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4706 | 2 | null | 4700 | 8 | null | Not really a formal definition, but I like the following slides: [Mixed models and why sociolinguists should use them](http://www.danielezrajohnson.com/johnson_panel.pdf), from Daniel Ezra Johnson. A brief recap' is offered on slide 4. Although it mostly focused on psycholinguistic studies, it is very useful as a first... | null | CC BY-SA 4.0 | null | 2010-11-19T07:50:50.317 | 2022-02-12T22:20:23.720 | 2022-02-12T22:20:23.720 | 919 | 930 | null |
4707 | 1 | null | null | 1 | 1957 | As we know, we can get the same eigenvector if we apply PCA to the same data. But, is it possible that we get the same eigenvectors after we apply PCA to two totally different data sets (still same dimension)?
| Can two different data sets get the same eigenvector in PCA? | CC BY-SA 2.5 | null | 2010-11-19T08:52:54.817 | 2011-12-05T08:31:49.897 | 2010-11-26T17:43:38.080 | 919 | null | [
"pca"
] |
4708 | 1 | null | null | 12 | 22584 | I am looking for a method to use to test for equality of two cumulative density functions.
| Comparing two cumulative density functions | CC BY-SA 2.5 | null | 2010-11-19T08:58:02.683 | 2010-11-19T13:29:47.970 | 2010-11-19T09:10:19.747 | 159 | null | [
"distributions",
"hypothesis-testing"
] |
4709 | 2 | null | 4708 | 3 | null | Plot their inverses against one another, i.e. make a quantile-quantile plot:
[http://en.wikipedia.org/wiki/Q-Q_plot](http://en.wikipedia.org/wiki/Q-Q_plot)
| null | CC BY-SA 2.5 | null | 2010-11-19T09:01:45.890 | 2010-11-19T09:01:45.890 | null | null | 2036 | null |
4710 | 2 | null | 4708 | 3 | null | Take a look at the [Kolmogorov–Smirnov test](http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test) ([ks.test](http://sekhon.berkeley.edu/stats/html/ks.test.html) in R.)
| null | CC BY-SA 2.5 | null | 2010-11-19T09:05:05.633 | 2010-11-19T09:05:05.633 | null | null | 439 | null |
4711 | 2 | null | 4707 | 6 | null | Any pure rotation of the dataset would also give the same set of principal components, in which case the answer would be trivially "yes", depending on the definition of "totally different" (arguably if two datasets have the same principal components then they can't be "totally" different).
| null | CC BY-SA 3.0 | null | 2010-11-19T09:08:43.633 | 2011-12-05T08:31:49.897 | 2011-12-05T08:31:49.897 | 930 | 887 | null |
4712 | 2 | null | 4551 | 34 | null | Something I see a surprising amount in conference papers and even journals is making multiple comparisons (e.g. of bivariate correlations) and then reporting all the p<.05s as "significant" (ignoring the rightness or wrongness of that for the moment).
I know what you mean about psychology graduates, as well- I've finis... | null | CC BY-SA 2.5 | null | 2010-11-19T09:49:52.633 | 2010-11-19T09:49:52.633 | null | null | 199 | null |
4713 | 1 | 4720 | null | 31 | 16510 | I have used the following r code to estimate the confidence intervals of a binomial proportion because I understand that that substitutes for a "power calculation" when designing receiver operating characteristic curve designs looking at detection of diseases in a population.
n is 150, and the disease, we believe, is 2... | Binomial confidence interval estimation - why is it not symmetric? | CC BY-SA 4.0 | null | 2010-11-19T10:01:37.860 | 2019-12-17T05:01:49.850 | 2019-12-17T05:01:49.850 | 92235 | 199 | [
"confidence-interval",
"binomial-distribution"
] |
4714 | 2 | null | 4713 | 7 | null | Binomial distribution is just not symmetric, yet this fact emerges especially for $p$ near $0$ or $1$ and for small $n$; most people use it for $p\approx 0.5$ and so the confusion.
| null | CC BY-SA 2.5 | null | 2010-11-19T10:12:28.887 | 2010-11-19T11:01:47.507 | 2010-11-19T11:01:47.507 | 930 | null | null |
4716 | 2 | null | 4713 | 27 | null | To see why it should not be symmetric, think of the situation where $p=0.9$ and you get 9 successes in 10 trials. Then $\hat{p}=0.9$ and the 95% CI for $p$ is [0.554, 0.997]. The upper limit cannot be greater than 1 obviously, so most of the uncertainty must fall to the left of $\hat{p}$.
| null | CC BY-SA 2.5 | null | 2010-11-19T11:13:46.303 | 2010-11-19T11:13:46.303 | null | null | 159 | null |
4717 | 1 | null | null | 68 | 132198 | In the literature on hierarchical/multilevel models I have often read about "nested models" and "non-nested models", but what does this mean? Could anyone maybe give me some examples or tell me about the mathematical implications of this phrasing?
| What is the difference between a "nested" and a "non-nested" model? | CC BY-SA 3.0 | null | 2010-11-19T11:32:02.027 | 2017-04-15T22:15:37.157 | 2017-04-15T20:49:28.490 | 28666 | 1082 | [
"hypothesis-testing",
"terminology",
"nested-models",
"nested-data"
] |
4719 | 2 | null | 4717 | 39 | null | Nested versus non-nested can mean a whole lot of things. You have nested designs versus crossed designs (see eg [this explanation](http://www.psychstat.missouristate.edu/introbook/sbk21m.htm)). You have nested models in model comparison. Nested means here that all terms of a smaller model occur in a larger model. This ... | null | CC BY-SA 2.5 | null | 2010-11-19T12:01:19.740 | 2010-11-19T12:01:19.740 | null | null | 1124 | null |
4720 | 2 | null | 4713 | 22 | null | They're believed to be symmetric because quite often a normal approximation is used. This one works well enough in case p lies around 0.5. `binom.test` on the other hand reports "exact" Clopper-Pearson intervals, which are based on the F distribution (see [here](http://people.ee.duke.edu/~kst/ECE257/confbin.pdf) for th... | null | CC BY-SA 3.0 | null | 2010-11-19T12:44:10.127 | 2017-07-31T15:27:39.443 | 2017-07-31T15:27:39.443 | 7290 | 1124 | null |
4721 | 2 | null | 4708 | 4 | null | The QQ-plot and the Kolmogorov-Smirnov test are two widely used options. A QQ-plot requires some level of expertise, as the decision is based on your own judgement. See also the answers to [this question](https://stats.stackexchange.com/questions/2492/normality-testing-essentially-useless/2498#2498) for more discussion... | null | CC BY-SA 2.5 | null | 2010-11-19T12:53:56.033 | 2010-11-19T12:53:56.033 | 2017-04-13T12:44:37.583 | -1 | 1124 | null |
4722 | 2 | null | 4708 | 1 | null | Lately I've been playing with comparing distributions by computing the difference between their empirical CDFs and then bootstrapping intervals on this difference. Differences between the distributions in location, scale, and each tail all have different and rather noticeable effects on the DECDF function.
