677
36
[ "r", "correlation", "predictive-models", "random-forest", "r-squared" ]
7358
1
7377
null
23
12515
I've got a particular MCMC algorithm which I would like to port to C/C++. Much of the expensive computation is in C already via Cython, but I want to have the whole sampler written in a compiled language so that I can just write wrappers for Python/R/Matlab/whatever. After poking around I'm leaning towards C++. A coupl...
C++ libraries for statistical computing
CC BY-SA 2.5
null
2011-02-18T02:40:12.390
2017-11-22T14:23:28.570
2017-11-22T14:23:28.570
11887
26
[ "markov-chain-montecarlo", "software", "c++", "computational-statistics" ]
7359
2
null
7357
66
null
The reason that the $R^2$ values are not matching is because `randomForest` is reporting variation explained as opposed to variance explained. I think this is a common misunderstanding about $R^2$ that is perpetuated in textbooks. I even mentioned this on another thread the other day. If you want an example, see the (o...
null
CC BY-SA 2.5
null
2011-02-18T03:31:08.217
2011-02-18T04:21:19.807
2011-02-18T04:21:19.807
2970
2970
null
7360
2
null
7358
1
null
There are numerous C/C++ libraries out there, most focusing on a particular problem domain of (e.g. PDE solvers). There are two comprehensive libraries I can think of that you may find especially useful because they are written in C but have excellent Python wrappers already written. 1) [IMSL C](http://www.roguewave.co...
null
CC BY-SA 2.5
null
2011-02-18T04:08:36.080
2011-02-19T02:40:37.700
2011-02-19T02:40:37.700
1080
1080
null
7361
2
null
7358
7
null
Boost Random from the Boost C++ libraries could be a good fit for you. In addition to many types of RNGs, it offers a variety of different distributions to draw from, such as - Uniform (real) - Uniform (unit sphere or arbitrary dimension) - Bernoulli - Binomial - Cauchy - Gamma - Poisson - Geometric - Triangle...
null
CC BY-SA 2.5
null
2011-02-18T04:25:52.087
2011-02-18T04:25:52.087
null
null
1537
null
7362
1
7368
null
3
4082
In Orwin's fail safe N test how to decide the values of criterion for a trivial log odd's ratio and mean log odds ratio in missing studies. I am a medical doctor. Please tell me in simple english. The data are ``` 1. Classic fail-safe N Z-value for observed studies 27.97543 P-value f...
Orwin's fail safe N test
CC BY-SA 2.5
null
2011-02-18T05:58:42.340
2011-02-18T10:01:57.817
2011-02-18T09:45:21.120
307
2956
[ "meta-analysis", "publication-bias" ]
7363
2
null
7326
0
null
I believe a chi-squared test is what you are looking for. Because your dataset has a long tail, many tags will not be sampled well or will not end up in your sample at all. You may want to look into Yates' chi-square test, which attempts to correct for this by loosening the standards of what is significant for rare tag...
null
CC BY-SA 2.5
null
2011-02-18T06:07:14.057
2011-02-18T06:07:14.057
null
null
2965
null
7364
1
null
null
4
125
The standard factor model formulation is $y=W x+\epsilon$ where $x \sim \mathcal{N}(0, I)$, $\epsilon \sim\mathcal{N}(0, \Sigma)$. $W$ and $\Sigma$ are typically estimated from MLE. The solution can be obtained numerically; in general there are no analytical solutions. Question: assume that $\Sigma$ belongs to some cla...
Factor models with small noises
CC BY-SA 2.5
null
2011-02-18T06:10:01.733
2011-02-18T06:10:01.733
null
null
30
[ "factor-analysis", "maximum-likelihood", "asymptotics" ]
7365
2
null
7308
7
null
The quotation in full [can be found here](http://books.google.com/books?id=cdBPOJUP4VsC&lpg=PP1&dq=wooldridge%20econometrics&hl=fr&pg=PA357#v=onepage&q=wooldridge%20econometrics&f=false). The estimate $\hat{\theta}_N$ is the solution of minimization problem ([page 344](http://books.google.com/books?id=cdBPOJUP4VsC&lpg=...
null
CC BY-SA 2.5
null
2011-02-18T08:56:34.040
2011-02-25T11:23:38.733
2011-02-25T11:23:38.733
2116
2116
null
7366
1
7373
null
2
2311
I am a beginner in statistics, therefore I hope I can state my problem in a correct manner. I have a some instances or samples and I can collect below statistical parameters for classification and regression problem: - Sample Size - Minimum value - Maximum value - Standard deviation - Variance - Mean And, I wan...
Is z-score meaningful in classification or regression?
