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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
4923 | 2 | null | 4920 | 7 | null | B is a linear transform of V. E represents an interaction between V and D. Have you considered specifying a model that is Y = Intercept + V + D + V:D? As @euphoria83 suggests, it seems likely that there is little variation in D, so it may not solve your problem; however it should at least make the independent contrib... | null | CC BY-SA 2.5 | null | 2010-11-26T03:36:26.110 | 2010-11-26T19:16:07.317 | 2010-11-26T19:16:07.317 | 196 | 196 | null |
4924 | 2 | null | 4360 | 4 | null | The conclusion you draw will be VERY dependent on the prior you choose for the probability of cheating and the prior probability that, given the flipper is lying, x heads are reported.
Putting the most mass on P(10000 heads reported|lying) is a little counter intuitive in my opinion. Unless the reporter is naive, I can... | null | CC BY-SA 2.5 | null | 2010-11-26T04:13:38.217 | 2010-11-26T05:06:35.820 | 2010-11-26T05:06:35.820 | 2144 | 2144 | null |
4925 | 2 | null | 4918 | 5 | null | I'm not sure if this is really what you are asking for, so please clarify or state otherwise if this isn't what you had in mind. In the mean time, here in an approach to calculate a 10% threshold and then also select the elements of that list which are above that threshold. This is using [R](http://www.r-project.org/).... | null | CC BY-SA 2.5 | null | 2010-11-26T04:34:08.287 | 2010-11-26T16:35:47.747 | 2010-11-26T16:35:47.747 | 696 | 696 | null |
4926 | 2 | null | 4920 | 32 | null | Both B and E are derived from V. B and E are clearly not truly "independent" variables from each other. The underlying variable that really matters here is V. You should probably disgard both B and E in this case and keep V only.
In a more general situation, when you have two independent variables that are very hi... | null | CC BY-SA 2.5 | null | 2010-11-26T05:43:31.740 | 2010-11-26T05:43:31.740 | null | null | 1329 | null |
4927 | 2 | null | 4868 | 1 | null | I'm not 100% clear on the question, but I have a few points to add:
I'm assuming that the error you are trying to estimate is the prediction error. If so, I agree that 10 fold cross validation would be good (and likely unbiased) approximation of the true prediction error IF your training sets are sufficiently large. La... | null | CC BY-SA 2.5 | null | 2010-11-26T05:57:08.417 | 2010-11-26T05:57:08.417 | null | null | 2144 | null |
4928 | 2 | null | 4908 | 1 | null | Sounds like you'll need a HMM to do that.
Have you read
Lawrence R. Rabiner (February 1989). ["A tutorial on Hidden Markov Models and selected applications in speech recognition"](http://www.ece.ucsb.edu/Faculty/Rabiner/ece259/Reprints/tutorial%20on%20hmm%20and%20applications.pdf)
There are a few examples of models par... | null | CC BY-SA 2.5 | null | 2010-11-26T06:24:56.867 | 2010-11-26T06:47:18.580 | 2010-11-26T06:47:18.580 | 1709 | 1709 | null |
4929 | 2 | null | 4920 | 7 | null | Here is an answer from the point of view of a machine learner, although I am afraid that I'll be beaten by real statisticians for it.
Is it possible for me to just "throw away" one of the variables?
Well, the question is what type of model you want to use for prediction. It depends e.g. on ...
- can the model with cor... | null | CC BY-SA 2.5 | null | 2010-11-26T08:13:43.497 | 2010-11-26T08:21:31.757 | 2010-11-26T08:21:31.757 | 264 | 264 | null |
4930 | 1 | 4931 | null | 11 | 12283 | Disclaimer: I posted this question on Stackoverflow, but I thought maybe this is better suited for this platform.
How do you test your own k-means implementation for multidimensional data sets?
