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2153 | 2 | null | 2149 | 52 | null | From Dan Simon's "Optimal State Estimation":
>
In a linear system with Gaussian noise, the Kalman filter is optimal. In a system that is nonlinear, the Kalman filter can be used for state estimation, but the particle filter may give better results at the price of additional computational effort. In a system that has n... | null | CC BY-SA 4.0 | null | 2010-08-27T06:23:29.647 | 2020-09-06T16:19:25.457 | 2020-09-06T16:19:25.457 | 7290 | 339 | null |
2154 | 1 | 2157 | null | 2 | 852 | (I know it is not quite appropriate to quote it as "part 2", but since the question has been dormant for quite a while, I hope by doing this will rise peoples' attention again, you may have a look of part I [here](https://stats.stackexchange.com/questions/1228/how-to-interpret-a-control-chart-containing-a-majority-of-z... | How to interpret a control chart containing a majority of zero values? (Part 2) | CC BY-SA 2.5 | null | 2010-08-27T07:32:57.340 | 2010-08-27T14:12:33.627 | 2017-04-13T12:44:24.667 | -1 | 588 | [
"control-chart"
] |
2155 | 2 | null | 2151 | 66 | null | It seems you are looking for multi-class ROC analysis, which is a kind of multi-objective optimization covered in a [tutorial](http://www.cs.bris.ac.uk/~flach/ICML04tutorial/) at ICML'04. As in several multi-class problem, the idea is generally to carry out pairwise comparison (one class vs. all other classes, one clas... | null | CC BY-SA 2.5 | null | 2010-08-27T08:12:12.627 | 2010-08-27T08:12:12.627 | null | null | 930 | null |
2156 | 2 | null | 1241 | 2 | null | In case you're interested in further references, an extensive list of papers is available on K.H. Zou's website, [Receiver Operating Characteristic (ROC) Literature Research](http://www.spl.harvard.edu/archive/spl-pre2007/pages/ppl/zou/roc.html).
ROC curves are also used when one is interested in comparing different cl... | null | CC BY-SA 2.5 | null | 2010-08-27T08:22:12.153 | 2010-08-27T08:22:12.153 | null | null | 930 | null |
2157 | 2 | null | 2154 | 3 | null | C-charts basically works like this: you collect all your observations (this is an approximation of getting only observations from "normal" periods) of a case count, then fit Poisson distribution to it (so here you apply all Poisson assumptions, mainly that each case occurance is independent to the others), and finally ... | null | CC BY-SA 2.5 | null | 2010-08-27T09:27:37.370 | 2010-08-27T13:37:10.033 | 2010-08-27T13:37:10.033 | null | null | null |
2158 | 2 | null | 1815 | 4 | null | [Experiments: Planning, Analysis and Optimization](http://rads.stackoverflow.com/amzn/click/0471699462) by Wu & Hamada.
I'm only a couple of chapters in, so not yet in a position to recommend confidently, but so far it looks like a good graduate text, reasonably detailed, comprehensive and up-to-date. Has more of a "no... | null | CC BY-SA 2.5 | null | 2010-08-27T09:36:24.300 | 2010-08-27T09:36:24.300 | null | null | 174 | null |
2159 | 2 | null | 1595 | 19 | null | I use Python for statistical analysis and forecasting. As mentioned by others above, Numpy and Matplotlib are good workhorses. I also use ReportLab for producing PDF output.
I'm currently looking at both Resolver and Pyspread which are Excel-like spreadsheet applications which are based on Python. Resolver is a comm... | null | CC BY-SA 2.5 | null | 2010-08-27T10:10:35.860 | 2010-08-27T10:10:35.860 | null | null | 1105 | null |
2160 | 2 | null | 1815 | 3 | null | Not really a book but a gentle introduction on DoE in R: [An R companion to Experimental Design](http://cran.r-project.org/doc/contrib/Vikneswaran-ED_companion.pdf).
| null | CC BY-SA 2.5 | null | 2010-08-27T11:15:23.930 | 2010-08-27T11:15:23.930 | null | null | 930 | null |
2163 | 2 | null | 1815 | 13 | null | Ronald Fisher's [The Design of Experiments](http://en.wikipedia.org/wiki/The_Design_of_Experiments) (link is Wikipedia rather than Amazon since it is long out of print) is interesting for historical context. The book is often credited as founding the whole field, and certainly did a lot to promote things like blocking,... | null | CC BY-SA 2.5 | null | 2010-08-27T14:38:12.360 | 2010-08-27T14:38:12.360 | null | null | 174 | null |
2166 | 2 | null | 213 | 5 | null | I'm not aware that anyone is doing this, but I generally like to try [dimensionality reduction](http://en.wikipedia.org/wiki/Dimensionality_reduction) when I have a problem like this. You might look into a method from manifold learning or [non-linear dimensionality reduction](http://en.wikipedia.org/wiki/Nonlinear_dim... | null | CC BY-SA 2.5 | null | 2010-08-27T16:44:31.610 | 2010-08-27T16:44:31.610 | null | null | 5 | null |
2167 | 1 | 2168 | null | 20 | 4439 | The [kernel trick](http://en.wikipedia.org/wiki/Kernel_trick) is used in several machine learning models (e.g. [SVM](http://en.wikipedia.org/wiki/Support_vector_machine)). It was first introduced in the "Theoretical foundations of the potential function method in pattern recognition learning" paper in 1964.