CC BY-SA 2.5
null
2011-02-18T09:09:36.343
2011-02-18T11:08:11.973
2011-02-18T10:05:42.170
930
2170
[ "classification", "z-statistic" ]
7367
2
null
7358
9
null
I would strongly suggest that you have a look at `RCpp` and `RcppArmadillo` packages for `R`. Basically, you would not need to worry about the wrappers as they are already "included". Furthermore the syntactic sugar is really sweet (pun intended). As a side remark, I would recommend that you have a look at `JAGS`, whic...
null
CC BY-SA 2.5
null
2011-02-18T09:32:00.917
2011-02-18T09:32:00.917
null
null
1443
null
7368
2
null
7362
6
null
The criterion for a 'trivial' effect size (odds ratio in your example) should be decided based on the size of effect that would be considered 'trivial' in the particular scenario, rather than on statistical grounds. If you're looking at an intervention that may be given to a considerable segment of the population with ...
null
CC BY-SA 2.5
null
2011-02-18T10:01:57.817
2011-02-18T10:01:57.817
null
null
449
null
7369
2
null
7344
4
null
In addition to @mpiktas's comment, you can also have a look at the [rms](http://cran.r-project.org/web/packages/rms/index.html) package from Frank Harrell. The advantage is that it handles both LM and GLM for model fitting and prediction; see for example the `plot.Predict()` function. If you're planning to do serious j...
null
CC BY-SA 2.5
null
2011-02-18T10:04:53.950
2011-02-18T10:04:53.950
null
null
930
null
7370
1
7372
null
2
136
I would like to check different gradient algorithms. For example: ``` fr <- function(x) { ## Rosenbrock Banana function x1 <- x[1] x2 <- x[2] print(c(x1,x2)) 100 * (x2 - x1 * x1)^2 + (1 - x1)^2 } optim(c(-1.2,1),fr,method="BFGS") ``` prints to the screen the values at which t...
How to store checks of gradient algorithm in a matrix using R?
CC BY-SA 2.5
null
2011-02-18T10:21:17.707
2016-03-04T12:19:38.220
2016-03-04T12:19:38.220
603
603
[ "r" ]
7372
2
null
7370
4
null
Use the function capture.output: ``` cc<-capture.output(vv<-optim(c(-1.2,1),fr,method="BFGS")) t(sapply(strsplit(gsub(" +"," ",cc)," "),function(l)as.numeric(l[2:3]))) ``` The variable `vv` is used so that the result of optim will not be printed only your calls to the function. Each call to the function results in one...
null
CC BY-SA 2.5
null
2011-02-18T11:00:21.777
2011-02-19T06:50:00.900
2011-02-19T06:50:00.900
2116
2116
null
7373
2
null
7366
3
null
In order to perform linear regression you'd need not only the means and variances of the variables but also all their covariances (or equivalently their correlations). If you can collect the means, variances and covariances/correlations separately in each of the classes you wish to classify, you can do [linear discrim...
null
CC BY-SA 2.5
null
2011-02-18T11:08:11.973
2011-02-18T11:08:11.973
null
null
449
null
7374
2
null
7351
2
null
You could try '[Teaching Bayesian Reasoning In Less Than Two Hours](https://www.apa.org/pubs/journals/releases/xge-1303380.pdf)'.
null
CC BY-SA 3.0
null
2011-02-18T12:10:29.613
2016-06-27T06:44:41.230
2016-06-27T06:44:41.230
22
22
null
7375
2
null
7351
8
null
If you'd like to try a few learn by examples, you may be interested in "[Bayesian Computation in R](http://bayes.bgsu.edu/bcwr/)" by Jim Albert. Its related R package is called LearnBayes.
null
CC BY-SA 3.0
null
2011-02-18T12:59:46.510
2012-05-15T07:17:04.137
2012-05-15T07:17:04.137
582
3306
null
7376
1
7378
null
30
18639
Inter-market analysis is a method of modeling market behavior by means of finding relationships between different markets. Often times, a correlation is computed between two markets, say S&P 500 and 30-Year US treasuries. These computations are more often than not based on price data, which is obvious to everyone that ...
Does correlation assume stationarity of data?
CC BY-SA 2.5
null
2011-02-18T13:07:06.643
2016-08-05T18:06:20.690
null
null
3306
[ "correlation", "stationarity" ]
7377
2
null
7358
18
null
We have spent some time making the wrapping from C++ into [R](http://www.r-project.org) (and back for that matter) a lot easier via our [Rcpp](http://dirk.eddelbuettel.com/code/rcpp.html) package. And because linear algebra is already such a well-understood and coded-for field, [Armadillo](http://arma.sf.net), a curr...
null
CC BY-SA 2.5
null
2011-02-18T15:41:38.457
2011-02-18T16:39:18.800
2011-02-18T16:39:18.800
334
334
null
7378
2
null
7376
42
null
The correlation measures linear relationship. In informal context relationship means something stable. When we calculate the sample correlation for stationary variables and increase the number of available data points this sample correlation tends to true correlation. It can be shown that for prices, which usually ar...
null
CC BY-SA 3.0
null
2011-02-18T15:46:08.050
2016-08-05T18:06:20.690
2016-08-05T18:06:20.690
31363
2116
null
7379
1
14670
null
4
195
I'm reading through someone else's code for plotting the results of a psychology experiment, and (according to the code comments) they calculate the accuracy error of their behavioral paradigm as follows: $\textit{accuracy error} = \sqrt{\frac{(\textit{accuracy}) (1-\textit{accuracy})}{\textit{total trials}}}$ It's out...
What is this measure of error?
