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218 | 2 | null | 1 | 2 | null | This interesting question is the subject of some research in [ACERA](http://www.acera.unimelb.edu.au/). The lead researcher is Andrew Speirs-Bridge, and his work is eminently google-able :)
| null | CC BY-SA 2.5 | null | 2010-07-20T05:13:21.963 | 2010-07-20T05:13:21.963 | null | null | 187 | null |
219 | 2 | null | 40 | 3 | null | The Xorshift PNG designed by George Marsaglia. Its period (2^128-1) is much shorter than the Mersenne-Twister but the algorithm is very simple to implement and lends itself to parallelization. Performs well on many-core architectures such as DSP chips and Nvidia's Tesla.
| null | CC BY-SA 2.5 | null | 2010-07-20T05:21:14.590 | 2010-07-20T05:33:00.140 | 2010-07-20T05:33:00.140 | 154 | 154 | null |
220 | 1 | 221 | null | 79 | 93750 | If $X_1, ..., X_n$ are independent identically-distributed random variables, what can be said about the distribution of $\min(X_1, ..., X_n)$ in general?
| How is the minimum of a set of IID random variables distributed? | CC BY-SA 4.0 | null | 2010-07-20T05:23:04.163 | 2020-06-30T20:49:14.163 | 2020-06-30T20:49:14.163 | 227013 | 85 | [
"distributions",
"random-variable",
"extreme-value"
] |
221 | 2 | null | 220 | 55 | null | If the cdf of $X_i$ is denoted by $F(x)$, then the cdf of the minimum is given by $1-[1-F(x)]^n$.
| null | CC BY-SA 3.0 | null | 2010-07-20T05:35:48.807 | 2012-04-12T23:26:05.790 | 2012-04-12T23:26:05.790 | 159 | 159 | null |
222 | 1 | 282 | null | 91 | 278937 | What are principal component scores (PC scores, PCA scores)?
| What are principal component scores? | CC BY-SA 3.0 | null | 2010-07-20T05:37:46.557 | 2022-07-25T13:56:39.230 | 2016-08-20T15:27:48.417 | 28666 | 191 | [
"pca",
"definition"
] |
223 | 1 | null | null | 6 | 388 | I have a friend who is an MD and wants to refresh his Statistics. So is there any recommended resource online (or offline) ? He did stats ~20 years ago.
| Intro to statistics for an MD? | CC BY-SA 2.5 | null | 2010-07-20T05:54:15.017 | 2022-11-23T13:18:24.017 | 2012-02-01T18:51:11.727 | 4872 | 79 | [
"references"
] |
224 | 1 | null | null | 9 | 2210 | Which visualization libraries (plots, graphs, ...) would you suggest to use in a standalone application (Linux, .Net, Windows, whatever). Reasonable performance would be nice as well.
| Recommended visualization libraries for standalone applications | CC BY-SA 3.0 | null | 2010-07-20T06:03:59.930 | 2011-05-27T03:36:21.040 | 2011-05-27T03:36:21.040 | 183 | 128 | [
"data-visualization",
"software"
] |
225 | 1 | 229 | null | 8 | 818 | Why is the average of the highest value from 100 draws from a normal distribution different from the 98% percentile of the normal distribution? It seems that by definition that they should be the same. But...
Code in R:
```
NSIM <- 10000
x <- rep(NA,NSIM)
for (i in 1:NSIM)
{
x[i] <- max(rnorm(100))
}
qnorm(.98)
q... | Why is the average of the highest value from 100 draws from a normal distribution different from the 98th percentile of the normal distribution? | CC BY-SA 2.5 | null | 2010-07-20T06:07:37.007 | 2012-04-01T04:18:55.447 | 2010-07-20T08:47:33.180 | 196 | 196 | [
"r",
"distributions",
"extreme-value"
] |
226 | 2 | null | 222 | 24 | null | Principal component analysis (PCA) is one popular approach analyzing variance when you are dealing with multivariate data. You have random variables X1, X2,...Xn which are all correlated (positively or negatively) to varying degrees, and you want to get a better understanding of what's going on. PCA can help.
What PCA ... | null | CC BY-SA 2.5 | null | 2010-07-20T06:23:21.623 | 2010-07-20T06:23:21.623 | null | null | 173 | null |
227 | 2 | null | 222 | 4 | null | Let $i=1,\dots,N$ index the rows and $j=1,\dots,M$ index the columns. Suppose you linearize the combination of variables (columns):
$$Z_{i,1} = c_{i,1}\cdot Y_{i,1} + c_{i,2}\cdot Y_{i,2} + ... + c_{i,M}\cdot Y_{i,M}$$
The above formula basically says to multiply row elements with a certain value $c$ (loadings) and sum... | null | CC BY-SA 3.0 | null | 2010-07-20T06:24:32.793 | 2012-07-02T02:33:13.853 | 2012-07-02T02:33:13.853 | 159 | 144 | null |
228 | 2 | null | 216 | 3 | null |
- http://insideria.com/2009/12/28-rich-data-visualization-too.html 28 Rich Data Visualization Tools
- http://www.rgraph.net/ R graph
- http://vis.stanford.edu/protovis/
| null | CC BY-SA 2.5 | null | 2010-07-20T06:27:16.233 | 2010-07-20T06:27:16.233 | null | null | 10 | null |
229 | 2 | null | 225 | 10 | null | The maximum does not have a normal distribution. Its cdf is $\Phi(x)^{100}$ where $\Phi(x)$ is the standard normal cdf. In general the moments of this distribution are tricky to obtain analytically. There is an ancient paper on this by [Tippett (Biometrika, 1925)](http://www.jstor.org/stable/2332087).
| null | CC BY-SA 3.0 | null | 2010-07-20T06:28:47.557 | 2012-03-31T07:26:34.197 | 2012-03-31T07:26:34.197 | 4856 | 159 | null |
230 | 2 | null | 224 | 6 | null | You could have a look at Processing: [http://processing.org/](http://processing.org/)
| null | CC BY-SA 2.5 | null | 2010-07-20T06:35:21.287 | 2010-07-20T06:35:21.287 | null | null | 173 | null |
231 | 2 | null | 223 | 5 | null | This is the one I've used successfully:
[Statistics Without Maths for Psychology: Using Spss for Windows](http://www.amazon.co.uk/Statistics-without-Psychology-Christine-Dancey/dp/013124941X).