The wiki... | Applying the "kernel trick" to linear methods? | CC BY-SA 2.5 | null | 2010-08-27T17:00:11.247 | 2020-10-14T20:03:08.280 | 2015-04-14T19:14:27.327 | 9964 | 5 | [
"machine-learning",
"kernel-trick"
] |
2168 | 2 | null | 2167 | 17 | null | The kernel trick can only be applied to linear models where the examples in the problem formulation appear as dot products (Support Vector Machines, PCA, etc).
| null | CC BY-SA 2.5 | null | 2010-08-27T17:16:04.163 | 2010-08-27T17:16:04.163 | null | null | 881 | null |
2169 | 1 | 2288 | null | 6 | 403 | I am trying to compute the standard error of the sample [spectral risk measure](http://en.wikipedia.org/wiki/Spectral_risk_measure), which is used as a metric for portfolio risk. Briefly, a sample spectral risk measure is defined as
$q = \sum_i w_i x_{(i)}$, where $x_{(i)}$ are the sample order statistics, and $w_i$ i... | How to compute the standard error of an L-estimator? | CC BY-SA 2.5 | null | 2010-08-27T18:23:40.470 | 2010-11-04T16:51:47.097 | 2010-11-04T15:56:08.473 | 930 | 795 | [
"estimation",
"finance",
"standard-error"
] |
2170 | 1 | 2177 | null | 7 | 718 | Say some previous findings identified a curvilinear effect of X on Y, (specifically that X had a positive effect on Y, and that X^2 had a negative effect). You want to see if the same holds for your entirely different sample (although everything else between studies, constructs/measures, are exactly the same). Neither ... | Preferred method for identifying curvilinear effect in multi-variable regression framework | CC BY-SA 2.5 | null | 2010-08-27T20:17:34.687 | 2010-09-03T17:57:15.193 | 2010-08-30T12:27:26.667 | 1036 | 1036 | [
"modeling",
"regression",
"methodology"
] |
2171 | 1 | 2172 | null | 19 | 2535 | I'm interested in learning how to create the type of visualizations you see at [http://flowingdata.com](http://flowingdata.com) and informationisbeautiful. EDIT: Meaning, visualizations that are interesting in of themselves -- kinda like the NY Times graphics, as opposed to a quick something for a report.
What kinds of... | Resources for learning to create data visualizations? | CC BY-SA 2.5 | null | 2010-08-27T22:00:32.020 | 2019-02-26T18:41:29.610 | 2010-08-28T04:31:24.107 | 1106 | 1106 | [
"data-visualization"
] |
2172 | 2 | null | 2171 | 20 | null | Flowing data regularly discusses the tools that he uses. See, for instance:
- 40 Essential Tools and Resources to Visualize Data
- What Visualization Tool/Software Should You Use? – Getting Started
He also shows in great detail how he makes graphics on occasion, such as:
- How to Make a US County Thematic Map Usi... | null | CC BY-SA 2.5 | null | 2010-08-27T22:50:35.313 | 2010-08-28T00:06:51.733 | 2017-04-13T12:44:27.570 | -1 | 5 | null |
2173 | 2 | null | 2171 | 2 | null | You'll spend a lot of time getting up to speed with R.
RapidMiner is free and open source and graphical, and has plenty of good visualizations, and you can export them.
If you have money to spare, or are a university staff/student then JMP is also very freaking nice. It can make some very pretty graphs, very very easi... | null | CC BY-SA 2.5 | null | 2010-08-27T23:47:09.177 | 2010-08-27T23:47:09.177 | null | null | 74 | null |
2174 | 2 | null | 2171 | 5 | null | Already mentioned processing has a nice set of books available. See: [1](http://rads.stackoverflow.com/amzn/click/0262182629), [2](http://rads.stackoverflow.com/amzn/click/144937980X), [3](http://rads.stackoverflow.com/amzn/click/0123736021), [4](http://rads.stackoverflow.com/amzn/click/159059617X), [5](http://rads.sta... | null | CC BY-SA 2.5 | null | 2010-08-28T00:26:17.800 | 2010-08-28T00:26:17.800 | null | null | 22 | null |
2175 | 7 | null | null | 0 | null | CrossValidated is for statisticians, data miners, and anyone else doing data analysis or interested in it as a discipline. If you have a question about
- statistical analysis, applied or theoretical
- designing experiments
- collecting data
- data mining
- machine learning
- visualizing data
- probability theory... | null | CC BY-SA 3.0 | null | 2010-08-28T01:20:33.947 | 2013-01-10T19:43:24.013 | 2014-04-23T13:43:43.010 | -1 | -1 | null |
2176 | 2 | null | 2104 | 5 | null | I generally recommend avoiding these types of sphericity tests altogether by using modern mixed modeling methods. If you are not working with few subjects this will give you a great deal of flexibility in modeling an appropriate covariance structure, freeing you from the strict assumption of sphericity when necessary.... | null | CC BY-SA 2.5 | null | 2010-08-28T02:32:13.413 | 2010-08-28T02:32:13.413 | null | null | 1107 | null |
2177 | 2 | null | 2170 | 6 | null | It sounds as though you are interested in formal inference and for that method 4 is best. Add X^2 to a model containing terms you wish to control for and conduct a test to assess the streght of evidence for the quadratic term given the terms in the model. Note however that "absence of evidence is not evidence of abse... | null | CC BY-SA 2.5 | null | 2010-08-28T04:34:44.940 | 2010-08-28T04:34:44.940 | null | null | 1107 | null |
2178 | 2 | null | 2167 | 7 | null | Two further references from [B. Schölkopf](http://www.kyb.mpg.de/~bs):
- Schölkopf, B. and Smola, A.J. (2002). Learning with kernels. The MIT Press.
- Schölkopf, B., Tsuda, K., and Vert, J.-P. (2004). Kernel methods in computational biology. The MIT Press.
and a website dedicated to [kernel machines](http://www.ker... | null | CC BY-SA 2.5 | null | 2010-08-28T07:52:54.063 | 2010-08-28T07:52:54.063 | null | null | 930 | null |
2179 | 1 | 2180 | null | 37 | 33076 | How to obtain a variable (attribute) importance using SVM?
| Variable importance from SVM | CC BY-SA 2.5 | null | 2010-08-28T13:34:42.963 | 2017-09-14T15:17:42.047 | null | null | null | [
"machine-learning",
"feature-selection",
"svm"
] |
2180 | 2 | null | 2179 | 23 | null | If you use l-1 penalty on the weight vector, it does automatic feature selection as the weights corresponding to irrelevant attributes are automatically set to zero. See [this paper](http://books.nips.cc/papers/files/nips16/NIPS2003_AA07.pdf). The (absolute) magnitude of each non-zero weights can give an idea about the... | null | CC BY-SA 2.5 | null | 2010-08-28T14:36:05.907 | 2010-08-28T14:36:05.907 | null | null | 881 | null |
2181 | 1 | null | null | 29 | 26770 | I'm interested in getting some books about multivariate analysis, and need your recommendations. Free books are always welcome, but if you know about some great non-free MVA book, please, state it.
| Book recommendations for multivariate analysis | CC BY-SA 2.5 | null | 2010-08-28T17:07:59.760 | 2016-06-23T19:39:00.613 | null | null | 1356 | [
"references",
"multivariate-analysis"
] |
2182 | 1 | null | null | 14 | 15016 | I need help explaining, and citing basic statistics texts, papers or other references, why it is generally incorrect to use the margin of error (MOE) statistic reported in polling to naively declare a statistical tie.