CC BY-SA 2.5
null
2011-02-18T16:40:42.403
2011-08-23T00:38:20.873
2011-02-18T16:54:52.120
919
2019
[ "binomial-distribution", "error" ]
7380
5
null
null
0
null
Econometrics is a field of statistics dealing with applications to economics. For econometrics resources, refer to the following questions: - Free econometrics textbooks - Introductory statistics and econometrics in R - Good econometrics textbooks?
null
CC BY-SA 3.0
null
2011-02-18T17:52:05.987
2013-09-02T13:46:59.017
2013-09-02T13:46:59.017
27581
2116
null
7381
4
null
null
0
null
Econometrics is a field of statistics dealing with applications to economics.
null
CC BY-SA 2.5
null
2011-02-18T17:52:05.987
2011-02-18T20:29:10.600
2011-02-18T20:29:10.600
2116
2116
null
7382
2
null
7376
14
null
> ...is the computation of correlation whose data is non-stationary even a valid statistical calculation? Let $W$ be a discrete random walk. Pick a positive number $h$. Define the processes $P$ and $V$ by $P(0) = 1$, $P(t+1) = -P(t)$ if $V(t) > h$, and otherwise $P(t+1) = P(t)$; and $V(t) = P(t)W(t)$. In other w...
null
CC BY-SA 2.5
null
2011-02-18T19:18:50.377
2011-02-18T19:18:50.377
null
null
919
null
7383
2
null
4762
1
null
To use SPSS for the Lack of fit test go to: Analyze>>Compare Means>>Means. Then in the dialogue box that appears assign your Independent and Dependent Variables. Select Options and a new dialogue box will appear. Check the option at the bottom of the screen that says "Test for Linearity".
null
CC BY-SA 2.5
null
2011-02-18T20:40:13.133
2011-02-18T20:40:13.133
null
null
null
null
7384
2
null
7268
6
null
Aggregation also works without using `zoo` (with random data from 2 variables for 3 days and 4 hosts like from JWM). I assume that you have data from all hosts for each hour. ``` nHosts <- 4 # number of hosts dates <- seq(as.POSIXct("2011-01-01 00:00:00"), as.POSIXct("2011-01-03 23:59:30"), by=30) hosts...
null
CC BY-SA 2.5
null
2011-02-18T20:53:58.767
2011-02-18T21:03:34.373
2011-02-18T21:03:34.373
1909
1909
null
7385
1
7418
null
14
5082
this is my first post. I'm truly grateful for this community. I am trying to analyze longitudinal count data that is zero-truncated (probability that response variable = 0 is 0), and the mean != variance, so a negative binomial distribution was chosen over a poisson. Functions/commands I've ruled out: R - gee() functi...
R/Stata package for zero-truncated negative binomial GEE?
CC BY-SA 2.5
null
2011-02-18T21:20:51.227
2013-08-13T14:53:07.500
2011-02-19T03:52:51.513
3309
3309
[ "r", "stata", "count-data", "panel-data", "truncation" ]
7386
6
null
null
0
null
I am reluctant to make this nomination because I have been happy with the moderators. I would be delighted to see them continue in their roles. However, to date only two people have entered nominations. (Is everyone else waiting until just before the deadline?) As you might guess from my activity here, I value this f...
null
CC BY-SA 2.5
null
2011-02-18T22:29:42.007
2011-02-18T22:29:42.007
2011-02-18T22:29:42.007
919
919
null
7387
2
null
7202
2
null
Mixed models are usually used to take account of the correlation structure likely with a model like this. Look up Analyze>Mixed Models (MIXED) or the newer Mixed Models>Generalized Linear if you have the latest version. HTH, Jon Peck
null
CC BY-SA 2.5
null
2011-02-18T22:55:09.213
2011-02-18T22:55:09.213
null
null
null
null
7389
1
7649
null
8
2223
My question deals with how to be able to assert that an "improved" evolutionary algorithm is indeed improved (at least from a statistic point of view) and not just random luck (a concern given the stochastic nature of these algorithms). Let's assume I am dealing with a standard GA (before) and an "improved" GA (after)....
How to check if modified genetic algorithm is significantly better than the original?
CC BY-SA 2.5
null
2011-02-18T23:34:23.113
2014-02-05T20:13:19.270
2011-02-20T23:52:35.640
null
10633
[ "t-test", "genetic-algorithms", "multiple-comparisons" ]
7391
1
35542
null
6
353
I have seen asserted that the problem of computing the null distribution of Kolmogorov's $D_n^+$ statistic for a finite sample size maps onto the problem of computing the number of lattice paths that stay below the diagonal, and thus can be solved by the [ballot theorem](http://en.wikipedia.org/wiki/Bertrand%27s_ballot...
Kolmogorov-Smirnov and lattice paths
CC BY-SA 2.5
null
2011-02-19T01:57:52.283
2023-01-03T18:35:41.610
2012-09-01T22:54:53.643
8413
21874
[ "kolmogorov-smirnov-test" ]
7392
2
null
7385
9
null
Hmm, good first question! I don't know of a package that meets your precise requirements. I think Stata's [xtgee](http://www.stata.com/help.cgi?xtgee) is a good choice if you also specify the `vce(robust)` option to give Huber-White standard errors, or `vce(bootstrap)` if that's practical. Either of these options will ...
null
CC BY-SA 2.5
null
2011-02-19T10:01:05.533
2011-02-19T10:01:05.533
null
null
449
null
7393
2
null
7389
4
null
It might not be what you want to hear, but from what I've seen the new algorithm is just compared to the old one on benchmark functions. E.g. as done here: [Efficient Natural Evolution Strategies, (Schaul, Sun Yi, Wierstra, Schmidhuber)](http://www.idsia.ch/~tom/publications/enes.pdf)
null
CC BY-SA 2.5
null
2011-02-19T10:03:01.937
2011-02-19T13:02:11.847
2011-02-19T13:02:11.847
2860
2860
null
7394
1
7395
null
6
8465
I have searched a lot, and I can only find tables that show critical values up to n=30. Can someone provide, or point me to, a simple method of estimating this value for different $\alpha$?