I just stumbled on this too, this might be useful:
[Statistics Notes in the British Medical Journal](http://www-users.york.ac.u... | null | CC BY-SA 4.0 | null | 2010-07-20T06:41:13.570 | 2022-11-23T13:18:24.017 | 2022-11-23T13:18:24.017 | 362671 | 199 | null |
232 | 2 | null | 196 | 15 | null |
- Mondrian: Exploratory data analysis with focus on large data and databases.
- iPlots: a package for the R statistical environment which provides high interaction statistical graphics, written in Java.
| null | CC BY-SA 2.5 | null | 2010-07-20T06:41:25.627 | 2010-07-20T07:26:11.410 | 2010-07-20T07:26:11.410 | 103 | 103 | null |
234 | 2 | null | 222 | 8 | null | Say you have a cloud of N points in, say, 3D (which can be listed in a 100x3 array). Then, the principal components analysis (PCA) fits an arbitrarily oriented ellipsoid into the data. The principal component score is the length of the diameters of the ellipsoid.
In the direction in which the diameter is large, the da... | null | CC BY-SA 2.5 | null | 2010-07-20T06:47:14.180 | 2010-07-20T06:47:14.180 | null | null | 198 | null |
235 | 2 | null | 216 | 5 | null | [RaphaelJS](http://raphaeljs.com/) can do some pretty amazing stuff and it just got some major backing from [Sencha](http://www.sencha.com/) (formerly ExtJS). Raphael is pretty smart about browsers by using a VML backend for Internet Explorer and SVG for everything else. However, the library is pretty low-level. For... | null | CC BY-SA 2.5 | null | 2010-07-20T07:17:58.993 | 2010-07-20T08:45:07.490 | 2010-07-20T08:45:07.490 | 13 | 13 | null |
236 | 2 | null | 224 | 0 | null | Unfortunately, it only runs on macs, but otherwise a great application (basically Processing in python):
- http://nodebox.net/code/index.php/Home
>
NodeBox is a Mac OS X application that lets you create 2D visuals (static, animated or interactive) using Python programming code and export them as a PDF or a QuickTim... | null | CC BY-SA 2.5 | null | 2010-07-20T07:30:34.160 | 2010-07-21T18:33:33.063 | 2010-07-21T18:33:33.063 | 138 | 138 | null |
237 | 2 | null | 173 | 2 | null | I'm going to leave the main question alone, because I think I will get it wrong (although I too analyse data for a healthcare provider, and to be honest, if I had these data, I would just analyse them using standard techniques and hope for the best, they look pretty okay to me).
As for R packages, I have found the TSA ... | null | CC BY-SA 2.5 | null | 2010-07-20T07:31:08.963 | 2010-08-09T12:18:10.497 | 2010-08-09T12:18:10.497 | 8 | 199 | null |
238 | 2 | null | 224 | 9 | null | There is always lovely gnuplot:
- http://www.gnuplot.info/
>
Gnuplot is a portable command-line driven graphing utility for linux, OS/2, MS Windows, OSX, VMS, and many other platforms. The source code is copyrighted but freely distributed (i.e., you don't have to pay for it). It was originally created to allow scie... | null | CC BY-SA 2.5 | null | 2010-07-20T07:33:09.067 | 2010-07-20T07:33:09.067 | 2020-06-11T14:32:37.003 | -1 | 138 | null |
240 | 2 | null | 213 | 4 | null | My first response would be that if you can do multivariate regression on the data, then to use the residuals from that regression to spot outliers. (I know you said it's not a regression problem, so this might not help you, sorry !)
I'm copying some of this from a [Stackoverflow question I've previously answered](https... | null | CC BY-SA 2.5 | null | 2010-07-20T07:55:30.107 | 2010-07-20T07:55:30.107 | 2017-05-23T12:39:26.203 | -1 | 114 | null |
241 | 2 | null | 213 | 6 | null | I'm not sure what you mean when you say you aren't thinking of a regression problem but of "true multivariate data". My initial response would be to calculate the Mahalanobis distance since it doesn't require that you specify a particular IV or DV, but at its core (as far as I understand it) it is related to a leverag... | null | CC BY-SA 2.5 | null | 2010-07-20T07:56:06.767 | 2010-07-20T07:56:06.767 | null | null | 196 | null |
242 | 1 | 306 | null | 13 | 892 | This is a bit of a flippant question, but I have a serious interest in the answer. I work in a psychiatric hospital and I have three years' of data, collected every day across each ward regarding the level of violence on that ward.
Clearly the model which fits these data is a time series model. I had to difference the ... | Using time series analysis to analyze/predict violent behavior | CC BY-SA 2.5 | null | 2010-07-20T07:56:16.297 | 2017-10-24T18:31:05.713 | 2010-07-20T15:53:21.083 | 5 | 199 | [
"time-series",
"forecasting"
] |
243 | 2 | null | 203 | 8 | null | Depending on the size of the dataset in question, a permutation test might be preferable to a bootstrap in that it may be able to provide an exact test of the hypothesis (and an exact CI).
| null | CC BY-SA 2.5 | null | 2010-07-20T08:05:04.060 | 2010-07-20T09:09:01.443 | 2010-07-20T09:09:01.443 | 196 | 196 | null |
244 | 2 | null | 224 | 18 | null | The Visualization Tool Kit [VTK](http://www.vtk.org) is pretty impressive for 3D visualizations of numerical data. Unfortunately, it is also pretty low level.