An example:
Candidate A leads Candidate B in a poll, $39 - 31$ percent, $4.5 \%$ margin-of-error for $... | Can you explain why statistical tie is not naively rejected when $p_1-p_2 < 2 \,\text {MOE}$? | CC BY-SA 3.0 | null | 2010-08-28T22:34:01.353 | 2020-02-19T01:06:57.893 | 2015-12-02T14:30:40.800 | 67822 | null | [
"polling"
] |
2183 | 2 | null | 2182 | 7 | null | My first attempt at an answer was flawed (see below for the flawed answer). The reason it is flawed is that the margin of error (MOE) that is reported applies to a candidate's polling percentage but not to the difference of the percentages. My second attempt explicitly addresses the question posed by the OP a bit bette... | null | CC BY-SA 2.5 | null | 2010-08-28T23:20:51.237 | 2010-08-29T02:31:19.680 | 2010-08-29T02:31:19.680 | null | null | null |
2184 | 2 | null | 2182 | 4 | null | Not only is that a bad way to term things but that's not even a statistical dead heat.
You don't use overlapping confidence intervals that way. If you really wanted to only say that Candidate A was going to win then Candidate A is definitely in the lead. The lead is 8% MOE 6.4%. The confidence interval of that subtrac... | null | CC BY-SA 4.0 | null | 2010-08-29T00:12:35.500 | 2020-02-19T01:06:57.893 | 2020-02-19T01:06:57.893 | 601 | 601 | null |
2185 | 2 | null | 665 | 7 | null | Similar to what Mark said, Statistics was historically called Inverse Probability, since statistics tries to infer the causes of an event given the observations, while probability tends to be the other way around.
| null | CC BY-SA 2.5 | null | 2010-08-29T01:35:44.567 | 2010-08-29T01:35:44.567 | null | null | 1106 | null |
2186 | 2 | null | 2181 | 17 | null | Off the top of my head, I would say that the following general purpose books are rather interesting as a first start:
- Izenman, J. Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning. Springer. companion website
- Tinsley, H. and Brown, S. (2000). Handbook of Applied Multiva... | null | CC BY-SA 2.5 | null | 2010-08-29T08:44:54.437 | 2010-08-29T08:44:54.437 | null | null | 930 | null |
2187 | 2 | null | 2181 | 9 | null | Here are some of my books on that field (in alphabetical order).
- AFIFI, A., CLARK, V. Computer-Aided
Multivariate Analysis. CHAPMAN & HALL, 2000
- AGRESTI, A. Categorical Data Analysis. WILEY, 2002
- HAIR, Multivariate Data Analysis. 6th Ed.
- ΗÄRDLE, W., SIMAR, L. Applied Multivariate Statistical Analysis. SPRI... | null | CC BY-SA 2.5 | null | 2010-08-29T08:58:43.240 | 2010-08-29T08:58:43.240 | null | null | 339 | null |
2188 | 2 | null | 490 | 12 | null | I have a slight preference for [Random Forests](http://www.stat.berkeley.edu/~breiman/RandomForests/) by Leo Breiman & Adele Cutleer for several reasons:
- it allows to cope with categorical and continuous predictors, as well as unbalanced class sample size;
- as an ensemble/embedded method, cross-validation is embed... | null | CC BY-SA 2.5 | null | 2010-08-29T12:04:51.210 | 2010-08-29T12:04:51.210 | null | null | 930 | null |
2189 | 2 | null | 2140 | 1 | null | I'm not sure if such a (non-parametric) permutation procedure could be applied here. Anyways, here is my idea:
```
a <- c(1.18, -0.41, -0.66, 0.98, 0.1)
b <- c(-0.36, -0.73, -1.47, 0.15, -0.31)
total <- c(a,b)
first <- combn(total,length(a))
second <- apply(first,2,function(z) total[is.na(pmatch(total,z))])
var.ratio <... | null | CC BY-SA 2.5 | null | 2010-08-29T14:07:55.913 | 2010-08-29T14:41:44.697 | 2010-08-29T14:41:44.697 | 339 | 339 | null |
2190 | 1 | null | null | 2 | 304 | I have a great prediction yet I am unsure how to uncover how the results were generated?
| How to reconstruct ensemble of trees from random forest? | CC BY-SA 2.5 | 0 | 2010-08-29T16:26:44.937 | 2010-09-28T19:53:38.997 | 2010-08-29T18:45:28.027 | 71 | null | [
"classification",
"random-forest"
] |
2191 | 2 | null | 2181 | 4 | null | [Analyzing Multivariate Data](http://rads.stackoverflow.com/amzn/click/0534349749) by James Lattin, J Douglas Carroll and Paul E Green.
| null | CC BY-SA 2.5 | null | 2010-08-29T17:15:22.733 | 2010-08-29T17:15:22.733 | null | null | 174 | null |
2192 | 2 | null | 224 | 1 | null | I've used [ZedGraph](http://zedgraph.org/) for .NET. It's open source, and supports all common 2D chart types.