I was thinking of running an already existing implementation (i.e., Matlab) on the data and compare the results with my algori... | How do you test an implementation of k-means? | CC BY-SA 2.5 | null | 2010-11-26T08:54:39.863 | 2015-09-14T14:47:57.047 | 2010-11-26T09:43:22.517 | 930 | 2147 | [
"clustering",
"algorithms"
] |
4931 | 2 | null | 4930 | 10 | null | The k-means includes a stochastic component, so it is very unlikely you will get the same result unless you have exactly the same implementation and use the same starting configuration. However, you could see if your results are in agreement with well-known implementations (don't know about Matlab, but implementation o... | null | CC BY-SA 2.5 | null | 2010-11-26T09:15:39.287 | 2010-11-26T09:15:39.287 | null | null | 930 | null |
4932 | 1 | 4933 | null | 2 | 58 | I have a data frame like this
```
User OS
A Windows
A Linux
B MacOS
C Linux
C FreeBSD
C Windows
D Windows
```
What I want to do is plot two types of statistics.
- The share of users with different number of OSs. So, it would be the fraction of the users with 1 OS... | R getting share of users with multiple of an element | CC BY-SA 2.5 | null | 2010-11-26T10:34:05.437 | 2010-11-26T10:51:53.453 | null | null | 2101 | [
"r",
"distributions",
"aggregation"
] |
4933 | 2 | null | 4932 | 4 | null | You could try something like
```
> df <- data.frame(User=sample(LETTERS[1:10], 100, rep=T),
OS=sample(c("Win","Lin","Mac"), 100, rep=T))
> (res <- with(df, tapply(OS, User, function(x) length(unique(x)))))
A B C D E F G H I J
2 3 3 3 3 3 3 3 3 3
> barplot(table(res)) # for counts
> barplot(table(i... | null | CC BY-SA 2.5 | null | 2010-11-26T10:45:18.043 | 2010-11-26T10:51:53.453 | 2017-04-13T12:44:20.840 | -1 | 930 | null |
4934 | 1 | 4935 | null | 14 | 6950 | Are there any good papers or books dealing with the use of coordinate descent for L1 (lasso) and/or elastic net regularization for linear regression problems?
| Coordinate descent for the lasso or elastic net | CC BY-SA 2.5 | null | 2010-11-26T11:00:49.113 | 2022-11-27T07:02:56.493 | 2019-02-03T01:00:12.907 | 11887 | 439 | [
"regression",
"references",
"lasso",
"regularization",
"elastic-net"
] |
4935 | 2 | null | 4934 | 16 | null | I earlier suggested the recent paper by Friedman and coll., [Regularization Paths for Generalized Linear Models via Coordinate Descent](http://www.jstatsoft.org/v33/i01/paper), published in the Journal of Statistical Software (2010). Here are some other references that might be useful:
- Pathwise coordinate optimizati... | null | CC BY-SA 2.5 | null | 2010-11-26T11:21:34.733 | 2010-11-26T11:21:34.733 | null | null | 930 | null |
4936 | 1 | 4938 | null | 14 | 4436 | What are the pros and cons of using LARS [1] versus using coordinate descent for fitting L1-regularized linear regression?
I am mainly interested in performance aspects (my problems tend to have `N` in the hundreds of thousands and `p` < 20.) However, any other insights would also be appreciated.
edit: Since I've poste... | LARS vs coordinate descent for the lasso | CC BY-SA 2.5 | null | 2010-11-26T11:28:53.567 | 2010-11-27T09:46:13.680 | 2020-06-11T14:32:37.003 | -1 | 439 | [
"regression",
"lasso",
"regularization"
] |
4937 | 2 | null | 4930 | 0 | null | Since k-means contains decisions that are randomly chosen (the initialization part only), I think the best way to try your algorithm is to select the initial points and let them fixed in your algorithm first and then choose another source code of the algorithm and fix the points in the same way. Then you can compare fo... | null | CC BY-SA 2.5 | null | 2010-11-26T11:53:26.917 | 2010-11-26T11:53:26.917 | null | null | 1808 | null |