How to estimate a critical value of Spearman's correlation for n=100?
CC BY-SA 2.5
null
2011-02-19T18:41:52.773
2011-02-19T19:16:55.457
null
null
977
[ "hypothesis-testing", "correlation", "spearman-rho" ]
7395
2
null
7394
3
null
For values over thirty the approximation (for a two-tailed test) is $$\frac{\Phi^{-1}\left(1-\tfrac{\alpha}{2}\right)}{\sqrt{n-1}}$$ so for example with $\alpha = 0.05$ and $n=100$ the numerator is about 1.96 and the denominator about 9.95, giving a critical value of about 0.197. This comes from $\rho$ having approxim...
null
CC BY-SA 2.5
null
2011-02-19T19:08:00.543
2011-02-19T19:16:17.797
2011-02-19T19:16:17.797
2958
2958
null
7396
2
null
7394
7
null
See Wikipedia: [Spearman's rank correlation coefficient#Determining significance](http://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient#Determining_significance): "One can test for significance using $$t = r \sqrt{\frac{n-2}{1-r^2}},$$ which is distributed approximately as Student's $t$ distribution wi...
null
CC BY-SA 2.5
null
2011-02-19T19:16:55.457
2011-02-19T19:16:55.457
null
null
449
null
7397
2
null
363
4
null
- Michael Oakes' Statistical Inference: A Commentary for the Social and Behavioral Sciences. - Elazar Pedhazur's Multiple Regression in Behavioral Research. If you can stand the immense detail and the self-important tone. In case you're interested, I've reviewed both on Amazon and at [https://yellowbrickstats.com...
null
CC BY-SA 4.0
null
2011-02-19T19:25:19.687
2021-03-11T13:59:49.813
2021-03-11T13:59:49.813
2669
2669
null
7398
2
null
363
3
null
Rice: [Mathematical Statistics and Data Analysis](http://goo.gl/wKbcW)
null
CC BY-SA 2.5
null
2011-02-19T19:47:16.733
2011-02-19T19:47:16.733
null
null
609
null
7399
6
null
null
0
null
I am nominating myself in part because of friendly pressure and because election is really election when there are more candidates than places to be filled. I came to this site nearly three months ago and became instantly hooked. Moderating would not take a lot out of me, since I am already visiting the site daily, re...
null
CC BY-SA 2.5
null
2011-02-19T19:49:46.760
2011-02-19T19:49:46.760
2011-02-19T19:49:46.760
2116
2116
null
7400
1
7405
null
53
81362
Given two histograms, how do we assess whether they are similar or not? Is it sufficient to simply look at the two histograms? The simple one to one mapping has the problem that if a histogram is slightly different and slightly shifted then we'll not get the desired result. Any suggestions?
How to assess the similarity of two histograms?
CC BY-SA 2.5
null
2011-02-19T18:52:26.557
2021-05-11T15:45:42.833
2011-02-21T06:40:35.937
183
3325
[ "histogram", "image-processing" ]
7401
2
null
7400
11
null
You're looking for the [Kolmogorov-Smirnov test](http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test). Don't forget to divide the bar heights by the sum of all observations of each histogram. Note that the KS-test is also reporting a difference if e.g. the means of the distributions are shifted relative to one...
null
CC BY-SA 2.5
null
2011-02-19T19:22:04.820
2011-02-19T20:09:43.253
null
null
198
null
7402
1
7404
null
14
48821
I know that a Type II error is where H1 is true, but H0 is not rejected. ### Question How do I calculate the probability of a Type II error involving a normal distribution, where the standard deviation is known?
How do I find the probability of a type II error?
CC BY-SA 2.5
null
2011-02-19T20:56:08.153
2018-11-19T08:55:24.940
2011-02-21T05:55:26.353
183
null
[ "probability", "statistical-power", "type-i-and-ii-errors" ]
7404
2
null
7402
32
null
In addition to specifying $\alpha$ (probability of a type I error), you need a fully specified hypothesis pair, i.e., $\mu_{0}$, $\mu_{1}$ and $\sigma$ need to be known. $\beta$ (probability of type II error) is $1 - \textrm{power}$. I assume a one-sided $H_{1}: \mu_{1} > \mu_{0}$. In R: ``` > sigma <- 15 # theoreti...
null
CC BY-SA 4.0
null
2011-02-19T21:13:06.140
2018-11-19T08:55:24.940
2018-11-19T08:55:24.940
1909
1909
null
7405
2
null
7400
11
null
A recent paper that may be worth reading is: [Cao, Y. Petzold, L.](http://dx.doi.org/10.1016/j.jcp.2005.06.012) Accuracy limitations and the measurement of errors in the stochastic simulation of chemically reacting systems, 2006. Although this paper's focus is on comparing stochastic simulation algorithms, essentially ...
null
CC BY-SA 2.5
null
2011-02-19T22:11:05.970
2011-02-19T22:11:05.970
null
null
8
null
7406
2
null
7211
0
null
Andrew McCallum (UMass) has a few NLP related software projects available on his [webpage](http://www.cs.umass.edu/~mccallum/code.html). These are all in Java (I think) with source code available.
null
CC BY-SA 2.5
null
2011-02-19T22:26:45.590
2011-02-19T22:26:45.590
null
null
1913
null
7407
1
null
null
6
300
I recently stumbled upon the concept of [sample complexity](http://www.google.com/search?q=%22sample%20complexity%22), and was wondering if there are any texts, papers or tutorials that provide: - An introduction to the concept (rigorous or informal) - An analysis of the sample complexity of established and popular c...