| null | CC BY-SA 2.5 | null | 2010-08-29T17:49:09.767 | 2010-08-29T17:49:09.767 | null | null | 956 | null |
2193 | 2 | null | 2190 | 1 | null | From the trees attributed to each class's output you can do a tree search on the similarities. You could do it manually, but that would be as tedious as examining the weights on a Neural network. So you want to find the overlaps in the decision tree structures. This can look for various features depending upon the prob... | null | CC BY-SA 2.5 | null | 2010-08-29T19:47:13.183 | 2010-08-29T19:47:13.183 | null | null | 1098 | null |
2194 | 2 | null | 2171 | 0 | null | R is great, but it is not that R is difficult to learn it's that the documentation is impossible to search for any other name like Rq would be great. So when you got a problem, searching for a solution is a nightmare, and the documentation is not great either. Matlab or Octave will be great. And to get those plots in R... | null | CC BY-SA 3.0 | null | 2010-08-29T19:54:09.083 | 2014-11-15T13:46:30.810 | 2014-11-15T13:46:30.810 | 22047 | 1098 | null |
2195 | 2 | null | 21 | 2 | null | I don't know about the first point. But for the second one, autoregressive (AR) functions could be simple. I would really chose a parametric method against a non-parametric one. The forecasting in AR is straight forward. And consensus data has lots of samples for each period so you can get robust parameter estimates at... | null | CC BY-SA 2.5 | null | 2010-08-29T20:01:34.300 | 2010-08-29T20:01:34.300 | null | null | 1098 | null |
2196 | 2 | null | 369 | 5 | null | You can try Latent Semantic Analysis, which basically provides a way to represent in a reduced space your news feeds and any term (in your case, keyword appearing in the title). As it relies on Singular Value Decomposition, I suppose you may then be able to check if there exists a particular association between those t... | null | CC BY-SA 2.5 | null | 2010-08-29T20:42:33.390 | 2010-08-29T20:42:33.390 | null | null | 930 | null |
2197 | 1 | 2206 | null | 7 | 384 | Let's say I have a dataset with 1000 observations in 10 variables, "A" through "J." I have 1000 responses/measures for each of the first 8 variables, through "H," but only the first 500 observations for "I" are not missing, and only the last 500 observations for "J" are not missing -- there are no observations for whic... | Precedent for Bootstrap-like procedure with "invented" data? | CC BY-SA 2.5 | null | 2010-08-29T22:50:57.957 | 2010-10-10T19:36:49.337 | 2010-08-29T23:18:38.910 | 1117 | 1117 | [
"correlation",
"pca",
"bootstrap"
] |
2198 | 1 | 2202 | null | 5 | 7467 | If given probability of $A$ is $a$ and probability of $B$ is $b$, how do I find min/max probability of intersection? Max value of intersection would be $\min(a,b)$, how do I find the min?
| Find range of possible values for probability of intersection given individual probabilities | CC BY-SA 2.5 | null | 2010-08-30T00:54:36.273 | 2010-08-30T06:25:16.763 | 2010-08-30T06:25:16.763 | null | 862 | [
"probability"
] |
2199 | 2 | null | 2181 | 4 | null | Tabachnick is the most cited on Google Scholar
Hair (6th ed) has the most ratings (with a score above 4.5) on Amazon
I recommend Hair, as I've read it, and it is written in plain language.
If you are a student or staff at a university, then I would see if your school has an account with SpringerLink, as the Hardle boo... | null | CC BY-SA 2.5 | null | 2010-08-30T01:22:20.390 | 2010-08-30T01:22:20.390 | null | null | 74 | null |
2200 | 2 | null | 2198 | 1 | null | The min is the smaller of two values: $\min(a,b) = a$ if $a < b$ and $b$ otherwise. Though I do not think this is what you are asking for...
| null | CC BY-SA 2.5 | null | 2010-08-30T02:51:15.950 | 2010-08-30T02:51:15.950 | null | null | 795 | null |
2201 | 2 | null | 2197 | 5 | null | An alternative approach would be to impute the missing raw data using a missing data replacement procedure. You could then run the PCA on the correlation matrix that resulted from the imputed dataset (see also [multiple imputation](http://www.stat.psu.edu/~jls/mifaq.html)).
Here are a few links on missing data imputati... | null | CC BY-SA 2.5 | null | 2010-08-30T03:31:36.610 | 2010-08-30T03:31:36.610 | null | null | 183 | null |
2202 | 2 | null | 2198 | 3 | null | if $a+b \le 1$, then presumably one can find disjoint sets $A$ and $B$ with ${\rm P}A = a$ and
${\rm P}B = b$. so in this case, the min is 0.
if $a+b > 1$, we get a smallest intersection by choosing $B$ to contain all of $A^C$, which has probability $1-a$ and then adding to that a piece of $A$ to bring ${\rm P}B$ up to... | null | CC BY-SA 2.5 | null | 2010-08-30T03:59:15.940 | 2010-08-30T03:59:15.940 | null | null | 1112 | null |
2203 | 2 | null | 2181 | 7 | null | JOHNSON R., WICHERN D., [Applied Multivariate Statistical Analysis](http://www.pearsonhighered.com/educator/academic/product/0,3110,0131877151,00.html), is what we used in our undergraduate Multivariate class at UC Davis, and it does a pretty good job (though it's a bit pricey).
| null | CC BY-SA 2.5 | null | 2010-08-30T04:55:48.270 | 2010-08-30T04:55:48.270 | null | null | 1118 | null |
2204 | 2 | null | 2072 | 8 | null | You could start with the following references:
- Comte (1999) "Discrete and continuous time cointegration", Journal of Econometrics.
- Ferstl (2009) "Cointegration in discrete and continuous time". Thesis.
[Citations of Comte](http://scholar.google.com/scholar?cites=9115376900789007179) may also be useful.
| null | CC BY-SA 3.0 | null | 2010-08-30T09:45:59.520 | 2014-01-13T01:53:34.157 | 2014-01-13T01:53:34.157 | 159 | 159 | null |
2205 | 2 | null | 2181 | 4 | null | Hastie, T., Tibshirani, R. and Friedman, J.: "The Elements of Statistical Learning: Data Mining, Inference, and Prediction.", Springer ([book home page](http://www-stat.stanford.edu/~tibs/ElemStatLearn/))
| null | CC BY-SA 2.5 | null | 2010-08-30T11:48:13.960 | 2010-08-30T11:48:13.960 | null | null | 961 | null |
2206 | 2 | null | 2197 | 5 | null |
- I don't know.
- What you've shown is a legitimate Monte Carlo simulation
- Bootstrap is also a Monte Carlo method, but it is more about estimating distributions.