[Graphviz](http://graphviz.org/) is used pretty extensively for visualizing graphs and other tree-like data structures.
[igraph](http://igraph.sourceforge.net/)... | null | CC BY-SA 2.5 | null | 2010-07-20T08:13:31.763 | 2010-07-20T08:47:44.613 | 2010-07-20T08:47:44.613 | 13 | 13 | null |
245 | 2 | null | 222 | 3 | null | Principal component scores are a group of scores that are obtained following a Principle Components Analysis (PCA). In PCA the relationships between a group of scores is analyzed such that an equal number of new "imaginary" variables (aka principle components) are created. The first of these new imaginary variables i... | null | CC BY-SA 2.5 | null | 2010-07-20T08:20:36.037 | 2010-07-20T08:20:36.037 | null | null | 196 | null |
246 | 2 | null | 242 | 6 | null | You fitted the model to the differences, which means that you're describing the change in levels of violence. You get a lag of 2 days. A lag is indicative of the memory of the process. In other words, the change in levels of violence today has some dependency on the change in levels of violence in the last two days. Fo... | null | CC BY-SA 2.5 | null | 2010-07-20T08:28:52.710 | 2010-07-20T08:28:52.710 | null | null | 198 | null |
247 | 2 | null | 224 | 3 | null | Might be a bit narrow in scope, but if you're doing any work in Clojure on the JVM there's the excellent [Incanter](http://incanter.org):
>
Incanter is a Clojure-based, R-like platform for statistical computing and graphics.
| null | CC BY-SA 2.5 | null | 2010-07-20T08:36:36.217 | 2010-07-20T08:36:36.217 | null | null | 171 | null |
248 | 2 | null | 196 | 4 | null | ggobi and the R links to Ggobi are really rather good for this. There are simpler visualisations (iPlots is very nice, also interactive, as mentioned).
But it depends whether you are doing something more specialised. For example TreeView lets you visualise the kind of cluster dendrograms you get out of microarrays.... | null | CC BY-SA 2.5 | null | 2010-07-20T08:38:38.223 | 2010-07-20T08:38:38.223 | null | null | 211 | null |
249 | 1 | null | null | 4 | 774 | I have a set of $N$ bodies, which is a random sample from a population whose mean and variance I want to estimate. A property of each body is being measured $m_i$ times ($m_i>1$) and different for each body index $i$ identifies which body it is; the property is expected to be distributed around zero). I would like to ... | Variance components | CC BY-SA 3.0 | null | 2010-07-20T08:49:13.050 | 2012-12-05T18:20:34.357 | 2012-12-05T18:20:34.357 | 17230 | 213 | [
"standard-deviation",
"variance",
"anova",
"random-effects-model"
] |
250 | 2 | null | 130 | 5 | null | Update (August 2014): as @gappy comments below, as of R version 3.0.0 the limits are higher and means R is capable of handling larger datasets.
Here's a data point: R has a ["big data ceiling"](http://www.bytemining.com/2010/05/hitting-the-big-data-ceiling-in-r/), useful to know if you plan on working with huge data se... | null | CC BY-SA 3.0 | null | 2010-07-20T08:53:15.833 | 2014-08-01T17:38:23.147 | 2014-08-01T17:38:23.147 | 171 | 171 | null |
252 | 2 | null | 73 | 6 | null | For me personally, I use the following three packages the most, all available from the awesome [Omega Project for Statistical Computing](http://www.omegahat.org) (I do not claim to be an expert, but for my purposes they are very easy to use):
- RCurl: It has lots of options which allows access to websites that the def... | null | CC BY-SA 2.5 | null | 2010-07-20T09:13:29.427 | 2010-07-28T10:02:05.600 | 2010-07-28T10:02:05.600 | 81 | 81 | null |
253 | 2 | null | 138 | 8 | null | If you're an economist/econometrician then Grant Farnworth's paper on using R is indispensable and is available on CRAN at:
[http://cran.r-project.org/doc/contrib/Farnsworth-EconometricsInR.pdf](http://cran.r-project.org/doc/contrib/Farnsworth-EconometricsInR.pdf)
| null | CC BY-SA 2.5 | null | 2010-07-20T09:26:05.113 | 2010-07-20T11:37:25.383 | 2010-07-20T11:37:25.383 | 215 | 215 | null |
254 | 2 | null | 249 | 5 | null | I think if I understand your description correctly, you need to use a [linear mixed model](http://en.wikipedia.org/wiki/Random_effects_model). However, this maybe overkill, since these models are used to find differences between groups. For example, if you have two types of bodies and you wish to determine if they are ... | null | CC BY-SA 2.5 | null | 2010-07-20T09:30:18.797 | 2010-07-20T10:50:24.037 | 2010-07-20T10:50:24.037 | 8 | 8 | null |
255 | 2 | null | 213 | 8 | null | It may be an overshoot, but you may train an unsupervised Random Forest on the data and use the object proximity measure to detect outliers. More details [here](http://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm#outliers).
| null | CC BY-SA 2.5 | null | 2010-07-20T09:30:51.697 | 2010-07-20T09:30:51.697 | null | null | null | null |
256 | 1 | 265 | null | 24 | 9466 | What is the easiest way to understand boosting?
Why doesn't it boost very weak classifiers "to infinity" (perfection)?
| How does boosting work? | CC BY-SA 3.0 | null | 2010-07-20T09:34:22.213 | 2015-08-25T12:17:32.040 | 2013-08-16T15:55:48.363 | 7290 | 217 | [
"machine-learning",
"boosting"
] |
257 | 1 | 262 | null | 17 | 11376 | We may assume that we have CSV file and we want a very basic line plot with several lines on one plot and a simple legend.
| What is the easiest way to create publication-quality plots under Linux? | CC BY-SA 2.5 | null | 2010-07-20T09:38:44.770 | 2022-05-22T13:23:32.747 | 2017-05-19T12:32:22.213 | 101426 | 217 | [
"data-visualization"
] |
258 | 1 | null | null | 14 | 3544 | Rules:
- one classifier per answer
- vote up if you agree
- downvote/remove duplicates.