Measuring and analyzing sample complexity
CC BY-SA 3.0
null
2011-02-19T22:41:23.000
2014-10-28T12:27:00.393
2012-05-02T14:19:06.373
2798
2798
[ "machine-learning" ]
7408
1
7409
null
4
890
Here's a real basic question. I'm trying to teach myself a bit of stats with Verzani's Using R for Introductory Statistics. In question 5.13 he asks: A sample of 100 people is drawn from a population of 600,000. If it is known that 40% of the population has a specific attribute, what is the probability that 35 or fewer...
Sampling from a fixed population
CC BY-SA 2.5
null
2011-02-19T23:46:53.130
2011-02-20T00:44:16.023
null
null
3317
[ "self-study", "sampling" ]
7409
2
null
7408
9
null
When sampling without replacement, the distribution is a hypergeometric one. The problem is usually presented as follows: in an urn with $n$ (600.000) marbles, $m$ (40% = 240.000) are red, $n-m$ (60% = 360.000) are black. What is the probability of picking $r$ (35) red marbles in a sample of $k$ (100) marbles? The erro...
null
CC BY-SA 2.5
null
2011-02-20T00:05:12.063
2011-02-20T00:44:16.023
2011-02-20T00:44:16.023
1909
1909
null
7410
2
null
7400
30
null
The standard answer to this question is the [chi-squared test](http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm). The KS test is for unbinned data, not binned data. (If you have the unbinned data, then by all means use a KS-style test, but if you only have the histogram, the KS test is not appropriate.)
null
CC BY-SA 2.5
null
2011-02-20T06:29:59.583
2011-02-20T06:29:59.583
null
null
21874
null
7411
2
null
3
3
null
[Meta.Numerics](https://web.archive.org/web/20110123164637/http://www.meta-numerics.net/) is a .NET library with good support for statistical analysis. Unlike R (an S clone) and Octave (a Matlab clone), it does not have a "front end". It is more like GSL, in that it is a library that you link to when you are writing yo...
null
CC BY-SA 4.0
null
2011-02-20T07:03:34.513
2022-11-27T23:08:57.587
2022-11-27T23:08:57.587
362671
21874
null
7412
1
null
null
4
1926
I want to model how traffic will flow on real networks (not just the internet, also, say, Intel's internal LAN). Is there a place I can get real network topologies data I can use?
Where can I get real data of big network topology?
CC BY-SA 2.5
null
2011-02-20T08:03:25.657
2012-06-04T09:15:27.240
null
null
3328
[ "networks", "topologies" ]
7413
2
null
7211
4
null
Here are two further integrated projects: - Python Natural Language Toolkit (easy installation, good documentation) - Java MALLET (no experience with it, but looks promising; included in the link given by @Nick) Both are open-source software.
null
CC BY-SA 2.5
null
2011-02-20T09:20:16.843
2011-02-20T09:20:16.843
null
null
930
null
7414
2
null
6234
11
null
This won't compete with @Shane's answer because circular displays are really well suited for displaying complex relationships with high-dimensional datasets. For Venn diagrams, I've been using the [venneuler](http://cran.r-project.org/web/packages/venneuler/index.html) R package. It has a simple yet intuitive interface...
null
CC BY-SA 2.5
null
2011-02-20T09:40:05.920
2011-02-20T09:48:31.850
2011-02-20T09:48:31.850
930
930
null
7415
1
null
null
10
25072
What are the statistical techniques to create a sample set, which is representative of the entire population (with a known confidence level)? Also, - How to validate, if the sample fits the overall dataset? - Is it possible, without parsing the entire dataset (which could be billions of records)?
How to make representative sample set from a large overall dataset?
CC BY-SA 2.5
null
2011-02-20T09:54:18.693
2011-02-20T19:28:51.147
2011-02-20T09:56:10.747
930
3292
[ "sampling", "sample-size", "validation" ]
7416
2
null
7048
8
null
In addition to linking quantitative or qualitative data to spatial patterns, as illustrated by @whuber, I would like to mention the use of EDA, with brushing and the various of linking plots together, for longitudinal and high-dimensional data analysis. Both are discussed in the excellent book, [Interactive and Dynami...
null
CC BY-SA 2.5
null
2011-02-20T10:46:02.080
2011-02-20T10:46:02.080
null
null
930
null
7417
2
null
7389
5
null
I used paired t-test to compare my algorithm to GA, although I had about 200 test cases. You can use a non-parametric alternative such as the Wilcoxon Ranks Test. Regardless of what you use to test the statistical significance, bear in mind the "real-life" significance. If the performance improvement that your algorit...
null
CC BY-SA 3.0
null
2011-02-20T11:18:24.227
2014-02-05T20:13:19.270
2014-02-05T20:13:19.270
35895
1496
null
7418
2
null
7385
12
null
For R two options spring to mind, both of which I am only vaguely familiar with at best. The first is the `pscl` package, which can fit zero truncated inflated and hurdle models in a very nice, flexible manner. The `pscl` package suggests the use of the `sandwich` package which provides "Model-robust standard error est...
null
CC BY-SA 3.0
null
2011-02-20T11:51:29.197
2012-01-21T18:35:40.003
2012-01-21T18:35:40.003
1390
1390
null
7419
1
7674
null
10
1588
I have been doing some casual internet research on biclusters. (I have read the Wiki article several times.) So far, it seems as if there are few definitions or standard terminology. - I was wondering if there were any standard papers or books that anybody who is interested in algorithms for finding biclusters shoul...