- In general yes, especially if imputation is giving poor results. In special cases when imputation works great, no. In simple words, it will be as goo... | null | CC BY-SA 2.5 | null | 2010-08-30T11:49:00.233 | 2010-10-10T19:36:49.337 | 2010-10-10T19:36:49.337 | 930 | null | null |
2207 | 2 | null | 354 | 9 | null | In ordinary least squares, the solution to (A'A)^(-1) x = A'b minimizes squared error loss, and is the maximum likelihood solution.
So, largely because the math was easy in this historic case.
But generally people minimize many different [loss functions](http://en.wikipedia.org/wiki/Loss_function), such as exponential,... | null | CC BY-SA 2.5 | null | 2010-08-30T13:44:51.723 | 2010-11-28T11:58:46.793 | 2010-11-28T11:58:46.793 | 930 | 1119 | null |
2208 | 2 | null | 409 | 0 | null | The reason the above works for uncertainty of the mean is because of the central limit theorem.
As long as the central limit theorem holds for your application, so will the above.
| null | CC BY-SA 2.5 | null | 2010-08-30T13:55:03.287 | 2010-08-30T13:55:03.287 | null | null | 1119 | null |
2209 | 2 | null | 125 | 19 | null | Its focus isn't strictly on Bayesian statistics, so it lacks some methodology, but David MacKay's Information Theory, Inference, and Learning Algorithms made me intuitively grasp Bayesian statistics better than others - most do the how quite nicely, but I felt MacKay explained why better.
| null | CC BY-SA 2.5 | null | 2010-08-30T14:00:17.647 | 2010-09-09T06:16:29.723 | 2010-09-09T06:16:29.723 | 1119 | 1119 | null |
2210 | 2 | null | 1164 | 7 | null | While they're not mutually exclusive, I think the growing popularity of Bayesian statistics is part of it. Bayesian statistics can achieve a lot of the same goals through priors and model averaging, and tend to be a bit more robust in practice.
| null | CC BY-SA 2.5 | null | 2010-08-30T14:11:06.037 | 2010-08-30T14:11:06.037 | null | null | 1119 | null |
2212 | 2 | null | 224 | 4 | null | For javascript protovis (http://vis.stanford.edu/protovis/) is very nice.
| null | CC BY-SA 2.5 | null | 2010-08-30T14:19:24.787 | 2010-08-30T14:19:24.787 | null | null | 1119 | null |
2213 | 1 | 2218 | null | 74 | 102624 | What is the difference between a [feed-forward](http://en.wikipedia.org/wiki/Feedforward_neural_network) and [recurrent](http://en.wikipedia.org/wiki/Recurrent_neural_networks) neural network?
Why would you use one over the other?
Do other network topologies exist?
| What's the difference between feed-forward and recurrent neural networks? | CC BY-SA 3.0 | null | 2010-08-30T15:33:28.180 | 2020-01-07T17:45:25.723 | 2017-10-17T23:25:36.790 | null | 5 | [
"machine-learning",
"neural-networks",
"terminology",
"recurrent-neural-network",
"topologies"
] |
2214 | 1 | null | null | 8 | 217 | One of the purported uses of L-estimators is the ability to 'robustly' estimate the parameters of a random variable drawn from a given class. One of the downsides of using [Levy $\alpha$-stable distributions](http://en.wikipedia.org/wiki/Stable_distribution) is that it is difficult to estimate the parameters given a sa... | Estimating parameters of sum-stable RV via L-estimators | CC BY-SA 2.5 | null | 2010-08-30T16:36:55.427 | 2020-09-27T06:26:57.433 | 2020-09-27T06:26:57.433 | 7290 | 795 | [
"distributions",
"estimation",
"robust",
"stable-distribution"
] |
2215 | 2 | null | 2197 | 5 | null |
- I think we need to know more about the nature of the data to make recommendations on how to deal with the missing values. An exploratory task that jumps out to me is to look at the behavior of variables A through H when I is present, versus A through H when J is present. Is there anything interesting to take into ac... | null | CC BY-SA 2.5 | null | 2010-08-30T16:54:55.467 | 2010-08-30T16:54:55.467 | null | null | 1080 | null |
2216 | 2 | null | 2072 | 4 | null | Although it may only be of little help, the problem you present to me is synonymous with the "[Change of Support](http://dx.doi.org/10.1198/016214502760047140)" problem encountered when using areal units. Although this work just presents a framework for what you describe as "reglarize and interpolate" using a method re... | null | CC BY-SA 2.5 | null | 2010-08-30T17:42:31.317 | 2010-08-30T17:42:31.317 | null | null | 1036 | null |
2217 | 2 | null | 423 | 226 | null | Another from [XKCD](http://xkcd.com/539/):
Mentioned [here](http://www.stat.columbia.edu/~cook/movabletype/archives/2009/02/cartoon.html) and [here](http://www.cerebralmastication.com/2009/02/box-plot-vs-violin-plot-in-r/).
| null | CC BY-SA 3.0 | null | 2010-08-30T18:02:22.737 | 2014-08-16T17:48:56.870 | 2014-08-16T17:48:56.870 | 3807 | 5 | null |
2218 | 2 | null | 2213 | 67 | null | [Feed-forward](http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.multil.jpg) ANNs allow signals to travel one way only: from input to output. There are no feedback (loops); i.e., the output of any layer does not affect that same layer. Feed-forward ANNs tend to be straightforward networks that associate ... | null | CC BY-SA 4.0 | null | 2010-08-30T18:23:24.283 | 2019-01-08T20:14:05.063 | 2019-01-08T20:14:05.063 | 79696 | 339 | null |
2219 | 1 | 2221 | null | 5 | 4414 | General question: Given a dartboard of unit radius, what's the probability that a dart randomly lands within a circle of radius 1/3 centered inside the dartboard?