- put your application in the comment
| What is the best out-of-the-box 2-class classifier for your application? | CC BY-SA 3.0 | null | 2010-07-20T09:43:23.910 | 2016-04-11T08:36:06.453 | 2011-11-17T00:45:57.047 | null | 217 | [
"machine-learning",
"classification",
"application"
] |
259 | 2 | null | 258 | 12 | null | [Support vector machine](http://en.wikipedia.org/wiki/Support_vector_machine)
| null | CC BY-SA 2.5 | null | 2010-07-20T09:44:11.807 | 2010-07-20T09:44:11.807 | null | null | 217 | null |
260 | 2 | null | 258 | 14 | null | [Random forest](http://en.wikipedia.org/wiki/Random_forest)
- easily captures complicated structure/nonlinear relationship
- invariant to variables' scale
- no need to create dummy variables for categorical predictors
- variable selection is not much needed
- relatively hard to overfit
| null | CC BY-SA 3.0 | null | 2010-07-20T09:45:06.377 | 2016-04-11T08:36:06.453 | 2016-04-11T08:36:06.453 | 85709 | 217 | null |
261 | 2 | null | 257 | 13 | null | It's hard to go past R for graphics. You could do what you want in 3 lines. For example, assuming the csv file has four columns:
```
x <- read.csv("file.csv")
matplot(x[,1],x[,2:4],type="l",col=1:3)
legend("topleft",legend=c("A","B","C"),lty=1,col=1:3)
```
| null | CC BY-SA 2.5 | null | 2010-07-20T09:45:18.933 | 2010-07-20T09:45:18.933 | null | null | 159 | null |
262 | 2 | null | 257 | 14 | null | The easiest way is to use R
Use `read.csv` to enter the data into R, then use a combination of the `plot` and `line` commands
If you want something really special, then look at the libraries [ggplot2](http://had.co.nz/ggplot2/) or [lattice](http://lmdvr.r-forge.r-project.org/figures/figures.html).
In `ggplot2` the foll... | null | CC BY-SA 4.0 | null | 2010-07-20T09:50:45.953 | 2022-05-22T13:23:32.747 | 2022-05-22T13:23:32.747 | 11887 | 8 | null |
263 | 2 | null | 257 | 11 | null | My favorite tool is Python with [matplotlib](https://matplotlib.org/).
The advantages:
- Immediate export from the environment where I do my experiments in
- Support for the scipy/numpy data structures
- Familiar syntax/options (matlab background)
- Full latex support for labels/legends etc. So same typesetting as ... | null | CC BY-SA 4.0 | null | 2010-07-20T09:53:11.583 | 2022-05-22T12:59:53.333 | 2022-05-22T12:59:53.333 | 313631 | 190 | null |
264 | 2 | null | 134 | 7 | null | [Here](https://dcc-backup.ligo.org/public/0027/T030168/000/T030168-00.pdf) is an article describing one possible algorithm. Source code included and a quite serious application (gravitational wave detection based on laser interferometry), so you can expect it to be well tested.
| null | CC BY-SA 3.0 | null | 2010-07-20T09:59:00.690 | 2018-02-27T15:34:22.913 | 2018-02-27T15:34:22.913 | 22047 | 217 | null |
265 | 2 | null | 256 | 28 | null | In plain English: If your classifier misclassifies some data, train another copy of it mainly on this misclassified part with hope that it will discover something subtle. And then, as usual, iterate. On the way there are some voting schemes that allow to combine all those classifiers' predictions in sensible way.
Becau... | null | CC BY-SA 2.5 | null | 2010-07-20T10:05:48.050 | 2010-07-20T10:17:16.153 | 2010-07-20T10:17:16.153 | null | null | null |
266 | 2 | null | 134 | 3 | null | As you mentioned sorting would be `O(n·log n)` for a window of length `n`. Doing this moving adds another `l=vectorlength` making the total cost `O(l·n·log n)`.
The simplest way to push this is by keeping an ordered list of the last n elements in memory when moving from one window to the next one. As removing/inserting... | null | CC BY-SA 2.5 | null | 2010-07-20T10:23:56.707 | 2010-07-20T10:23:56.707 | null | null | 128 | null |
267 | 1 | 271 | null | 9 | 10166 | If I have two lists A and B, both of which are subsets of a much larger list C, how can I determine if the degree of overlap of A and B is greater than I would expect by chance?
Should I just randomly select elements from C of the same lengths as lists A and B and determine that random overlap, and do this many times t... | How do I calculate if the degree of overlap between two lists is significant? | CC BY-SA 2.5 | null | 2010-07-20T10:35:55.960 | 2013-07-17T02:30:07.350 | null | null | 194 | [
"statistical-significance"
] |
268 | 2 | null | 47 | 3 | null | You could of for a supervised self-organizing map (e.g. with [kohonen](http://cran.r-project.org/web/packages/kohonen/index.html) package for R), and use the login frequency as dependent variable. That way, the clustering will focus on separating the frequent visitors from the rare visitors. By plotting the number of u... | null | CC BY-SA 2.5 | null | 2010-07-20T11:01:06.313 | 2010-07-20T11:01:06.313 | null | null | 107 | null |
269 | 1 | 416 | null | 45 | 423555 | What is the difference between a population and a sample? What common variables and statistics are used for each one, and how do those relate to each other?