4938 | 2 | null | 4936 | 13 | null | In scikit-learn the implementation of [Lasso with coordinate descent](http://scikit-learn.sourceforge.net/modules/linear_model.html#lasso) tends to be faster than our implementation of LARS although for small p (such as in your case) they are roughly equivalent (LARS might even be a bit faster with the latest optimizat... | null | CC BY-SA 2.5 | null | 2010-11-26T13:15:57.283 | 2010-11-27T09:46:13.680 | 2010-11-27T09:46:13.680 | 2150 | 2150 | null |
4939 | 1 | null | null | 9 | 2850 | 
I am given 15 points. The control limits are at +/- 3 $\sigma$. Points 1, 4, 5, 6, 7, 8, 9, 10, 11, 13, and 15 fall within the control limits. Points 2, 3, 12, and 14 are outside of the control limits, with 2 being ... | Given a control chart that shows the mean and upper/lower control limits, how do I tell if the cause of out of control points is assignable or not? | CC BY-SA 2.5 | null | 2010-11-26T14:09:15.643 | 2010-11-30T11:58:59.917 | 2010-11-26T16:26:40.237 | 110 | 110 | [
"control-chart",
"engineering-statistics"
] |
4940 | 2 | null | 4901 | 21 | null | Cox and Wermuth (1996) or Cox (1984) discussed some methods for detecting interactions. The problem is usually how general the interaction terms should be. Basically, we
(a) fit (and test) all second-order interaction terms, one at a time, and (b) plot their corresponding p-values (i.e., the No. terms as a function of... | null | CC BY-SA 4.0 | null | 2010-11-26T14:58:38.717 | 2018-07-14T18:05:53.047 | 2018-07-14T18:05:53.047 | 79696 | 930 | null |
4941 | 2 | null | 4934 | 5 | null | I've just come across this [lecture](https://web.archive.org/web/20100904040041/http://videolectures.net/kdd08_hastie_rpcd/) by Hastie and thought that others might find it interesting.
| null | CC BY-SA 4.0 | null | 2010-11-26T15:07:41.943 | 2022-11-27T07:02:56.493 | 2022-11-27T07:02:56.493 | 362671 | 439 | null |
4942 | 1 | 4951 | null | 3 | 5051 | The fisher linear classifier for two classes is a classifier with this discriminant function:
$h(x) = V^{T}X + v_0$
where
$V = \left[ \frac{1}{2}\Sigma_1 + \frac{1}{2}\Sigma_2\right]^{-1}(M_2-M_1)$
and $M_1$, $M_2$ are means and $\Sigma_1$,$\Sigma_2$ are covariances of the classes.
$V$ can be calculated easily but t... | Threshold for Fisher linear classifier | CC BY-SA 2.5 | null | 2010-11-26T15:22:47.893 | 2010-11-26T20:33:56.237 | null | null | 2148 | [
"classification",
"optimization"
] |
4943 | 2 | null | 4939 | 5 | null | My understanding of control charts is a little bit different... After the first signal at observation 2, wouldn't the process would be stopped and checked for problems, and then restarted?
In any case, you could use a p-value argument. The probability of observing 4 or more observations (out of 15) beyond their control... | null | CC BY-SA 2.5 | null | 2010-11-26T15:45:12.343 | 2010-11-26T19:39:31.937 | 2010-11-26T19:39:31.937 | 2144 | 2144 | null |
4944 | 2 | null | 4939 | 7 | null | Yes, you should find and assignable cause for every point that's outside the limits. But things are a little more complicated.
First you have to determine if the process is in control, since a control chart is meaningless when the process is out of control. Nearly 1/4 of your observations falling outside the limits is ... | null | CC BY-SA 2.5 | null | 2010-11-26T16:24:12.580 | 2010-11-30T11:58:59.917 | 2010-11-30T11:58:59.917 | 666 | 666 | null |
4945 | 1 | null | null | 10 | 22288 | I [posted a question earlier](https://stats.stackexchange.com/q/4914/919) but failed miserably in trying to explain what I am looking for (thanks to those who tried to help me anyway). Will try again, starting with a clean sheet.