Standard answer: The dart is thrown such that it hits each point with equal likelihood. The probability that it lands within the inner circle is the ratio of... | Two answers to the dartboard problem | CC BY-SA 2.5 | null | 2010-08-30T18:42:30.753 | 2010-08-31T13:43:39.357 | 2010-08-31T13:43:39.357 | 8 | 401 | [
"probability",
"games"
] |
2220 | 1 | 2222 | null | 9 | 9248 | Permutation tests are significance tests based on permutation resamples drawn at random from the original data. Permutation resamples are drawn without replacement, in contrast to bootstrap samples, which are drawn with replacement. Here is [an example I did in R](https://stackoverflow.com/questions/2449226/randomized-... | How do we create a confidence interval for the parameter of a permutation test? | CC BY-SA 4.0 | null | 2010-08-30T18:47:48.040 | 2018-12-13T15:08:07.167 | 2018-12-13T15:08:07.167 | 339 | 339 | [
"confidence-interval",
"bootstrap",
"permutation-test"
] |
2221 | 2 | null | 2219 | 3 | null | Intuitively, imagine modeling the second formulation as follows: randomly select an angle to the $x$-axis, calling it $\theta$, then model the location of the dart as falling uniformly in a very thin rectangle along the line $y = (\tan\theta) x$. Approximately, the dart is in the inner circle with probability $1/3$. H... | null | CC BY-SA 2.5 | null | 2010-08-30T18:53:38.447 | 2010-08-30T18:53:38.447 | null | null | 795 | null |
2222 | 2 | null | 2220 | 7 | null | It's OK to use permutation resampling. It really depends on a number of factors. If your permutations are a relatively low number then your estimation of your confidence interval is not so great with permutations. Your permutations are in somewhat of a gray area and probably are fine.
The only difference from your p... | null | CC BY-SA 2.5 | null | 2010-08-30T19:49:10.880 | 2010-08-30T20:24:38.670 | 2010-08-30T20:24:38.670 | 601 | 601 | null |
2223 | 1 | null | null | 1 | 208 | I would like to know if anyone could recommend a book that deals more with the practical issues around conducting a meta-analysis?
Thanking you in advance
Andrew Vitiello
| Books covering how to conduct a meta-anlysis | CC BY-SA 2.5 | null | 2010-08-30T19:54:28.290 | 2010-08-30T20:33:07.587 | null | null | 431 | [
"meta-analysis"
] |
2224 | 2 | null | 2223 | 4 | null | I asked this question last week and obtained two excellent answers. The question is readily accessible through links on your "meta-analysis" tag. Here's the URL:
[Looking for good introductory treatment of meta-analysis](https://stats.stackexchange.com/questions/1963/looking-for-good-introductory-treatment-of-meta-an... | null | CC BY-SA 2.5 | null | 2010-08-30T20:33:07.587 | 2010-08-30T20:33:07.587 | 2017-04-13T12:44:52.277 | -1 | 919 | null |
2225 | 2 | null | 2219 | 1 | null | Think of the board as a filter -- it just converts the positions on board into an id of a field that dart hit. So that the output will be only a deterministically converted input -- and thus it is obvious that different realization of throwing darts will result in distribution of results.
The paradox itself is purely l... | null | CC BY-SA 2.5 | null | 2010-08-30T21:07:57.217 | 2010-08-30T21:07:57.217 | null | null | null | null |
2226 | 2 | null | 2219 | 3 | null | It seems to me that the fundamental issue is that the two scenarios assume different data generating process for the position of a dart which results in different probabilities.
The first situation's data generating process looks like so: (a) Pick a $x \in U[-1,1]$ and (b) Pick a $y$ uniformly subject to the constrain... | null | CC BY-SA 2.5 | null | 2010-08-30T22:37:36.583 | 2010-08-30T22:37:36.583 | null | null | null | null |
2227 | 2 | null | 423 | 97 | null | There is [this one](http://www.isds.duke.edu/~mw/ABS04/Lecture_Slides/4.Stats_Regression.pdf) on Bayesian learning:
| null | CC BY-SA 3.0 | null | 2010-08-30T23:04:11.447 | 2012-05-04T22:21:31.813 | 2012-05-04T22:21:31.813 | 919 | 881 | null |
2228 | 2 | null | 2104 | 2 | null | ez has now been updated to version 2.0. Among other improvements, the bug that caused it to fail to work for this example has been fixed.
| null | CC BY-SA 2.5 | null | 2010-08-31T00:03:12.787 | 2010-08-31T00:03:12.787 | null | null | 364 | null |
2229 | 2 | null | 1531 | 7 | null | There is no single exact confidence interval for the ratio of two proportions. Generally speaking, an exact 95% confidence interval is any interval-generating procedure that guarantees at least 95% coverage of the true ratio, irrespective of the values of the underlying proportions.
An interval formed by the Fisher Exa... | null | CC BY-SA 2.5 | null | 2010-08-31T00:32:34.883 | 2010-08-31T02:24:01.933 | 2010-08-31T02:24:01.933 | 1122 | 1122 | null |
2230 | 1 | 2232 | null | 104 | 49356 | I've never really grokked the difference between these two measures of convergence. (Or, in fact, any of the different types of convergence, but I mention these two in particular because of the Weak and Strong Laws of Large Numbers.)
Sure, I can quote the definition of each and give an example where they differ, but I ... | Convergence in probability vs. almost sure convergence | CC BY-SA 2.5 | null | 2010-08-31T03:57:21.193 | 2022-11-05T12:15:45.517 | 2010-08-31T08:21:26.447 | null | 1106 | [
"probability",
"random-variable"
] |
2231 | 2 | null | 2230 | 7 | null | I understand it as follows,
Convergence in probability
The probability that the sequence of random variables equals the target value is asymptotically decreasing and approaches 0 but never actually attains 0.
Almost Sure Convergence
The sequence of random variables will equal the target value asymptotically but you can... | null | CC BY-SA 2.5 | null | 2010-08-31T04:39:45.463 | 2018-10-23T18:33:37.603 | 2018-10-23T18:33:37.603 | 7290 | null | null |
2232 | 2 | null | 2230 | 110 | null | From my point of view the difference is important, but largely for philosophical reasons. Assume you have some device, that improves with time. So, every time you use the device the probability of it failing is less than before.
Convergence in probability says that the chance of failure goes to zero as the number o... | null | CC BY-SA 2.5 | null | 2010-08-31T06:53:32.093 | 2010-10-02T04:41:28.330 | 2010-10-02T04:41:28.330 | 352 | 352 | null |
2233 | 2 | null | 1531 | 13 | null | Check out the R [Epi](http://cran.r-project.org/web/packages/Epi/index.html) and [epitools](http://cran.r-project.org/web/packages/epitools/index.html) packages, which include many functions for computing exact and approximate CIs/p-values for various measures of association found in epidemiological studies, including ... | null | CC BY-SA 2.5 | null | 2010-08-31T07:47:14.557 | 2010-08-31T11:14:57.893 | 2010-08-31T11:14:57.893 | 930 | 930 | null |
2234 | 1 | 2235 | null | 59 | 18867 | I would like as many algorithms that perform the same task as logistic regression. That is algorithms/models that can give a prediction to a binary response (Y) with some explanatory variable (X).