| What is the difference between a population and a sample? | CC BY-SA 2.5 | null | 2010-07-20T11:07:42.403 | 2017-06-16T02:01:31.063 | 2010-08-07T17:55:39.090 | null | 62 | [
"standard-deviation",
"variance",
"sample",
"population"
] |
270 | 1 | 279 | null | 18 | 7841 | Due to the factorial in a poisson distribution, it becomes unpractical to estimate poisson models (for example, using maximum likelihood) when the observations are large. So, for example, if I am trying to estimate a model to explain the number of suicides in a given year (only annual data are available), and say, ther... | Poisson regression with large data: is it wrong to change the unit of measurement? | CC BY-SA 2.5 | null | 2010-07-20T11:08:47.770 | 2022-04-22T11:18:35.717 | 2010-10-08T16:05:24.073 | 8 | 90 | [
"modeling",
"poisson-distribution",
"large-data"
] |
271 | 2 | null | 267 | 9 | null | If I understand your question correctly, you need to use the [Hypergeometric distribution](http://en.wikipedia.org/wiki/Hypergeometric_distribution). This distribution is usually associated with urn models, i.e there are $n$ balls in an urn, $y$ are painted red, and you draw $m$ balls from the urn. Then if $X$ is the n... | null | CC BY-SA 3.0 | null | 2010-07-20T11:10:42.150 | 2013-07-17T02:30:07.350 | 2013-07-17T02:30:07.350 | 805 | 8 | null |
272 | 2 | null | 161 | 4 | null | Also, for some elaborate discussion (including bashing of ADF / PP / KPSS :) you might want to have a look at the book by Maddala and Kim:
[http://www.amazon.com/Cointegration-Structural-Change-Themes-Econometrics/dp/0521587824](http://rads.stackoverflow.com/amzn/click/0521587824)
Quite extensive and not very easy to r... | null | CC BY-SA 2.5 | null | 2010-07-20T11:14:41.487 | 2010-07-20T11:14:41.487 | null | null | 216 | null |
273 | 2 | null | 25 | 1 | null |
- Clearly R
- RadidMiner is nice, but switching to thinking in terms of operators takes a moment
- Matlab / Octave
If you describe a specific problem, I may be able to get more specific.
| null | CC BY-SA 2.5 | null | 2010-07-20T11:18:01.390 | 2010-07-20T11:18:01.390 | null | null | 216 | null |
274 | 2 | null | 269 | 14 | null | The population is the whole set of values, or individuals, you are interested in. The sample is a subset of the population, and is the set of values you actually use in your estimation.
So, for example, if you want to know the average height of the residents of China, that is your population, ie, the population of Chin... | null | CC BY-SA 2.5 | null | 2010-07-20T11:21:59.493 | 2010-07-20T11:21:59.493 | null | null | 90 | null |
275 | 2 | null | 270 | 7 | null | In case of Poisson it is bad, since counts are counts -- their unit is an unity. On the other hand, if you'd use some advanced software like R, its Poisson handling functions will be aware of such large numbers and would use some numerical tricks to handle them.
Obviously I agree that normal approximation is another go... | null | CC BY-SA 2.5 | null | 2010-07-20T11:29:53.070 | 2010-07-20T12:26:55.800 | 2010-07-20T12:26:55.800 | null | null | null |
276 | 1 | 553 | null | 13 | 10659 | Is there a rule-of thumb or even any way at all to tell how large a sample should be in order to estimate a model with a given number of parameters?
So, for example, if I want to estimate a least-squares regression with 5 parameters, how large should the sample be?
Does it matter what estimation technique you are usi... | How large should a sample be for a given estimation technique and parameters? | CC BY-SA 2.5 | null | 2010-07-20T11:43:25.013 | 2010-09-16T22:25:36.037 | null | null | 90 | [
"sample-size",
"estimation",
"least-squares",
"maximum-likelihood"
] |
277 | 1 | null | null | 28 | 14538 | When would one prefer to use a Conditional Autoregressive model over a Simultaneous Autoregressive model when modelling autocorrelated geo-referenced aerial data?
| Spatial statistics models: CAR vs SAR | CC BY-SA 3.0 | null | 2010-07-20T11:49:02.490 | 2016-06-23T07:40:23.197 | 2016-06-23T07:40:23.197 | 7486 | 215 | [
"modeling",
"spatial"
] |
278 | 1 | null | null | 8 | 339 | When a non-hierarchical cluster analysis is carried out, the order of observations in the data file determine the clustering results, especially if the data set is small (i.e, 5000 observations). To deal with this problem I usually performed a random reorder of data observations. My problem is that if I replicate the a... | How to deal with the effect of the order of observations in a non hierarchical cluster analysis? | CC BY-SA 2.5 | null | 2010-07-20T11:49:27.543 | 2010-09-17T20:36:37.643 | 2010-09-17T20:36:37.643 | null | 221 | [
"clustering"
] |
279 | 2 | null | 270 | 19 | null | When you're dealing with a Poisson distribution with large values of \lambda (its parameter), it is common to use a normal approximation to the Poisson distribution.
As [this site](http://www.stat.ucla.edu/~dinov/courses_students.dir/Applets.dir/NormalApprox2PoissonApplet.html) mentions, it's all right to use the norm... | null | CC BY-SA 2.5 | null | 2010-07-20T11:54:15.197 | 2010-07-20T11:54:15.197 | null | null | 62 | null |
280 | 2 | null | 138 | 5 | null | The [R project](http://www.r-project.org/) website has lots of manuals to start, and I suggest you the [Nabble R forum](http://r.789695.n4.nabble.com/) and the [R-bloggers](http://www.r-bloggers.com/) site as well.
| null | CC BY-SA 2.5 | null | 2010-07-20T11:54:50.530 | 2010-07-20T11:54:50.530 | null | null | 221 | null |
281 | 2 | null | 73 | 4 | null | Day-to-day the most useful package must be "foreign" which has functions for reading and writing data for other statistical packages e.g. Stata, SPSS, Minitab, SAS, etc. Working in a field where R is not that commonplace means that this is a very important package.
| null | CC BY-SA 2.5 | null | 2010-07-20T11:59:56.727 | 2012-08-27T17:52:32.967 | 2012-08-27T17:52:32.967 | 919 | 215 | null |
282 | 2 | null | 222 | 78 | null | First, let's define a score.