Standard deviations are sensitive to scale. Since I am trying to perform a statistical tes... | "Normalized" standard deviation | CC BY-SA 2.5 | null | 2010-11-26T16:34:00.810 | 2017-03-09T21:24:29.600 | 2017-04-13T12:44:37.420 | -1 | 2137 | [
"standard-deviation"
] |
4946 | 2 | null | 4930 | 6 | null | The mapping between two sets of results is easy to compute, because the information you obtain in a test can be represented as a set of three-tuples: the first component is a (multidimensional) point, the second is an (arbitrary) cluster label supplied by your algorithm, and the third is an (arbitrary) cluster label su... | null | CC BY-SA 2.5 | null | 2010-11-26T16:46:09.033 | 2010-11-26T19:55:50.543 | 2010-11-26T19:55:50.543 | 930 | 919 | null |
4947 | 2 | null | 4914 | 5 | null | Smoothing, rolling averages, running means... are all nice ways (perhaps) to display data. But using the results of smoothed data as an input to any statistical analysis is likely to give misleading results, especially when done by novices. William Briggs emphasizes this point in his excellent blog in [this article](ht... | null | CC BY-SA 2.5 | null | 2010-11-26T16:47:25.097 | 2010-11-26T16:53:01.127 | 2010-11-26T16:53:01.127 | 25 | 25 | null |
4948 | 2 | null | 4912 | 6 | null | You are conducting a one-sided test of a difference of proportions. Because all four outcomes--A, not A, B, not B--occur often (70 times or more in this case), the Normal approximation to the Binomial distribution will be just fine. Let $a$ be the number of occurrences of A, $b$ the number of occurrences of B, and $n... | null | CC BY-SA 2.5 | null | 2010-11-26T17:23:03.043 | 2010-11-28T19:19:27.373 | 2010-11-28T19:19:27.373 | 919 | 919 | null |
4949 | 1 | 5858 | null | 12 | 19995 | If two classes $w_1$ and $w_2$ have normal distribution with known parameters ($M_1$, $M_2$ as their means and $\Sigma_1$,$\Sigma_2$ are their covariances) how we can calculate error of the Bayes classifier for them theorically?
Also suppose the variables are in N-dimensional space.
Note: A copy of this question is als... | Calculating the error of Bayes classifier analytically | CC BY-SA 2.5 | null | 2010-11-26T19:36:32.340 | 2019-08-06T12:29:57.810 | 2017-04-13T12:19:38.800 | -1 | 2148 | [
"probability",
"self-study",
"normality-assumption",
"naive-bayes",
"bayes-optimal-classifier"
] |
4950 | 2 | null | 4939 | 2 | null | I found something interesting tucked away in a study document from the IEEE geared toward this exam:
>
Data points falling within the UCL and LCL range are considered to be in control and caused by chance causes.
Outliers falling above the UCL or below the LCL are considered to be out of control and caused by assigna... | null | CC BY-SA 2.5 | null | 2010-11-26T20:16:29.420 | 2010-11-26T20:16:29.420 | null | null | 110 | null |
4951 | 2 | null | 4942 | 3 | null | When $X$ is normally distributed with known mean $M_1$ and covariance $\Sigma_1$ or with mean $M_2$ and covariance $\Sigma_2$, as indicated in comments to the question, then $V^{\ '}X$ is normally distributed either with mean $\mu_1 = V^{\ '} M_1$ and covariance $\sigma_1^2 = V^{\ '} \Sigma_1 V$ or with mean $\mu_2 = V... | null | CC BY-SA 2.5 | null | 2010-11-26T20:33:56.237 | 2010-11-26T20:33:56.237 | null | null | 919 | null |
4952 | 2 | null | 4939 | 4 | null | (Sorry for posting a new answer, I can't reply to comments directly yet)
I don't really agree with the statement:
"Apparently, if you cross either the UCL or LCL, there has to be an assignable cause"
To keep things simple, if your in control distribution is N(0,1), then you will still obtain false alarms once every 37... | null | CC BY-SA 2.5 | null | 2010-11-26T20:46:32.820 | 2010-11-26T20:46:32.820 | null | null | 2144 | null |
4953 | 2 | null | 4901 | 8 | null | I'll preface this response as I entirely agree with Gavin, and if you're interested in fitting any type of model it should be reflective of the phenomenon under study. What the problem is with the logic of identifying any and all effects (and what Gavin refers to when he says data dredging) is that you could fit an inf... | null | CC BY-SA 3.0 | null | 2010-11-27T03:38:45.647 | 2016-04-21T09:54:50.017 | 2016-04-21T09:54:50.017 | 17230 | 1036 | null |
4954 | 1 | null | null | 1 | 591 | I am trying to estimate parameters of a two dimensional Normal distribution using Gibbs sampling. While it was very easy transform the posterior equation for mean vector to a single dimension normal function for sampling, I am not able to same for sigma(covariance).