| null | CC BY-SA 2.5 | null | 2010-11-19T13:16:41.517 | 2010-11-19T13:16:41.517 | null | null | 364 | null |
4723 | 2 | null | 4708 | 5 | null | Might be worth looking at some variant of the [Anderson-Darling](http://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test) or [Cramer-von Mises](http://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93von-Mises_criterion) statistics. The latter is essentially a weighted least-squares distance between two CDFs.
| null | CC BY-SA 2.5 | null | 2010-11-19T13:29:47.970 | 2010-11-19T13:29:47.970 | null | null | 887 | null |
4724 | 2 | null | 4717 | 13 | null | Nested vs non-nested models come up in conjoint analysis and [IIA](http://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives). Consider the "red bus blue bus problem". You have a population where 50% of people take a car to work and the other 50% take the red bus. What happens if you add a blue bus which has... | null | CC BY-SA 2.5 | null | 2010-11-19T13:33:31.053 | 2010-11-26T15:10:17.447 | 2010-11-26T15:10:17.447 | 696 | 696 | null |
4725 | 2 | null | 4713 | 9 | null | @Joris mentioned the symmetric or "asymptotic" interval, that is most likely the one you are expecting. @Joris also mentioned the "exact" Clopper-Pearson intervals and gave you a reference which looks very nice. There is another confidence interval for proportions which you will likely encounter (note it is also not ... | null | CC BY-SA 2.5 | null | 2010-11-19T13:37:37.487 | 2010-11-19T13:37:37.487 | null | null | null | null |
4726 | 2 | null | 4707 | 2 | null | An eigenvector is just a statistic. You can get copies of almost any useful statistic from a wide variety of different data, as long as they are similar in the relevant manner.
The eigenvector represents a particular linear relationship between the variables. As long as you use variables with the same units and what ap... | null | CC BY-SA 2.5 | null | 2010-11-19T14:12:05.453 | 2010-11-19T14:12:05.453 | null | null | 2456 | null |
4727 | 1 | null | null | 5 | 420 | I am interested in comparing a non-linear model with up to 12 parameters to many datasets. However, each instance of the model takes a significant amount of time to compute (~1 hour), so I am pre-computing instances of the model for various parameter values and then comparing these to all the different datasets.
There ... | Non-linear model fitting in many dimensions | CC BY-SA 2.5 | null | 2010-11-19T14:30:36.020 | 2013-02-07T03:11:53.160 | null | null | 2052 | [
"modeling"
] |
4728 | 2 | null | 4685 | 5 | null | Based on the paper you linked to, I would argue that the term EM usually refers to the "soft" version. The key distinction seems to be that instead of taking an expectation in the E-step, the "hard" version finds a mode.
A good explanation of the distinction is available in chapters 20-22 of David Mackay's book (which ... | null | CC BY-SA 2.5 | null | 2010-11-19T14:31:20.210 | 2010-11-19T14:31:20.210 | null | null | 495 | null |
4729 | 1 | 4746 | null | 6 | 483 | I am about to do a laboratory experiment in the scientific field of soil ecology and hydrology. Beforehand I want to make sure not to make any crucial mistakes, and therefore I would appreciate any hints and comments from your side. The main issue is how to deal with high natural variability (~25%) and a rather small s... | How to setup a laboratory experiment in Ecological Research under high natural variability | CC BY-SA 3.0 | null | 2010-11-19T14:48:02.893 | 2016-08-12T17:32:40.960 | 2016-08-12T17:32:40.960 | 22468 | 2063 | [
"anova",
"mixed-model",
"experiment-design",
"statistical-power",
"degrees-of-freedom"
] |
4730 | 2 | null | 4686 | 4 | null | Despite promising not to, I have thought about this problem further. This approach differs enough from the previous one I outlined that it seems worthwhile posting it as a separate reply.
---
Both @Aniko and @shabbychef are right: you need to "almost exhaust the population" with "greedy sampling." But there's a tw... | null | CC BY-SA 2.5 | null | 2010-11-19T15:56:00.497 | 2010-11-22T15:43:17.257 | 2010-11-22T15:43:17.257 | 919 | 919 | null |
4731 | 2 | null | 4727 | 1 | null | My understanding is that the optimal methodology is going to depend on the surface texture of parametrization errors. That is, how often do parameters reflect or manifest as interactions? If each parameter is an individual value that has its own distinct minima independent of all other parameters, model fitting shoul... | null | CC BY-SA 2.5 | null | 2010-11-19T17:03:45.997 | 2010-11-19T17:03:45.997 | null | null | 196 | null |
4733 | 1 | null | null | 3 | 256 | Can you suggest a tutorial or book chapter on basics of data analysis with exponentially distributed data / exponential noise,
at undergraduate level?
By "basics" I mean:
- is a given set of data exponentially distributed?
- should one generally use median instead of mean for exponential data?
Should one simply trim ... | Basics of data analysis with exponential data/noise? | CC BY-SA 2.5 | null | 2010-11-19T17:53:49.017 | 2010-12-19T19:44:26.317 | 2010-11-19T18:07:59.837 | null | 557 | [
"robust",
"references"
] |
4734 | 1 | 4760 | null | 4 | 5493 | I know what you're thinking, this is a duplicate of "[What are the differences between Factor Analysis and Principal Component Analysis](https://stats.stackexchange.com/questions/1576/what-are-the-differences-between-factor-analysis-and-principal-component-analysis)", but it isn't really.