John, Mike and Kate get the following percentages for exams in Maths, Science, English and Music as follows:
```
Maths Science English Music
John 80 85 60 55
Mike 90 85 70 45
Kate 95 80 40 50
```
In t... | null | CC BY-SA 4.0 | null | 2010-07-20T12:02:26.817 | 2022-07-25T13:56:39.230 | 2022-07-25T13:56:39.230 | 919 | 81 | null |
283 | 1 | 307 | null | 71 | 98662 | What is meant when we say we have a saturated model?
| What is a "saturated" model? | CC BY-SA 2.5 | null | 2010-07-20T12:09:08.457 | 2022-03-24T21:14:54.740 | 2010-07-20T14:26:17.513 | null | 215 | [
"modeling",
"regression"
] |
284 | 2 | null | 50 | 6 | null | A random variable, usually denoted X, is a variable where the outcome is uncertain. The observation of a particular outcome of this variable is called a realisation. More concretely, it is a function which maps a probability space into a measurable space, usually called a state space. Random variables are discrete (can... | null | CC BY-SA 2.5 | null | 2010-07-20T12:25:30.920 | 2010-07-20T12:25:30.920 | null | null | 215 | null |
285 | 2 | null | 47 | 1 | null | You might consider transforming (perhaps a log) the positively skewed variables.
If after exploring various clustering algorithms you find that the four variables simply reflect varying intensity levels of usage, you might think about a theoretically based classification. Presumably this classification is going to be u... | null | CC BY-SA 2.5 | null | 2010-07-20T12:26:39.483 | 2010-07-20T12:26:39.483 | null | null | 183 | null |
286 | 2 | null | 170 | 23 | null | There's a superb Probability book here:
[https://web.archive.org/web/20100102085337/http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html](https://web.archive.org/web/20100102085337/http://www.dartmouth.edu/%7Echance/teaching_aids/books_articles/probability_book/book.html)
which you c... | null | CC BY-SA 4.0 | null | 2010-07-20T12:28:32.410 | 2023-06-02T11:50:50.423 | 2023-06-02T11:50:50.423 | 362671 | 211 | null |
287 | 1 | 506 | null | 16 | 5784 | Can someone explain to me the difference between method of moments and GMM (general method of moments), their relationship, and when should one or the other be used?
| What is the difference/relationship between method of moments and GMM? | CC BY-SA 2.5 | null | 2010-07-20T12:29:17.607 | 2021-02-26T17:25:32.740 | 2013-10-22T14:58:47.763 | 5739 | 90 | [
"estimation",
"method-of-moments",
"generalized-moments"
] |
288 | 1 | null | null | 7 | 3063 | Suppose that I culture cancer cells in n different dishes g₁, g₂, … , gn and observe the number of cells ni in each dish that look different than normal. The total number of cells in dish gi is ti. There is individual differences between individual cells, but also differences between the populations in different dish... | Estimating beta-binomial distribution | CC BY-SA 2.5 | null | 2010-07-20T12:29:34.187 | 2012-11-15T07:31:15.177 | 2010-07-21T03:10:58.123 | null | 220 | [
"estimation",
"beta-binomial-distribution"
] |
289 | 2 | null | 224 | 5 | null | For visualizing graphs in a Java/SWT environment, check out Zest: [http://eclipse.org/gef/zest](http://eclipse.org/gef/zest)
| null | CC BY-SA 2.5 | null | 2010-07-20T12:32:41.060 | 2010-07-20T12:32:41.060 | null | null | 80 | null |
290 | 1 | 445 | null | 9 | 2053 | I know of Cameron and Trivedi's Microeconometrics Using Stata.
What are other good texts for learning Stata?
| Resources for learning Stata | CC BY-SA 3.0 | null | 2010-07-20T12:33:30.577 | 2017-10-12T15:20:16.267 | 2015-10-31T10:17:52.700 | 22468 | 189 | [
"references",
"stata"
] |
291 | 2 | null | 7 | 11 | null | A good place to look is Carnegie Mellon University's [Data and Story Library or DASL](http://lib.stat.cmu.edu/DASL/), which contains data files that "illustrate the use of basic statistics methods... A good example can make a lesson on a particular statistics method vivid and relevant. DASL is designed to help teachers... | null | CC BY-SA 3.0 | null | 2010-07-20T12:35:43.100 | 2016-03-29T09:06:44.293 | 2016-03-29T09:06:44.293 | 22228 | 211 | null |
292 | 2 | null | 276 | 2 | null | It should always be large enough! ;)
All parameter estimates come with an estimate uncertainty, which is determined by the sample size. If you carry out a regression analysis, it helps to remind yourself that the Χ2 distribution is constructed from the input data set. If your model had 5 parameters and you had 5 data p... | null | CC BY-SA 2.5 | null | 2010-07-20T12:38:38.663 | 2010-07-20T12:38:38.663 | null | null | 56 | null |
293 | 2 | null | 192 | 4 | null | I think you need to rework this question. It all depends on the problem/data which has generated the cross-tab.
| null | CC BY-SA 2.5 | null | 2010-07-20T12:43:02.087 | 2010-07-20T12:43:02.087 | null | null | 211 | null |
294 | 2 | null | 53 | 61 | null | Bernard Flury, in his excellent book introducing multivariate analysis, described this as an anti-property of principal components. It's actually worse than choosing between correlation or covariance. If you changed the units (e.g. US style gallons, inches etc. and EU style litres, centimetres) you will get substan... | null | CC BY-SA 2.5 | null | 2010-07-20T12:47:39.550 | 2010-07-20T12:47:39.550 | null | null | 211 | null |
295 | 2 | null | 31 | 18 | null | A nice definition of p-value is "the probability of observing a test statistic at least as large as the one calculated assuming the null hypothesis is true".