I would be glad if after you name the algorithm, if you would also show how to implement it in R. Here is a code that ca... | Alternatives to logistic regression in R | CC BY-SA 3.0 | null | 2010-08-31T10:02:07.947 | 2016-09-26T17:18:55.707 | 2016-09-26T17:18:55.707 | 7290 | 253 | [
"r",
"regression",
"logistic",
"classification",
"predictive-models"
] |
2235 | 2 | null | 2234 | 30 | null | Popular right now are randomForest and gbm (called MART or Gradient Boosting in machine learning literature), rpart for simple trees. Also popular is bayesglm, which uses MAP with priors for regularization.
```
install.packages(c("randomForest", "gbm", "rpart", "arm"))
library(randomForest)
library(gbm)
library(rpart... | null | CC BY-SA 2.5 | null | 2010-08-31T10:13:21.270 | 2010-08-31T10:13:21.270 | null | null | 1119 | null |
2236 | 2 | null | 2234 | 15 | null | I agree with Joe, and would add:
Any classification method could in principle be used, although it will depend on the data/situation. For instance, you could also use a SVM, possibly with the popular C-SVM model. Here's an example from kernlab using a radial basis kernel function:
```
library(kernlab)
x <- rbind(matr... | null | CC BY-SA 2.5 | null | 2010-08-31T13:02:43.247 | 2010-08-31T13:02:43.247 | null | null | 5 | null |
2237 | 1 | null | null | 4 | 531 | My question is based on the "forecast" package for R used in [Forecasting with Exponential Smoothing. The State Space Approach](http://rads.stackoverflow.com/amzn/click/3540719164) - Hyndman et al. 2008. I am using the `ets` function to estimate the parameters of a model.
Is there a way to obtain standard errors for ... | Standard errors for estimates of smoothing parameters | CC BY-SA 3.0 | null | 2010-08-31T14:26:41.777 | 2012-09-02T02:55:29.943 | 2012-09-02T02:55:29.943 | 3826 | 443 | [
"time-series",
"forecasting"
] |
2238 | 2 | null | 2237 | 4 | null | Not all methods lead to analytic expressions (preferably based on proper asymptotic results) that provides this.
But the bootstrap allows you to approximate this via simulation. In essence, you generate (lots of) surrogate 'fake' data sets, employ your estimator on each of these and then use the population of your esti... | null | CC BY-SA 2.5 | null | 2010-08-31T14:30:58.947 | 2010-08-31T14:30:58.947 | null | null | 334 | null |
2239 | 2 | null | 2234 | 25 | null | Actually, that depends on what you want to obtain. If you perform logistic regression only for the predictions, you can use any supervised classification method suited for your data. Another possibility : discriminant analysis ( lda() and qda() from package MASS)
```
r <- lda(y~x) # use qda() for quadratic discriminant... | null | CC BY-SA 2.5 | null | 2010-08-31T15:30:46.797 | 2010-08-31T15:30:46.797 | null | null | 1124 | null |
2240 | 2 | null | 2220 | 5 | null | As a permutation test is an exact test, giving you an exact p-value. Bootstrapping a permutation test doesn't make sense.
Next to that, determining a confidence interval around a test statistic doesn't make sense either, as it is calculated based on your sample and not an estimate. You determine confidence intervals a... | null | CC BY-SA 3.0 | null | 2010-08-31T15:55:59.283 | 2012-06-13T12:06:40.830 | 2017-05-23T12:39:26.523 | -1 | 1124 | null |
2241 | 2 | null | 423 | 53 | null | I found this [from a NoSQL presentation](http://www.erlang-factory.com/upload/presentations/282/neo4j-is-not-erlang-but-i-still-heart-you-2010-06-10.pdf), but the cartoon can be found directly at
[http://browsertoolkit.com/fault-tolerance.png](http://browsertoolkit.com/fault-tolerance.png)
 My favorite was created by Emanuel Parzen, appearing in [IMA preprint 663](http://www.ima.umn.edu/preprints/July90Series/663.pdf), but this illustrates my degenerate sense of humor.
Gorbachev says to Bush: "that's a very nice golfcar... | null | CC BY-SA 2.5 | null | 2010-08-31T17:41:55.473 | 2010-08-31T17:41:55.473 | null | null | 795 | null |
2244 | 1 | 2246 | null | 9 | 1987 | What is the best package to to do some survival analysis and plots in R? I have tried some tutorials but I couldn't find a definite answer.
TIA
| Kaplan-Meier, survival analysis and plots in R | CC BY-SA 2.5 | null | 2010-08-31T18:56:09.437 | 2016-06-26T20:59:39.213 | 2010-09-16T12:33:07.553 | null | 1088 | [
"r",
"data-visualization",
"survival"
] |
2245 | 1 | 2251 | null | 62 | 6671 | In his 1984 paper ["Statistics and Causal Inference"](http://www-unix.oit.umass.edu/~stanek/pdffiles/causal-holland.pdf), Paul Holland raised one of the most fundamental questions in statistics:
>
What can a statistical model say about
causation?
This led to his motto:
>
NO CAUSATION WITHOUT MANIPULATION
which ... | Statistics and causal inference? | CC BY-SA 2.5 | null | 2010-08-31T19:13:04.883 | 2018-12-25T22:19:26.480 | 2010-09-16T06:32:59.970 | null | 5 | [
"causality"
] |
2246 | 2 | null | 2244 | 6 | null | Try CRAN Task View: [http://cran.at.r-project.org/web/views/Survival.html](http://cran.at.r-project.org/web/views/Survival.html)
| null | CC BY-SA 2.5 | null | 2010-08-31T19:41:55.037 | 2010-08-31T19:41:55.037 | null | null | null | null |
2247 | 2 | null | 2244 | 11 | null | I think that it's fair to say that the [survival](http://cran.r-project.org/web/packages/survival/) package is the "recommended" package in general, as it's included in base R (i.e. does not need to be installed separately). There are many good tutorials online for this. But you need to be more specific to get a more... | null | CC BY-SA 2.5 | null | 2010-08-31T19:48:40.107 | 2010-08-31T19:48:40.107 | null | null | 5 | null |
2248 | 1 | null | null | 7 | 7949 | I have a series of observations that fall into bins (or "scores"); that is, the data can be 0, 1, 2, 3 or 4. There are two groups of such data, control and treated. I know the number of individuals with each score for each group.