That other question deals with... | What is the difference between Exploratory Factor Analysis and Principal Components Analysis (PCA)? | CC BY-SA 2.5 | null | 2010-11-19T18:55:37.910 | 2010-12-13T04:50:07.943 | 2017-04-13T12:44:56.303 | -1 | 74 | [
"pca",
"factor-analysis"
] |
4735 | 1 | 4738 | null | 17 | 11693 | These terms get thrown around together a lot, but I would like to know what you think the differences are, if any.
Thanks
| What are the differences among latent semantic analysis (LSA), latent semantic indexing (LSI), and singular value decomposition (SVD)? | CC BY-SA 3.0 | null | 2010-11-19T19:01:58.203 | 2012-07-16T09:24:10.440 | 2012-07-16T09:24:10.440 | null | 74 | [
"pca",
"text-mining",
"svd"
] |
4736 | 2 | null | 4733 | 2 | null | One of the basic techniques for working with skewed positive data is to analyse it on the log-scale. However its appropriateness depends on what you are really trying to achieve.
| null | CC BY-SA 2.5 | null | 2010-11-19T19:28:52.357 | 2010-11-19T19:28:52.357 | null | null | 279 | null |
4737 | 1 | 4740 | null | 4 | 10331 | I have a class with a set of descriptive statistic functions (mean, median, kurtosis, etc...).
Now I need to include weight (array) into my equations. My first thought was to just create a weighted version of the functions where the additional weight array is passed.
However, I was wondering if there is a way to alter ... | How to add weight to data in descriptive statistics? | CC BY-SA 4.0 | null | 2010-11-19T19:33:02.400 | 2019-12-11T17:31:13.773 | 2019-12-11T17:31:13.773 | 18417 | 2060 | [
"descriptive-statistics",
"algorithms",
"weights"
] |
4738 | 2 | null | 4735 | 13 | null | LSA and LSI are mostly used synonymously, with the information retrieval community usually referring to it as LSI. LSA/LSI uses SVD to decompose the term-document matrix A into a term-concept matrix U, a singular value matrix S, and a concept-document matrix V in the form: A = USV'. The wikipedia page has a detailed de... | null | CC BY-SA 2.5 | null | 2010-11-19T20:00:45.343 | 2010-11-19T20:00:45.343 | null | null | 881 | null |
4739 | 2 | null | 4659 | 1 | null | In Bayesian land, the Beta distribution is the conjugate prior for the p parameter of the Binomial distribution.
| null | CC BY-SA 2.5 | null | 2010-11-19T20:26:32.220 | 2010-11-19T20:26:32.220 | null | null | 1860 | null |
4740 | 2 | null | 4737 | 5 | null | It isn't entirely clear from your question what sort of 'weight' you are talking about. But I imagine it is a simple matter of wanting to count certain observations more than than others...
If you wanted to, and your weights were integer values (or you can find the lowest common denominator to multiply by that will g... | null | CC BY-SA 2.5 | null | 2010-11-19T20:34:51.880 | 2010-11-19T20:34:51.880 | null | null | 196 | null |
4741 | 1 | 4743 | null | 2 | 1764 | I do a counting experiment where I count observations as a function of two float parameters $x_1$ and $x_2$. This leads to a two-dimensional histogram where each bin corresponds to the number of observations with $x_1$ and $x_2$ in some range.
I now see a lot of bins with zero counts in them (even though more counts ar... | Uncertainty on zero counts for binned result | CC BY-SA 2.5 | null | 2010-11-19T20:35:06.833 | 2010-11-20T04:59:03.040 | null | null | 56 | [
"confidence-interval",
"poisson-distribution"
] |
4742 | 2 | null | 4737 | 7 | null | Weights can arise in data analysis through various mechanisms, each of which requires its own formulas:
- A dataset with many duplicate results can be summarized by listing each unique result together with its frequency of occurrence. This is the definition @drknexus assumes in order to provide a definite answer (aft... | null | CC BY-SA 2.5 | null | 2010-11-19T21:49:43.513 | 2010-11-19T21:49:43.513 | null | null | 919 | null |
4743 | 2 | null | 4741 | 2 | null | Nothing wrong with what you've done so far. The null model includes only a constant, i.e. a flat event rate. Fitting more complex [Poisson regression](http://en.wikipedia.org/wiki/Poisson_regression) models will allow the expected value to vary. It's hard to tell what forms the more complex models should take as you've... | null | CC BY-SA 2.5 | null | 2010-11-19T21:59:27.513 | 2010-11-19T21:59:27.513 | null | null | 449 | null |
4744 | 2 | null | 4713 | 10 | null | There are symmetric confidence intervals for the Binomial distribution: asymmetry is not forced on us, despite all the reasons already mentioned. The symmetric intervals are usually considered inferior in that
- Although they are numerically symmetric, they are not symmetric in probability: that is, their one-tailed ... | null | CC BY-SA 2.5 | null | 2010-11-19T22:03:50.017 | 2010-11-19T22:03:50.017 | null | null | 919 | null |
4746 | 2 | null | 4729 | 3 | null | Whether you have a reasonable chance of obtaining (i.e. power to obtain) reliable conclusions depends on how big the effects are you wish to be able to detect. With such small numbers they'll have to be very large. Clearly having fewer treatments and more replications per treatment will give you at least a bit more pow... | null | CC BY-SA 2.5 | null | 2010-11-19T22:16:04.327 | 2010-11-19T23:09:37.230 | 2010-11-19T23:09:37.230 | 449 | 449 | null |
4750 | 2 | null | 4655 | 5 | null | It seems to me that if $f$ is strictly monotonic, $m \circ f=f \circ m$, and the question reduces to $\mu\circ f>f\circ\mu$, which is covered by Jensen's inequality. So strict convexity and strict monotonicity together would be a sufficient condition.
| null | CC BY-SA 2.5 | null | 2010-11-20T03:29:37.537 | 2010-12-01T05:56:23.050 | 2010-12-01T05:56:23.050 | 2456 | 2456 | null |
4751 | 2 | null | 4741 | 1 | null | Try running a nonparametric smoother (also called a kernel density estimate) over your data to estimate the expected value (and therefore proportion
If you do have covariate data, see how the nonparametric smooth compares to the regression model that onestop recommends. A parametric model is usually a lot less wigg... | null | CC BY-SA 2.5 | null | 2010-11-20T04:59:03.040 | 2010-11-20T04:59:03.040 | null | null | 5792 | null |
4752 | 2 | null | 4735 | 8 | null | Notably while LSA and LSI use SVD to do their magic, there is a computationally and conceptually simpler method called HAL (Hyperspace Analogue to Language) that sifts through text keeping track of preceding and subsequent contexts. Vectors are extracted from these (often weighted) co-occurrence matrices and specific ... | null | CC BY-SA 2.5 | null | 2010-11-20T07:05:49.040 | 2010-11-20T07:05:49.040 | null | null | 196 | null |
4753 | 1 | null | null | 8 | 2351 | I am interested in finding some practical (and reasonably well accepted) techniques for finding the underlying factors of a sparse matrix.