Getting started with biclustering
CC BY-SA 2.5
null
2011-02-20T12:13:24.220
2011-12-21T08:32:30.810
2011-12-21T08:32:30.810
264
847
[ "clustering", "data-mining" ]
7420
2
null
7415
2
null
On your second question first, you might ask, "how was the data entered?" If you think that the data was entered in a relatively arbitrary fashion (i.e., independent of any observable or unobservable characteristics of your observations that might influence your ultimate analysis using the data), then you might conside...
null
CC BY-SA 2.5
null
2011-02-20T16:16:58.580
2011-02-20T16:24:28.540
2011-02-20T16:24:28.540
401
401
null
7422
1
null
null
3
1663
I have network traffic data in the following for for each hour of a ten day period as follows in a R dataset. ``` Day Hour Volume Category 0 00 100 P2P 0 00 50 email 0 00 200 gaming 0 00 200 ...
Calculating hourly volatility and peak-to-average ratio in R
CC BY-SA 2.5
null
2011-02-20T16:48:57.387
2011-02-21T14:28:56.023
2011-02-21T14:28:56.023
919
2101
[ "r", "aggregation" ]
7423
2
null
7422
2
null
Check out the [plyr package](http://cran.r-project.org/web/packages/plyr/index.html), which has [great documentation](http://had.co.nz/plyr/). While you could solve your problem with `aggregate()` function, I'd argue that learning the plyr family of functions will be worth it in the end. For your specific problem, this...
null
CC BY-SA 2.5
null
2011-02-20T18:24:48.317
2011-02-20T18:24:48.317
null
null
364
null
7424
2
null
7415
8
null
If you don't wish to parse the entire data set then you probably can't use [stratified sampling](http://en.wikipedia.org/wiki/Stratified_sampling), so I'd suggest taking a large [simple random sample](http://en.wikipedia.org/wiki/Simple_random_sample). By taking a random sample, you ensure that the sample will, on aver...
null
CC BY-SA 2.5
null
2011-02-20T18:49:31.990
2011-02-20T19:28:51.147
2011-02-20T19:28:51.147
449
449
null
7425
2
null
7175
7
null
I think the best quality measure for clustering is the cluster assumption, as given by Seeger in [Learning with labeled and unlabeled data](http://webcache.googleusercontent.com/search?q=cache:http://people.kyb.tuebingen.mpg.de/seeger/papers/review.pdf): > For example, assume X = Rd and the validity of the “cluster as...
null
CC BY-SA 3.0
null
2011-02-20T19:52:06.927
2013-07-02T04:33:56.040
2013-07-02T04:33:56.040
7290
2860
null
7426
1
7428
null
3
11200
How can I conduct an Egger's test using SPSS17? For each study included in the meta-analysis I know effect size and sample size of patients and controls groups.
Egger's test in SPSS
CC BY-SA 2.5
null
2011-02-20T21:27:02.557
2011-02-23T04:50:37.073
2011-02-20T23:42:57.017
null
3333
[ "spss", "meta-analysis", "funnel-plot", "publication-bias" ]
7427
2
null
7426
2
null
I don't use PASW anymore, but implementation of the Egger's test for asymmetry is quite simple. First please look at the Egger's [paper](http://goo.gl/6gnEj) where he propose "theory" behind the test. Basically you have two variables: (i) normalized effect estimate (your estimate divided by its standard error), and (ii...
null
CC BY-SA 2.5
null
2011-02-20T21:53:59.553
2011-02-23T04:50:37.073
2011-02-23T04:50:37.073
609
609
null
7428
2
null
7426
5
null
In order to conduct Egger's regression test you will also need the standard errors ($SE_i$) of your effect sizes ($ES_i$). Then generate the so called standard normal deviate (SND) which is defined as effect size divided by its standard error ($ES_i / SE_i$). Next, generate the precision which is $\frac{1}{SE_i}$. The ...
null
CC BY-SA 2.5
null
2011-02-20T22:12:41.893
2011-02-20T22:12:41.893
2017-04-13T12:44:29.013
-1
307
null
7429
1
7431
null
4
5551
What should I do if the expected value in a Chi-square goodness-of-fit test is zero? I know there's Fisher's test but I have a very large table!
Computing chi-square for large tables with some expected cell counts equal to zero
CC BY-SA 2.5
null
2011-02-21T00:53:30.507
2011-02-21T08:14:45.830
2011-02-21T08:08:14.360
449
3338
[ "chi-squared-test", "goodness-of-fit" ]
7430
1
7434
null
7
8274
A uniform prior for a scale parameter (like the variance) is uniform on the logarithmic scale. What functional form does this prior have on the linear scale? And why so?