What is the best way to determine whether these groups are different or not?
A colleag... | How to test group differences on a five point variable? | CC BY-SA 3.0 | null | 2010-08-31T20:57:50.950 | 2013-04-26T12:52:46.923 | 2013-04-26T12:52:46.923 | 183 | null | [
"nonparametric",
"statistical-significance",
"discrete-data",
"scales"
] |
2249 | 2 | null | 2248 | 5 | null | Three things come to mind:
- Contingency table analysis using Fisher's exact test or Chi Square (but will only tell you that somewhere in the table there is a difference that is significant. You'd have to visualize your data or do post-hoc tests to know where this difference is.) Not my preferred solution.
- A non-pa... | null | CC BY-SA 2.5 | null | 2010-08-31T21:33:24.810 | 2010-09-01T01:57:27.007 | 2010-09-01T01:57:27.007 | 561 | 561 | null |
2250 | 2 | null | 2248 | 6 | null | What you are looking for seems to be a test for comparing two groups where observations are kind of ordinal data. In this case, I would suggest to apply a trend test to see if there are any differences between the CTL and TRT group.
Using a t-test would not acknowledge the fact your data are discrete, and the Gaussian... | null | CC BY-SA 2.5 | null | 2010-08-31T21:49:30.223 | 2010-09-01T14:32:30.520 | 2017-04-13T12:44:48.803 | -1 | 930 | null |
2251 | 2 | null | 2245 | 33 | null | This is a broad question, but given the Box, Hunter and Hunter quote is true I think what it comes down to is
- The quality of the experimental design:
randomization, sample sizes, control of confounders,...
- The quality of the implementation of the design:
adherance to protocol, measurement error, data handling,... | null | CC BY-SA 3.0 | null | 2010-08-31T23:26:46.003 | 2016-09-06T21:28:32.410 | 2016-09-06T21:28:32.410 | 49647 | 1107 | null |
2252 | 2 | null | 2230 | 6 | null | If you enjoy visual explanations, there was a nice ['Teacher's Corner' article](http://dx.doi.org/doi:10.1198/tas.2009.0032) on this subject in the American Statistician (cite below). As a bonus, the authors included an [R package](http://www.biostatisticien.eu/ConvergenceConcepts/) to facilitate learning.
```
@articl... | null | CC BY-SA 2.5 | null | 2010-09-01T00:00:38.753 | 2010-09-01T00:23:54.000 | 2010-09-01T00:23:54.000 | 159 | 1107 | null |
2253 | 2 | null | 2248 | 4 | null | This question is a little unusual because the nature of "different" is unspecified. This response is formulated in the spirit of trying to detect as many kinds of differences as possible, not just changes of location ("trend").
One approach that might have more power than most, while remaining agnostic about the relat... | null | CC BY-SA 2.5 | null | 2010-09-01T00:27:21.270 | 2010-09-01T00:27:21.270 | null | null | 919 | null |
2254 | 5 | null | null | 0 | null |
# Usage on CV
`R`-based questions are frequently migrated between [Cross Validated](http://stats.stackexchange.com/) (CV) and [Stack Overflow](http://stackoverflow.com/) (SO). CV fields questions with statistical content or of statistical interest and SO fields questions of programming and implementation.
Your quest... | null | CC BY-SA 4.0 | null | 2010-08-30T10:31:13.000 | 2022-07-26T19:57:40.550 | 2022-07-26T19:57:40.550 | 919 | null | null |
2255 | 2 | null | 93 | 3 | null | This is probably a stupid answer (I am new here), but if you want to estimate the hazard function from observations of an initial population that slowly died away (i.e. had events and then were censored), isn't that what the Nelson-Aalen estimator was built to do?
We could have another conversation about the reliabilit... | null | CC BY-SA 2.5 | null | 2010-09-01T03:35:33.823 | 2010-09-01T03:35:33.823 | null | null | 1122 | null |
2256 | 1 | 2257 | null | 5 | 5395 | I have a dataset forwhich i have performed an mds and visualized the results using scatterplot3d library. However i would like to see the names of the points on the 3d plot. How do i accomplish that? Each column belongs to a certain group i would like to see which points belong to which groups on the 3dplot.
```
#gener... | Adding labels to points using mds and scatter3d package with R | CC BY-SA 2.5 | null | 2010-09-01T05:55:30.923 | 2010-09-18T21:56:35.090 | 2010-09-18T21:56:35.090 | 930 | 18462 | [
"r",
"multidimensional-scaling"
] |
2257 | 2 | null | 2256 | 5 | null | Basically, what you need is to store your `scatterplot3d` in a variable and reuse it like this:
```
x <- replicate(10,rnorm(100))
x.mds <- cmdscale(dist(x), eig=TRUE, k=3)
s3d <- scatterplot3d(x.mds$points[,1:3])
text(s3d$xyz.convert(0,0,0), labels="Origin")
```
Replace the coordinates and text by whatever you want to... | null | CC BY-SA 2.5 | null | 2010-09-01T06:11:00.007 | 2010-09-01T06:11:00.007 | null | null | 930 | null |
2258 | 1 | 2279 | null | 1 | 433 | Given a function mapping between two sample spaces $S_1$ and $S_2$, if $S_2$,$F_2$ is measurable how do I show that preimage of $S_2$,$F_2$ in $S_1$ is measurable set?
| How to prove that preimage of measurable space is measurable? | CC BY-SA 2.5 | null | 2010-09-01T07:09:34.870 | 2010-09-02T00:32:21.437 | 2010-09-02T00:32:21.437 | 159 | 862 | [
"probability"
] |
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