Specifically, I have a very large sparse matrix whose cells appear to be populated from an approximately geometric distribution. In its natural form the matrix is square. The va... | How can one extract meaningful factors from a sparse matrix? | CC BY-SA 2.5 | null | 2010-11-20T07:22:34.117 | 2011-05-26T15:05:23.787 | 2017-04-13T12:44:20.840 | -1 | 196 | [
"r",
"pca",
"factor-analysis",
"matrix-decomposition"
] |
4754 | 2 | null | 4597 | 2 | null | A moving standard deviation sounds like a reasonable thing to use... here is a toy example in poorly written untested poorly optimized pseudo-C, things may go out of bounds or not work as I expect, but you should get the general idea:
```
const int NPixelColumns; //The number of pixels columns
const int WindowSize; //T... | null | CC BY-SA 2.5 | null | 2010-11-20T07:53:17.650 | 2010-11-20T08:07:46.623 | 2010-11-20T08:07:46.623 | 196 | 196 | null |
4756 | 1 | null | null | 60 | 41084 | I have a random sample of Bernoulli random variables $X_1 ... X_N$, where $X_i$ are i.i.d. r.v. and $P(X_i = 1) = p$, and $p$ is an unknown parameter.
Obviously, one can find an estimate for $p$: $\hat{p}:=(X_1+\dots+X_N)/N$.
My question is how can I build a confidence interval for $p$?
| Confidence interval for Bernoulli sampling | CC BY-SA 3.0 | null | 2010-11-20T12:05:26.533 | 2022-06-09T03:28:28.347 | 2022-06-09T03:28:28.347 | 11887 | null | [
"confidence-interval",
"binomial-distribution",
"bernoulli-distribution",
"faq"
] |
4759 | 1 | 4782 | null | 8 | 1530 | just for curiosity...
What language is used most here?
R? MATLAB? Python? Java?
What for prototype or for production?
For example I think MATLAB is mostly used for prototyping, python for both prot. and production...
| What programming language for statistical inference? | CC BY-SA 2.5 | null | 2010-11-20T14:57:19.843 | 2016-06-12T06:52:39.940 | 2010-11-21T20:26:44.323 | null | 2046 | [
"r",
"matlab",
"python",
"java"
] |
4760 | 2 | null | 4734 | 5 | null | Essentially, principal components analysis breaks down the data into chunks which represent the variance of your matrix.
Factor analysis does the same, BUT it only examines the variance which is common to multiple items. Basically, EFA is a tool for determining latent structure, while PCA is a tool for reducing the num... | null | CC BY-SA 2.5 | null | 2010-11-20T16:31:27.420 | 2010-11-20T16:31:27.420 | null | null | 656 | null |
4761 | 2 | null | 4759 | 6 | null | It should be clear by [looking at the most popular tags](https://stats.stackexchange.com/tags) that R is the most popular language on this site. Whether that makes it the most popular language for statistical analysis can't be inferred directly, but one might suppose as much.
| null | CC BY-SA 2.5 | null | 2010-11-20T19:19:08.980 | 2010-11-20T19:19:08.980 | 2017-04-13T12:44:53.777 | -1 | 5 | null |
4762 | 1 | 7383 | null | 2 | 8532 | Some googling revealed that doing the F-test for Lack-of-Fit in SPSS is not so trivial. It seems one has to “trick” SPSS to do that. See for example [this](http://www.math.umt.edu/olear/STAT458/Lab%205.pdf). Can anybody suggest a better source of information on how this can be done? I have SPSS 16. Of course I know it ... | F-test for Lack-of-Fit in SPSS | CC BY-SA 2.5 | null | 2010-11-20T20:22:06.530 | 2011-02-18T20:40:13.133 | null | null | 339 | [
"regression",
"anova",
"spss"
] |
4763 | 2 | null | 4564 | 6 | null | GBP includes the junction tree algorithm as a special case, and since junction tree is exact, GBP will be exact whenever the region graph corresponds to a junction tree. This is the only general case where GBP is exact, as shown by Theorem 14 of [Pakzad and Anantharam (Neural Computation, 2005)](http://www.eecs.berkel... | null | CC BY-SA 2.5 | null | 2010-11-20T21:51:48.870 | 2010-11-20T23:51:23.590 | 2010-11-20T23:51:23.590 | 2074 | 2074 | null |
4765 | 2 | null | 4759 | 8 | null | Well, you can PAY for MATLAB, and then either (1) program the stuff you really need from the ground up or (2) PAY MORE for MATLAB toolboxes. And discover that doing useful statistics in MATLAB was an afterthought handled in the increasingly less useful Statistics Toolbox. Or...you can download R for FREE and search for... | null | CC BY-SA 2.5 | null | 2010-11-21T02:00:15.490 | 2010-11-21T02:00:15.490 | null | null | 5792 | null |
4766 | 1 | null | null | 7 | 3202 | Randomized SVD decomposes a matrix by extracting the first k singular values/vectors using k+p random projections. This works surprisingly well for large matrices.
My question concerns the singular values that are output from the algorithm. Why aren't the values equal to the first k-singular values if you do the full S... | Randomized SVD and singular values | CC BY-SA 2.5 | null | 2010-11-21T04:17:20.387 | 2010-11-28T16:01:55.277 | 2017-05-23T12:39:26.203 | -1 | 2078 | [
"matrix-decomposition",
"svd"
] |
4767 | 2 | null | 4695 | 2 | null | This is a pretty general problem in time series analysis. I'd probably start by looking at some descriptive statistics like the cross-correlation to see if the samples are roughly independent over time. You could also test whether the correlation between successive samples is significant.