The problem with that is that it requires an understanding of "test statistic" and "null hypothesis". But, that's easy to get across. If the null hypothesis is t... | null | CC BY-SA 2.5 | null | 2010-07-20T12:52:55.920 | 2010-07-20T12:52:55.920 | null | null | 62 | null |
296 | 2 | null | 7 | 13 | null | [MLComp](https://web.archive.org/web/20100730170034/http://mlcomp.org/) has quite a few interesting datasets, and as a bonus your algorithm will get ranked if you upload it.
| null | CC BY-SA 4.0 | null | 2010-07-20T12:54:28.273 | 2022-11-22T02:51:53.290 | 2022-11-22T02:51:53.290 | 362671 | 127 | null |
297 | 2 | null | 3 | 7 | null | I really enjoy working with [RooFit](http://roofit.sourceforge.net/) for easy proper fitting of signal and background distributions and [TMVA](http://tmva.sourceforge.net/) for quick principal component analyses and modelling of multivariate problems with some standard tools (like genetic algorithms and neural networks... | null | CC BY-SA 2.5 | null | 2010-07-20T13:08:42.907 | 2010-07-20T13:08:42.907 | null | null | 56 | null |
298 | 1 | null | null | 214 | 501393 | Am I looking for a better behaved distribution for the independent variable in question, or to reduce the effect of outliers, or something else?
| In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? | CC BY-SA 2.5 | null | 2010-07-20T13:11:50.297 | 2021-12-09T20:01:45.203 | 2021-08-24T07:10:36.977 | 35989 | 125 | [
"regression",
"distributions",
"data-transformation",
"logarithm",
"faq"
] |
299 | 2 | null | 298 | 16 | null | One typically takes the log of an input variable to scale it and change the distribution (e.g. to make it normally distributed). It cannot be done blindly however; you need to be careful when making any scaling to ensure that the results are still interpretable.
This is discussed in most introductory statistics text... | null | CC BY-SA 2.5 | null | 2010-07-20T13:16:29.303 | 2010-07-20T13:22:18.760 | 2010-07-20T13:22:18.760 | 5 | 5 | null |
300 | 2 | null | 278 | 4 | null | A "right" answer cannot depend on an arbitrary ordering of some method you are using.
You need to consider all possible orderings (or some representative sample) and estimate your parameters for every case. This will give you distributions for the parameters you are trying to estimate. Estimate the "true" parameter val... | null | CC BY-SA 2.5 | null | 2010-07-20T13:19:31.293 | 2010-07-20T13:19:31.293 | null | null | 56 | null |
301 | 2 | null | 298 | 11 | null | You tend to take logs of the data when there is a problem with the residuals. For example, if you plot the residuals against a particular covariate and observe an increasing/decreasing pattern (a funnel shape), then a transformation may be appropriate. Non-random residuals usually indicate that your model assumptions a... | null | CC BY-SA 2.5 | null | 2010-07-20T13:22:40.320 | 2010-07-20T13:22:40.320 | null | null | 8 | null |
302 | 2 | null | 276 | 2 | null | I've heard two rules of thumb in this regard. One holds that so long as there are enough observations in the error term to evoke the central limit theorem, e.g. 20 or 30, you are fine. The other holds that for each estimated slope one should have at least 20 or 30 observations. The difference between using 20 or 30 ... | null | CC BY-SA 2.5 | null | 2010-07-20T14:04:12.107 | 2010-07-20T14:04:12.107 | null | null | 196 | null |
303 | 2 | null | 288 | 3 | null | You have a hierarchical bayesian model. Brief details below:
Likelihood Function:
$$f(n_i | p_i, t_i) = (t_i n_i) p_i^{n_i} (1-p_i)^{(t_i - n_i)}$$
Priors on $p_i, \alpha, \beta$:
$$pi \sim Beta(\alpha, \beta)$$
$$\alpha ~ N(\alpha_{mean}, \alpha_{var}) I(\alpha > 0)$$
$$\beta ~ N(\beta_{mean}, \beta_{var}) I(\beta > ... | null | CC BY-SA 3.0 | null | 2010-07-20T14:08:42.377 | 2012-11-15T07:31:15.177 | 2012-11-15T07:31:15.177 | 9007 | null | null |
304 | 2 | null | 298 | 3 | null | Shane's point that taking the log to deal with bad data is well taken. As is Colin's regarding the importance of normal residuals. In practice I find that usually you can get normal residuals if the input and output variables are also relatively normal. In practice this means eyeballing the distribution of the trans... | null | CC BY-SA 2.5 | null | 2010-07-20T14:13:50.103 | 2010-07-20T14:13:50.103 | null | null | 196 | null |
305 | 1 | 796 | null | 53 | 36585 | It seems like when the assumption of homogeneity of variance is met that the results from a Welch adjusted t-test and a standard t-test are approximately the same. Why not simply always use the Welch adjusted t?
| When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df? | CC BY-SA 2.5 | null | 2010-07-20T14:19:41.383 | 2022-11-07T16:03:40.413 | 2010-07-26T13:05:38.663 | 159 | 196 | [
"variance",
"t-test",
"heteroscedasticity"
] |
306 | 2 | null | 242 | 9 | null | The model that fits the data doesn't have to be a time series model; I would advise thinking outside the box a little.
If you have multiple variables (e.g. age, gender, diet, ethnicity, illness, medication) you can use these for a different model. Maybe having certain patients in the same room is an important predic... | null | CC BY-SA 2.5 | null | 2010-07-20T14:21:37.820 | 2010-07-20T14:21:37.820 | null | null | 5 | null |
307 | 2 | null | 283 | 46 | null | A saturated model is one in which there are as many estimated parameters as data points. By definition, this will lead to a perfect fit, but will be of little use statistically, as you have no data left to estimate variance.