Creating a uniform prior on the logarithmic scale
CC BY-SA 2.5
null
2011-02-21T02:44:28.760
2019-06-30T03:10:08.347
2011-02-21T05:59:30.047
183
1098
[ "bayesian", "prior" ]
7431
2
null
7429
6
null
If the expected value of a cell is zero in a goodness of fit test (I'm assuming you really mean goodness of fit, where the fit is to a theoretical distribution, not another observed distribution) then there are two possibilities: - You also observed this value zero times. Just discard the zero expected value and try ...
null
CC BY-SA 2.5
null
2011-02-21T02:54:03.923
2011-02-21T02:54:03.923
null
null
1347
null
7432
1
null
null
5
10621
In SPSS Version 19 there seems to be a new feature called Automatic Linear Modelling. It creates a 'Model' (which is new to me) and the function seems to combine a number of the functions that is typically required for prediction model development. The functionality seems incomplete with only a subset of prediction se...
Is automatic linear modelling in SPSS a good or bad thing?
CC BY-SA 3.0
null
2011-02-21T03:21:45.580
2011-08-18T21:40:36.737
2011-08-18T18:13:53.687
null
3189
[ "regression", "modeling", "spss" ]
7433
2
null
7432
5
null
I had a quick look at the [IBM SPSS advertising material](ftp://public.dhe.ibm.com/common/ssi/ecm/en/ytd03023usen/YTD03023USEN.PDF). It sounds like it is part of a general move on the part of IBM/SPSS to get involved with predictive analytics. Terms like automatic data preparation, boosting, bagging, and automated mode...
null
CC BY-SA 2.5
null
2011-02-21T03:36:42.370
2011-02-21T05:38:03.153
2011-02-21T05:38:03.153
183
183
null
7434
2
null
7430
15
null
It's just a standard change of variables; the (monotone & 1-1) transformation is $y = \exp(x)$ with inverse $x=\log(y)$ and Jacobian $\frac{dx}{dy} = \frac{1}{y}$. With a uniform prior $p_y(y) \propto 1$ on $\mathbb{R}$ we get $p_x(x) = p_y(x(y)) |\frac{dx}{dy}| \propto \frac{1}{y}$ on $(0, \infty)$. Edit: Wikipedia h...
null
CC BY-SA 2.5
null
2011-02-21T05:27:07.727
2011-02-21T07:00:52.987
2011-02-21T07:00:52.987
26
26
null
7435
2
null
7402
1
null
To supplement caracal's answer, if you are looking for a user-friendly GUI option for calculating Type II error rates or power for many common designs including the ones implied by your question, you may wish to check out the free software, [G Power 3](http://www.psycho.uni-duesseldorf.de/abteilungen/aap/gpower3/).
null
CC BY-SA 2.5
null
2011-02-21T06:37:28.657
2011-02-21T06:37:28.657
null
null
183
null
7436
2
null
7429
3
null
If you are using [Pearson's chi-square test as a test independence](http://en.wikipedia.org/wiki/Pearson%27s_chi-square_test#Test_of_independence) of two variables in a two-way [contingency table](http://en.wikipedia.org/wiki/Contingency_table), you'll get a zero expected value only if you have a whole row of zeroes or...
null
CC BY-SA 2.5
null
2011-02-21T08:14:45.830
2011-02-21T08:14:45.830
null
null
449
null
7438
1
null
null
1
10776
As a basic question in Regression Analysis, I wanted to ask how can I calculate Margin of Error when I fit a straight line to a set of data. Assume that I have variation of parameter $A$ as a function of parameter $B$, then $A=mB \pm e$, where $m$ is the tangent of the fitted straight line and $e$ is what i'm looking f...
How to calculate margin of error in linear regression?
CC BY-SA 2.5
null
2011-02-21T09:57:19.063
2011-02-21T19:18:51.447
2011-02-21T10:07:55.150
2116
null
[ "regression" ]
7439
1
7444
null
33
61965
You can have data in wide format or in long format. This is quite an important thing, as the useable methods are different, depending on the format. I know you have to work with `melt()` and `cast()` from the reshape package, but there seems some things that I don't get. Can someone give me a short overview how you do ...
How to change data between wide and long formats in R?
CC BY-SA 2.5
null
2011-02-21T10:27:05.680
2016-05-10T18:01:17.903
2011-02-21T16:30:39.317
8
3140
[ "data-transformation", "r" ]
7440
1
7449
null
143
176928
I need to determine the KL-divergence between two Gaussians. I am comparing my results to [these](http://allisons.org/ll/MML/KL/Normal/), but I can't reproduce their result. My result is obviously wrong, because the KL is not 0 for KL(p, p). I wonder where I am doing a mistake and ask if anyone can spot it. Let $p(x) =...
KL divergence between two univariate Gaussians
CC BY-SA 4.0
null
2011-02-21T10:30:18.527
2022-12-27T09:52:24.333
2022-12-27T09:31:54.853
362671
2860
[ "normal-distribution", "kullback-leibler" ]
7441
2
null
7438
2
null
It seems that you want the residuals of linear regression without the intercept term where dependent variable is $A$ and the independent variable is $B$. This can be done with various statistical packages. Here is the implementation in R. ``` aa <-"(39.7678, 2320.3}, {30.8438, 1614.21}, {125.846, 3078.81}, {55.2345, 1...
null
CC BY-SA 2.5
null
2011-02-21T10:30:24.187
2011-02-21T19:18:51.447
2011-02-21T19:18:51.447
2116
2116
null
7443
2
null
7440
56
null
I did not have a look at your calculation but here is mine with a lot of details. Suppose $p$ is the density of a normal random variable with mean $\mu_1$ and variance $\sigma^2_1$, and that $q$ is the density of a normal random variable with mean $\mu_2$ and variance $\sigma^2_2$. The Kullback-Leibler distance from $q...