Or you could go the model-fitt... | null | CC BY-SA 2.5 | null | 2010-11-21T04:25:37.277 | 2010-11-21T04:25:37.277 | null | null | 2077 | null |
4768 | 1 | 4772 | null | 27 | 17434 | I was asked this question during an interview for a trading position with a proprietary trading firm. I would very much like to know the answer to this question and the intuition behind it.
Amoeba Question:
A population of amoebas starts with 1. After 1 period that amoeba can divide into 1, 2, 3, or 0 (it can die) wit... | Amoeba Interview Question | CC BY-SA 4.0 | null | 2010-11-21T05:20:48.913 | 2020-10-05T21:42:31.727 | 2018-05-18T17:08:45.177 | 44269 | 2079 | [
"probability"
] |
4769 | 2 | null | 4768 | 7 | null | This sounds related to the [Galton Watson](http://en.wikipedia.org/wiki/Galton%E2%80%93Watson_process) process, originally formulated to study the survival of surnames. The probability depends on the expected number of sub-amoebas after a single division. In this case that expected number is $3/2,$ which is greater tha... | null | CC BY-SA 2.5 | null | 2010-11-21T05:45:09.687 | 2010-11-21T18:05:47.807 | 2010-11-21T18:05:47.807 | 795 | 795 | null |
4770 | 2 | null | 4267 | 2 | null | Witten, Tibshirani - Penalized matrix decomposition
[http://www.biostat.washington.edu/~dwitten/Papers/pmd.pdf](http://www.biostat.washington.edu/~dwitten/Papers/pmd.pdf)
[http://cran.r-project.org/web/packages/PMA/index.html](http://cran.r-project.org/web/packages/PMA/index.html)
Martinsson, Rokhlin, Szlam, Tygert - R... | null | CC BY-SA 2.5 | null | 2010-11-21T09:44:03.770 | 2010-11-22T19:18:52.707 | 2010-11-22T19:18:52.707 | 2078 | 2078 | null |
4771 | 2 | null | 2806 | 12 | null | you could trying using a couple of options.
1- Penalized Matrix Decomposition. You apply some penalty constraints on the u's and v's to get some sparsity. Quick algorithm that has been used on genomics data
See Whitten Tibshirani. They also have an R-pkg. " A penalized matrix decomposition, with applications to sparse ... | null | CC BY-SA 2.5 | null | 2010-11-21T09:56:02.610 | 2010-11-21T09:56:02.610 | null | null | 2078 | null |
4772 | 2 | null | 4768 | 38 | null | Cute problem. This is the kind of stuff that probabilists do in their heads for fun.
The technique is to assume that there is such a probability of extinction, call it $P$. Then, looking at a one-deep decision tree for the possible outcomes we see--using the Law of Total Probability--that
$P=\frac{1}{4} + \frac{1}{4}P... | null | CC BY-SA 2.5 | null | 2010-11-21T11:47:10.303 | 2010-11-21T18:41:24.833 | 2010-11-21T18:41:24.833 | null | 5792 | null |
4773 | 2 | null | 4768 | 22 | null | Some back of the envelope calculation (litterally - I had an envelope lying around on my desk) gives me a probability of 42/111 (38%) of never reaching a population of 3.
I ran a quick Python simulation, seeing how many populations had died off by 20 generations (at which point they usually either died out or are in th... | null | CC BY-SA 2.5 | null | 2010-11-21T11:48:51.067 | 2010-11-21T11:48:51.067 | null | null | 1737 | null |
4774 | 2 | null | 4172 | 1 | null | First of all, a question if interest: If you want the measurements not to differ significantly, why change the tool at all? Simply to get more frequent measurements, or for economical reasons?
Now for the reply.
I do not entirely understand how you gathered the data. You say both instruments were colocated, and that in... | null | CC BY-SA 2.5 | null | 2010-11-21T15:17:02.290 | 2010-11-21T15:17:02.290 | null | null | 2456 | null |
4775 | 1 | 4776 | null | 27 | 13360 | I was wondering if it is possible to do symbolic computation in R?
For example,
I was hoping to get the inverse of a symbolic covariance matrix of 3D Gaussian distribution.
Also can I do symbolic integration and differentiation in R?
| Symbolic computation in R? | CC BY-SA 4.0 | null | 2010-11-21T16:24:16.763 | 2019-01-26T23:44:32.410 | 2019-01-26T23:44:32.410 | 11887 | 1005 | [
"r"
] |
4776 | 2 | null | 4775 | 22 | null | Yes. There is the [Ryacas package](http://cran.r-project.org/web/packages/Ryacas/index.html) which is hosted on Google Code [here](http://code.google.com/p/ryacas/). Ryacas has recently been expanded/converted to the rMathpiper package which is hosted [here](http://code.google.com/p/rmathpiper/). I have used Ryacas ... | null | CC BY-SA 2.5 | null | 2010-11-21T16:35:20.947 | 2010-11-21T16:35:20.947 | null | null | null | null |
4777 | 2 | null | 4775 | 19 | null | Some things are also in base R --- see `help(deriv)` or `help(D)`.
A simple example from that help page:
```
R> trig.exp <- expression(sin(cos(x + y^2)))
R> ( D.sc <- D(trig.exp, "x") )
-(cos(cos(x + y^2)) * sin(x + y^2))
R> all.equal(D(trig.exp[[1]], "x"), D.sc)
[1] TRUE
R>
```
| null | CC BY-SA 2.5 | null | 2010-11-21T17:29:00.630 | 2010-11-21T17:29:00.630 | null | null | 334 | null |
4778 | 2 | null | 4775 | 6 | null | It makes more sense to use a "real" CAS like [Maxima](http://en.wikipedia.org/wiki/Maxima_%28software%29).
| null | CC BY-SA 2.5 | null | 2010-11-21T17:51:35.997 | 2010-11-21T23:40:42.427 | 2010-11-21T23:40:42.427 | 449 | 1966 | null |
4779 | 2 | null | 4700 | 18 | null | The distinction is only meaningful in the context of non-Bayesian statistics. In Bayesian statistics, all model parameters are "random".