For example, if you have 6 data points and fit a 5th-order polynomial to the data, you would ha... | null | CC BY-SA 2.5 | null | 2010-07-20T14:23:30.843 | 2010-07-20T14:23:30.843 | null | null | 229 | null |
308 | 2 | null | 290 | 2 | null | There are couple of good links with introductory material at Princeton Uni Library [website](http://libguides.princeton.edu/content.php?pid=27916&sid=459449).
| null | CC BY-SA 3.0 | null | 2010-07-20T14:38:07.360 | 2015-08-07T12:32:14.717 | 2015-08-07T12:32:14.717 | 22047 | 22 | null |
309 | 2 | null | 305 | 3 | null | The fact that something more complex reduces to something less complex when some assumption is checked is not enough to throw the simpler method away.
| null | CC BY-SA 2.5 | null | 2010-07-20T14:40:32.910 | 2010-07-20T14:40:32.910 | null | null | null | null |
310 | 2 | null | 270 | 1 | null | You can simply ignore the 'factorial' when using maximum likelihood. Here is the reasoning for your suicides example. Let:
λ : Be the expected number of suicides per year
ki: Be the number of suicides in year i.
Then you would maximize the log-likelihood as:
LL = ∑ ( ki log(λ) - λ - ki! )
Maximizing the above is equiva... | null | CC BY-SA 2.5 | null | 2010-07-20T14:41:33.560 | 2010-07-20T14:41:33.560 | null | null | null | null |
311 | 2 | null | 220 | 23 | null | Rob Hyndman gave the easy exact answer for a fixed n. If you're interested in asymptotic behavior for large n, this is handled in the field of [extreme value theory](http://en.wikipedia.org/wiki/Extreme_value_theory). There is a small family of possible limiting distributions; see for example the first chapters of [t... | null | CC BY-SA 2.5 | null | 2010-07-20T14:47:31.380 | 2010-07-20T14:47:31.380 | null | null | 89 | null |
312 | 1 | 318 | null | 5 | 171 | I'm a physics graduate who ended up doing infosec so most of the statistics I ever learned is useful for thermodynamics. I'm currently trying to think of a model for working out how many of a population of computers are infected with viruses, though I assume the maths works out the same way for real-world diseases so r... | What approach could be used for modelling virus infections? | CC BY-SA 2.5 | null | 2010-07-20T15:03:40.450 | 2022-11-30T05:56:14.203 | null | null | null | [
"distributions",
"modeling",
"poisson-distribution",
"binomial-distribution",
"disease"
] |
313 | 2 | null | 31 | 13 | null | Imagine you have a bag containing 900 black marbles and 100 white, i.e. 10% of the marbles are white. Now imagine you take 1 marble out, look at it and record its colour, take out another, record its colour etc.. and do this 100 times. At the end of this process you will have a number for white marbles which, ideally, ... | null | CC BY-SA 2.5 | null | 2010-07-20T15:10:15.333 | 2010-07-21T00:33:56.993 | 2010-07-21T00:33:56.993 | 226 | 226 | null |
314 | 2 | null | 257 | 12 | null | R is definitely the answer. I would just add to what Rob and Colin already said:
To improve the quality of your plots, you should consider using [the Cairo package](http://cran.r-project.org/web/packages/Cairo/index.html) for the output device. That will greatly improve the quality of the final graphics. You simply ... | null | CC BY-SA 2.5 | null | 2010-07-20T15:10:34.927 | 2010-07-20T15:10:34.927 | null | null | 5 | null |
315 | 2 | null | 224 | 6 | null | If you can use R try [ggplot2](http://had.co.nz/ggplot2/).
| null | CC BY-SA 2.5 | null | 2010-07-20T15:15:57.377 | 2010-07-20T15:15:57.377 | null | null | 36 | null |
316 | 2 | null | 73 | 8 | null | ggplot2 - hands down best visualization for R.
RMySQL/RSQLite/RODBC - for connecting to a databases
sqldf - manipulate data.frames with SQL queries
Hmisc/rms - packages from Frank Harrell containing convenient miscellaneous functions and nice functions for regression analyses.
GenABEL - nice package for genome-wide ass... | null | CC BY-SA 2.5 | null | 2010-07-20T15:20:38.567 | 2010-07-20T15:28:42.347 | 2010-07-20T15:28:42.347 | 36 | 36 | null |
317 | 2 | null | 114 | 18 | null | [The Endeavour](http://www.johndcook.com/blog/) sometimes features statistics posts. Otherwise it is mostly around the interplay of computer science and math.
| null | CC BY-SA 2.5 | null | 2010-07-20T15:21:01.857 | 2010-07-20T15:21:01.857 | null | null | 56 | null |
318 | 2 | null | 312 | 5 | null | Computer virus propagation is structurally similar to infectious diseases propagation (vaccinations = anti-virus software, virus via email = getting a virus from someone etc).
Use the following links: [Mathematical modelling of infectious disease](https://en.wikipedia.org/wiki/Mathematical_modelling_of_infectious_disea... | null | CC BY-SA 4.0 | null | 2010-07-20T15:23:53.653 | 2022-11-30T05:56:14.203 | 2022-11-30T05:56:14.203 | 362671 | null | null |
319 | 2 | null | 31 | 34 | null | No amount of verbal explanation or calculations really helped me to understand at a gut level what p-values were, but it really snapped into focus for me once I took a course that involved simulation. That gave me the ability to actually see data generated by the null hypothesis and to plot the means/etc. of simulated... | null | CC BY-SA 2.5 | null | 2010-07-20T15:33:42.533 | 2010-07-20T15:33:42.533 | null | null | 71 | null |
320 | 2 | null | 283 | 28 | null | A saturated model is a model that is overparameterized to the point that it is basically just interpolating the data. In some settings, such as image compression and reconstruction, this isn't necessarily a bad thing, but if you're trying to build a predictive model it's very problematic.
In short, saturated models le... | null | CC BY-SA 2.5 | null | 2010-07-20T15:47:04.940 | 2010-07-20T15:47:04.940 | null | null | 61 | null |
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