null
CC BY-SA 4.0
null
2011-02-21T10:58:18.427
2022-12-27T09:52:24.333
2022-12-27T09:52:24.333
362671
3019
null
7444
2
null
7439
29
null
There are several resources on Hadley Wickham's [website](http://had.co.nz/reshape/) for the package (now called `reshape2`), including a link to a [paper](http://www.jstatsoft.org/v21/i12) on the package in the Journal of Statistical Software. Here is a brief example from the paper: ``` > require(reshape2) Loading req...
null
CC BY-SA 2.5
null
2011-02-21T11:09:33.423
2011-02-21T11:09:33.423
null
null
1390
null
7446
2
null
7439
8
null
- Quick-R has simple example of using reshape package - See also ?reshape (LINK) for the Base R way of moving between wide and long format.
null
CC BY-SA 2.5
null
2011-02-21T11:14:36.693
2011-02-21T11:14:36.693
null
null
183
null
7447
1
null
null
15
4577
Both [Root Mean Square](http://en.wikipedia.org/wiki/Root_mean_square) and [Average absolute deviation](http://en.wikipedia.org/wiki/Absolute_deviation#Average_absolute_deviation) seem like the measures of the magnitude of variability (especially when the variates are both +ve and -ve). What are the rules of thumb to c...
Root mean square vs average absolute deviation?
CC BY-SA 2.5
null
2011-02-21T11:40:25.130
2011-02-21T11:52:42.560
2011-02-21T11:50:01.563
null
3292
[ "regression", "standard-deviation" ]
7448
2
null
7447
16
null
In theory, this should be determined by how important different sized errors are to you, or in other words, your loss function. In the real world, people put ease of use first. So RMS deviations (or the related variances) are easier to combine, and easier to calculate in a single pass, while average absolute deviati...
null
CC BY-SA 2.5
null
2011-02-21T11:52:42.560
2011-02-21T11:52:42.560
null
null
2958
null
7449
2
null
7440
103
null
OK, my bad. The error is in the last equation: \begin{align} KL(p, q) &= - \int p(x) \log q(x) dx + \int p(x) \log p(x) dx\\\\ &=\frac{1}{2} \log (2 \pi \sigma_2^2) + \frac{\sigma_1^2 + (\mu_1 - \mu_2)^2}{2 \sigma_2^2} - \frac{1}{2} (1 + \log 2 \pi \sigma_1^2)\\\\ &= \log \frac{\sigma_2}{\sigma_1} + \frac{\sigma_1^2 + ...
null
CC BY-SA 3.0
null
2011-02-21T11:55:19.103
2022-12-27T08:40:09.397
2022-12-27T08:40:09.397
2116
2116
null
7450
1
null
null
12
5193
I have a problem with the estimation parameter for Zipf. My situation is the following: I have a sample set (measured from an experiment that generates calls that should follow a Zipf distribution). I have to demonstrate that this generator really generates calls with zipf distribution. I already read this Q&A [How t...
How to estimate parameters for Zipf truncated distribution from a data sample?
CC BY-SA 2.5
null
2011-02-21T13:51:50.393
2011-04-08T01:51:15.640
2017-04-13T12:44:41.980
-1
3342
[ "distributions", "estimation", "pareto-distribution", "zipf" ]
7452
2
null
7450
5
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The paper Clauset, A et al, [Power-law Distributions in Empirical Data](http://arxiv.org/abs/0706.1062). 2009 contains a very good description of how to go about fitting power law models. The associated [web-page](http://tuvalu.santafe.edu/~aaronc/powerlaws/) has code samples. Unfortunately, it doesn't give code for tr...
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CC BY-SA 2.5
null
2011-02-21T14:36:44.550
2011-02-21T14:36:44.550
null
null
8
null
7454
2
null
7439
7
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You don't have to use `melt` and `cast`. Reshaping data can be done lots of ways. In your particular example on your cite using `recast` with `aggregate` was redundant because `aggregate` does the task fine all on it's own. ``` aggregate(cbind(LPMVTUZ, LPMVTVC, LPMVTXC) ~ year, dtm, sum) # or even briefer by first r...
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CC BY-SA 3.0
null
2011-02-21T15:25:54.473
2014-05-25T07:14:03.977
2014-05-25T07:14:03.977
601
601
null
7455
1
7473
null
16
4726
Can someone refer me to a good reference that explains the connection between Bayesian statistics and generative modeling techniques? Why do we usually use generative models with Bayesian techniques? Why it is especially appealing to use Bayesian statistics in the absence of complete data, if at all? Note that I come f...
The connection between Bayesian statistics and generative modeling
CC BY-SA 2.5
null
2011-02-21T16:34:03.293
2012-10-16T13:51:01.003
2011-02-22T07:53:42.247
2116
3347
[ "bayesian", "generative-models" ]
7456
2
null
7438
3
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You are asking to estimate the typical size of the error. This is usually done by estimating the variance of the random variable $e$ and taking its square root. It is often called the "root mean square error". These data look like they are formatted for Mathematica. A Mathematica 8 solution is ``` {a, b} = {{39.7678...
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CC BY-SA 2.5
null
2011-02-21T16:44:01.187
2011-02-21T16:44:01.187
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null
919
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