| null | CC BY-SA 2.5 | null | 2010-11-21T18:00:46.553 | 2010-11-21T18:00:46.553 | null | null | 1966 | null |
4780 | 2 | null | 4766 | 4 | null | I do not think the singular values should match those of the full matrix. You are computing an approximation of the input matrix by projection onto $k+p$ random vectors. For a rank $k+p$ matrix to approximate a rank $n \gg k+p$ matrix, the trace should probably be the same, but then if the first $k$ singular values are... | null | CC BY-SA 2.5 | null | 2010-11-21T18:37:03.600 | 2010-11-21T18:37:03.600 | null | null | 795 | null |
4781 | 2 | null | 4267 | 3 | null | Maybe, you can find interesting
- [Learning with Matrix Factorizations] PhD thesis by Nathan Srebro,
- [Investigation of Various Matrix Factorization Methods for Large Recommender Systems], Gábor Takács et.al. and almost the same technique described here
The last two links show how sparse matrix factorizations ar... | null | CC BY-SA 2.5 | null | 2010-11-21T19:28:40.950 | 2010-11-23T09:02:09.487 | 2010-11-23T09:02:09.487 | 1725 | 1725 | null |
4782 | 2 | null | 4759 | 7 | null | I couldnt agree more with a vote for R. R is the "Lingua Franca" of the statistics world. It is the definition of cutting edge, while most packages for MATLAB and SAS take several months. The language is very simple to understand as opposed to SAS. It also gives you the power to connect with C/C++/Python and databases.... | null | CC BY-SA 2.5 | null | 2010-11-21T21:02:25.647 | 2010-11-21T21:02:25.647 | null | null | 2078 | null |
4783 | 1 | null | null | 21 | 15046 | I have some cumulative frequency data. A line $y=ax+b$ looks like it fits the data extremely well, but there is cyclic/periodic wiggle in the line. I would like to estimate when the cumulative frequency will reach a certain value $c$. When I plot the residuals vs. fitted values, I get a beautiful sinusoidal behavior.
... | How to add periodic component to linear regression model? | CC BY-SA 2.5 | null | 2010-11-21T21:21:46.837 | 2016-09-30T16:01:15.320 | 2010-11-21T23:08:42.967 | null | 2083 | [
"time-series",
"regression"
] |
4784 | 2 | null | 4783 | 9 | null | You could try the wonderful `stl()` method -- it decomposes (using iterated `loess()` fitting) into trend and seasonal and remainder. This may just pick up your oscillations here.
| null | CC BY-SA 2.5 | null | 2010-11-21T21:55:09.817 | 2010-11-21T21:55:09.817 | null | null | 334 | null |
4785 | 2 | null | 4783 | 8 | null | If you know the frequency of the oscillation, you can include two additional predictors, sin(2π w t) and cos(2π w t) -- set w to get the desired wavelength -- and this will model the oscillation. You need both terms to fit the amplitude and the phase angle. If there is more than one frequency, you will need a sine an... | null | CC BY-SA 2.5 | null | 2010-11-21T22:57:47.480 | 2010-11-21T22:57:47.480 | null | null | 5792 | null |
4786 | 1 | null | null | 5 | 1202 | I am looking at using Interior Point method for optimizing a convex function. The convex function is basically the log-likelihood of a binary logistic regression model. Can I use this technique?
In generally, is there anything that prevents applying a constrained optimization technique to an unconstrained problem? From... | Can constrained optimization techniques be applied to unconstrained problems? | CC BY-SA 2.5 | null | 2010-11-21T23:09:28.083 | 2010-11-22T12:52:59.547 | 2010-11-21T23:10:19.877 | null | 2071 | [
"optimization"
] |
4787 | 2 | null | 4786 | 3 | null | As far as I know, there is no reason to stop you from applying constrained optimization to an unconstrainted problem. However, this may not be a great idea in terms of computational complexity and convergence. For example, fitting a logistic regression model can done efficiently with the Newton-Raphson approach (or the... | null | CC BY-SA 2.5 | null | 2010-11-22T00:09:23.823 | 2010-11-22T00:09:23.823 | null | null | 530 | null |
4788 | 2 | null | 4786 | 3 | null | The general sense in optimization is that if you have a convex function and no constraints, you want to use the "powerful stuff", gradient descent, Newton, etc. Without constraints interior point methods are not very good (competitive).
In particular for the problem you're studying (binary logistic regression) you sho... | null | CC BY-SA 2.5 | null | 2010-11-22T05:03:20.090 | 2010-11-22T09:03:55.123 | 2010-11-22T09:03:55.123 | 1540 | 1540 | null |
4789 | 2 | null | 4759 | 4 | null | R and SAS have each their pros and cons. I think more statisticians need to embrace the fact that lots of great statistical software is available, rather than endlessly bicker about which is superior.
R is free. SAS is very expensive. R gives you the ability to do just about anything. SAS may or may not. R has amazing ... | null | CC BY-SA 3.0 | null | 2010-11-22T05:44:40.397 | 2016-06-12T06:52:39.940 | 2016-06-12T06:52:39.940 | 22047 | null | null |
4790 | 2 | null | 4663 | 13 | null | The "no free lunch" theorems suggest that there are no a-priori distinctions between statistical inference algorithms, i.e. whether LARS or LASSO works best depends on the nature of the particular dataset. In practice then, it is best to try both and use some reliable estimator of generalisation performance to decide ... | null | CC BY-SA 2.5 | null | 2010-11-22T10:56:39.330 | 2010-11-22T11:25:15.910 | 2010-11-22T11:25:15.910 | 887 | 887 | null |
4793 | 2 | null | 4786 | 4 | null | As far as I'm concerned, constrained optimization is a less-than-optimal way of avoiding strong fluctuations in your parameters for the independents due to a bad model-specification. Pretty often a constraint is "needed" when the variance-covariance matrix is ill-structured, when there is a lot of (unaccounted) correla... | null | CC BY-SA 2.5 | null | 2010-11-22T12:52:59.547 | 2010-11-22T12:52:59.547 | null | null | 1124 | null |
4794 | 2 | null | 4783 | 4 | null | Let's begin by observing that ordinary least squares fitting for these data is likely inappropriate. If the individual data being accumulated are assumed, as usual, to have random error components, then the error in the cumulative data (not the [cumulative frequencies](http://en.wikipedia.org/wiki/Cumulative_frequency... | null | CC BY-SA 2.5 | null | 2010-11-22T15:13:43.460 | 2010-11-22T15:13:43.460 | null | null | 919 | null |
4795 | 2 | null | 4759 | 7 | null | "Popularity" depends on the community and the definition of "statistics". World-wide, taking a broad view of "statistical inference" as including any methods of drawing conclusions or taking actions based on quantitative data, there is little question that [Excel](http://www.pcworld.com/businesscenter/article/166123/f... | null | CC BY-SA 2.5 | null | 2010-11-22T15:36:31.757 | 2010-11-22T15:36:31.757 | null | null | 919 | null |
4796 | 1 | 4797 | null | 2 | 884 | To me, the two are similar in the sense that [slice sampling](http://.wikipedia.org/wiki/Slice_sampling) is just [Gibbs sampling](http://en.wikipedia.org/wiki/Gibbs_sampling) for the uniform distribution over the area under the plot of the density function. Is that right?
I was wondering if someone can compare between ... | Comparison of Slice sampling and Gibbs sampling | CC BY-SA 2.5 | null | 2010-11-22T15:42:04.420 | 2010-11-30T16:40:59.760 | 2010-11-30T16:40:59.760 | 8 | 1005 | [
"bayesian",
"markov-chain-montecarlo",
"gibbs",
"simulation"
] |
4797 | 2 | null | 4796 | 1 | null | I am not sure if the question is well posed.
If you can use both the gibbs sampler and slice sampling to sample from a posterior I would use the gibbs sampler as the slice sampler seems unnecessary to me. Use of a slice sampler introduces additional variables which at the very least increases run time for the sampler.... | null | CC BY-SA 2.5 | null | 2010-11-22T15:54:00.333 | 2010-11-22T15:54:00.333 | null | null | null | null |
4798 | 2 | null | 4783 | 2 | null | Clearly the dominant oscillation has period one day. Looks like there are also lower-frequency components relating to the day of the week, so add a component with frequency one week (i.e. one-seventh of a day) and its first few harmonics. That gives a model of the form:
$$\mbox{E}(y) = c + a_0 \cos(2\pi t) + b_0 \sin(2... | null | CC BY-SA 2.5 | null | 2010-11-22T17:43:59.917 | 2010-11-22T17:43:59.917 | null | null | 449 | null |
4799 | 1 | null | null | 8 | 3672 | Where can I find a good proof that CRF based models and logistic regression based models are convex? Is there a general trick to test/prove that a model or objective function is convex?
| Proof that CRF models and logistic models are convex functions | CC BY-SA 2.5 | null | 2010-11-22T18:41:41.273 | 2010-11-23T19:16:41.050 | 2010-11-23T15:24:42.790 | null | 2071 | [
"logistic",
"optimization"
] |
4800 | 2 | null | 4799 | 7 | null | One trick is to rewrite objective functions in terms of functions which are known to be convex.
Objective function of ML trained log-linear model is a sum of negative log-likelihoods, so it's sufficient to show that negative log-likelihood for each datapoint is convex.
Considering datapoint fixed, we can write its nega... | null | CC BY-SA 2.5 | null | 2010-11-22T19:30:36.430 | 2010-11-23T19:16:41.050 | 2010-11-23T19:16:41.050 | 511 | 511 | null |
4802 | 1 | null | null | 3 | 349 | I am trying to determine if I can model my system as a M/M/1 queue and if so do the numbers I get from it help me at all.
I can model my system like this:
System Description
A. I want to spec out the max number of clients I can have connect to my system. Each client... | How to predict and optimize a queue? | CC BY-SA 2.5 | null | 2010-11-22T21:25:42.370 | 2011-05-13T11:45:54.837 | 2011-04-13T10:33:37.850 | 449 | 2095 | [
"modeling",
"experiment-design",
"queueing"
] |
4803 | 1 | 4841 | null | 2 | 368 | I'm analyzing a noisy time series where where the inter-event interval is known to follow a two-gamma mixture distribution. If there was a simple model that would generate that kind of thing, it would be pretty simple to implement into BUGS. But otherwise, I can't think of anything that wouldn't be prohibitively kludg... | Modeling a gamma-mixture waiting model in BUGS | CC BY-SA 2.5 | null | 2010-11-22T21:32:18.330 | 2011-03-27T16:02:58.457 | 2011-03-27T16:02:58.457 | 919 | 996 | [
"bayesian",
"markov-chain-montecarlo",
"bugs",
"mixture-distribution"
] |
4804 | 2 | null | 4799 | 2 | null | First, convexity is not only a feature of a function, but rather, a function and the domain over which it is defined.
To address your question more directly, another trick (rather another formulation) is to compute the Hessian matrix of your likelihood function. A per [wiki](http://en.wikipedia.org/wiki/Convex_function... | null | CC BY-SA 2.5 | null | 2010-11-22T21:38:15.220 | 2010-11-22T21:50:21.293 | 2010-11-22T21:50:21.293 | 603 | 603 | null |
4805 | 1 | 7469 | null | 5 | 1405 | SAS EM has a node that generates the transformation for a dataset that makes it best fit a normal distribution. I can't imagine the people at SAS are the only ones to figure out how to do this. Is there any documentation out there on methodologies that do the same? Or an open source implementation?
| Methodology for data transform that best fits normal | CC BY-SA 2.5 | null | 2010-11-22T21:43:45.823 | 2011-02-21T20:55:54.027 | 2010-11-22T21:58:02.020 | 919 | 1951 | [
"data-transformation",
"normal-distribution"
] |
4806 | 2 | null | 4597 | 0 | null | You might try to find the correlation of the series of differences with the moving average of the series of differences using some scale for the moving average (for example, use a 10 point moving average as the scale). This way you can get an idea about how "wiggly" the series is at different scales. This tells you whe... | null | CC BY-SA 2.5 | null | 2010-11-22T22:26:51.780 | 2010-11-22T22:26:51.780 | null | null | 1146 | null |
4807 | 1 | null | null | 7 | 349 | I study labor and delivery as an epidemiologist. It is well established that a large fetus has a higher risk of causing maternal birth trauma. But a large baby is also likely to be delivered by cesarean section due to difficult labor. Those delivered by cesarean section will not have any risk for maternal birth traum... | Informative censoring caused by cesarean section | CC BY-SA 2.5 | null | 2010-11-22T23:14:02.377 | 2013-07-25T12:09:30.270 | null | null | null | [
"censoring"
] |
4808 | 2 | null | 4805 | 1 | null | Maybe the Box–Cox transformation or other sort of [power transform](http://en.wikipedia.org/wiki/Power_transform)?
| null | CC BY-SA 2.5 | null | 2010-11-22T23:51:15.713 | 2010-11-22T23:51:15.713 | null | null | 449 | null |
4809 | 1 | 15516 | null | 1 | 875 | I'm working on a meta-analysis and have generated a quirky question for which I'm at a bit of a loss. The MA is for a large set of factorial experiments. Calculating the Log Response Ratio (LRR) and variance in said ratio for the experimental data is a cinch, and we're comparing the effects of one type of treatment t... | Determining variance of meta-analysis log-response ratio generated from fitted curve | CC BY-SA 2.5 | null | 2010-11-22T23:57:08.500 | 2011-09-13T20:28:24.587 | null | null | 101 | [
"variance",
"meta-analysis"
] |
4810 | 1 | 4885 | null | 14 | 18931 | This may be too much of a general question but I hope I can find help here. I am starting a RA job in my university and my topic will be related to Internet Traffic Analysis. I am fairly new to the world of analysis but I guess in the world of research this is what I have to do a lot of.
I've been through a few papers ... | How to use CDF and PDF statistics for analysis | CC BY-SA 2.5 | null | 2010-11-23T01:18:41.480 | 2012-05-01T19:32:12.390 | null | null | 2101 | [
"mathematical-statistics"
] |
4812 | 1 | 4813 | null | 13 | 4127 | I'm currently working as a teaching assistant at my university, in an introductory statistics course (for medical students).
Offline, there are many books available with information to aid the teacher. However, what I am interested to know is if you might direct me to any (good) resources that provide exercises (with ... | Online resources for learning statistics, exercises (with solutions)? | CC BY-SA 3.0 | null | 2010-11-23T06:53:05.397 | 2016-12-20T18:21:34.180 | 2016-12-20T18:21:34.180 | 22468 | 253 | [
"probability",
"references",
"inference",
"descriptive-statistics",
"teaching"
] |
4813 | 2 | null | 4812 | 9 | null | This is a totally amazing online resource for multi-level modelling, not sure if that's any good to you:
[http://www.cmm.bristol.ac.uk/](http://www.cmm.bristol.ac.uk/)
Even includes a test at the start to give you an idea of where to start.
And should this be community wiki?
| null | CC BY-SA 2.5 | null | 2010-11-23T07:50:07.560 | 2010-11-23T07:50:07.560 | null | null | 199 | null |
4814 | 1 | 4815 | null | 7 | 1797 | I have two LME models with the same interaction, one containing both main effects and one containing only one main effect, say :
$$ H\_CE = Season + Crownlevel + Season:Crownlevel , random = 1|CollectorID $$
and
$$ H\_CE = Season + Season:Crownlevel , random = 1|CollectorID $$
There are 4 levels of each, and every comb... | Why do I get equal AIC, BIC and log likelihood for different models in LME framework? | CC BY-SA 3.0 | null | 2010-11-23T09:38:30.733 | 2012-10-10T14:12:14.540 | 2017-04-13T12:44:48.343 | -1 | 1124 | [
"r",
"mixed-model",
"maximum-likelihood",
"aic",
"bic"
] |
4815 | 2 | null | 4814 | 6 | null | The models are exactly equivalent. In both models you effectively specify one parameter for each combination of levels of Season and Crownlevel - the only difference is the parameterization:
In the first model, you fit main effects for Season and Crownlevel and an interaction effect to capture the combination-specific... | null | CC BY-SA 2.5 | null | 2010-11-23T10:00:56.627 | 2010-11-23T10:00:56.627 | null | null | 1979 | null |
4816 | 1 | 4821 | null | 19 | 14254 | Let $X \sim \chi^2_k$ be a chi-squared distributed random variable with $k$ degrees of freedom. What are the sharpest known bounds for the following probabilities
$$
\mathbb{P}[X > t] \leq 1 - \delta_1(t, k)
$$
and
$$
\mathbb{P}[X < z] \leq 1 - \delta_2(z, k)
$$
where $\delta_1$ and $\delta_2$ are some functions.... | What are the sharpest known tail bounds for $\chi_k^2$ distributed variables? | CC BY-SA 2.5 | null | 2010-11-23T10:12:46.490 | 2022-08-12T20:27:22.900 | null | null | 168 | [
"probability",
"chi-squared-test"
] |
4817 | 1 | 4956 | null | 6 | 1431 | I wasn't able to find one on Google, and was wondering if one exists...
| Is there an unpaired version of the sign test? | CC BY-SA 2.5 | null | 2010-11-23T10:48:00.267 | 2010-11-27T07:53:59.150 | 2010-11-23T16:27:15.573 | 919 | 253 | [
"hypothesis-testing",
"nonparametric",
"median",
"sign-test"
] |
4818 | 1 | 4822 | null | 13 | 4188 | I just noticed how the non exact McNemar's test uses the $\chi^{2}$ asymptotic distribution. But since the exact test (for the two case table) relies on the binomial distribution, how come it is not common to suggest the normal approximation to the binomial distribution?
| Why does the McNemar's test use $\chi^{2}$ and not the normal distribution? | CC BY-SA 4.0 | null | 2010-11-23T10:51:09.000 | 2021-02-03T19:43:36.443 | 2021-02-03T19:43:36.443 | 11887 | 253 | [
"distributions",
"normal-distribution",
"binomial-distribution",
"mcnemar-test",
"chi-squared-distribution"
] |
4819 | 2 | null | 4817 | 2 | null | The extension goes thorugh introducing rank to somewhat regulate the order of data and the result are Wilcoxon tests (Mann-Whitney in particular).
| null | CC BY-SA 2.5 | null | 2010-11-23T10:56:34.037 | 2010-11-23T10:56:34.037 | null | null | null | null |
4820 | 2 | null | 4817 | 3 | null | I'm not sure if such a test can exist conceptually. The sign test uses the pairing of the data to decide whether one value is bigger than the corresponding other value. But in an unpaired situation there is nothing like a corresponding other value (every value in the other group could be a potential counterpart for com... | null | CC BY-SA 2.5 | null | 2010-11-23T11:51:57.410 | 2010-11-23T11:51:57.410 | null | null | 1573 | null |
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