Do I need to use the Wishart distribution as prior an... | Posterior expression for Gibbs sampling | CC BY-SA 2.5 | null | 2010-11-27T06:11:33.187 | 2010-11-27T12:27:28.083 | 2010-11-27T11:42:17.817 | 449 | 2157 | [
"markov-chain-montecarlo",
"gibbs"
] |
4956 | 2 | null | 4817 | 3 | null | O.k,
I found that there is an unpaired solution to a sign test (A test of medians). It is called "Median test" And you can read about it [in Wikipedia](http://en.wikipedia.org/wiki/Median_test).
| null | CC BY-SA 2.5 | null | 2010-11-27T07:53:59.150 | 2010-11-27T07:53:59.150 | null | null | 253 | null |
4957 | 2 | null | 4949 | 0 | null | Here you might find several clues for your question, maybe is not there the full response but certainly very valuable parts of it.
[http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2766788/](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2766788/)
| null | CC BY-SA 2.5 | null | 2010-11-27T12:13:06.333 | 2010-11-27T12:13:06.333 | null | null | 1808 | null |
4958 | 2 | null | 4954 | 3 | null | The Wishart distribution is the conjugate prior for the likelihood that comes from assuming a normally distributed error term for the linear regression model. You have to assume that either the covariance matrix is an inverted-wishart or the precision matrix (i.e., the inverse of the covariance matrix) is a wishart dis... | null | CC BY-SA 2.5 | null | 2010-11-27T12:27:28.083 | 2010-11-27T12:27:28.083 | null | null | null | null |
4959 | 1 | 4960 | null | 12 | 2509 | If $X_i$ is exponentially distributed $(i=1,...,n)$ with parameter $\lambda$ and $X_i$'s are mutually independent, what is the expectation of
$$ \left(\sum_{i=1}^n {X_i} \right)^2$$
in terms of $n$ and $\lambda$ and possibly other constants?
Note: This question has gotten a mathematical answer on [https://math.stackexc... | How do you calculate the expectation of $\left(\sum_{i=1}^n {X_i} \right)^2$? | CC BY-SA 3.0 | null | 2010-11-27T14:54:04.023 | 2017-05-30T08:11:13.273 | 2017-04-13T12:19:38.853 | -1 | 2148 | [
"expected-value",
"exponential-distribution",
"gamma-distribution"
] |
4960 | 2 | null | 4959 | 31 | null | If $x_i \sim Exp(\lambda)$, then (under independence), $y = \sum x_i \sim Gamma(n, 1/\lambda)$, so $y$ is gamma distributed (see [wikipedia](http://en.wikipedia.org/wiki/Exponential_distribution)). So, we just need $E[y^2]$. Since $Var[y] = E[y^2] - E[y]^2$, we know that $E[y^2] = Var[y] + E[y]^2$. Therefore, $E[y^2] =... | null | CC BY-SA 2.5 | null | 2010-11-27T15:46:40.613 | 2010-11-27T15:46:40.613 | null | null | 1934 | null |
4961 | 1 | 18765 | null | 82 | 47507 | Unlike other articles, I found the [wikipedia](http://en.wikipedia.org/wiki/Regularization_%28mathematics%29) entry for this subject unreadable for a non-math person (like me).
I understood the basic idea, that you favor models with fewer rules. What I don't get is how do you get from a set of rules to a 'regularizatio... | What is regularization in plain english? | CC BY-SA 2.5 | null | 2010-11-27T16:24:53.693 | 2021-01-31T09:41:52.540 | null | null | 749 | [
"regularization"
] |
4962 | 2 | null | 423 | 16 | null | From [xkcd](http://xkcd.com/815/):
Almost a Chi square...
>
As the CoKF approaches 0, productivity goes negative as you pull OTHER people into chair-spinning contests.
| null | CC BY-SA 3.0 | null | 2010-11-27T18:14:10.090 | 2011-10-25T20:59:20.577 | 2011-10-25T20:59:20.577 | 5880 | 253 | null |
4964 | 1 | 4965 | null | 32 | 23306 | All of my variables are continuous. There are no levels. Is it possible to even have interaction between the variables?
| Is interaction possible between two continuous variables? | CC BY-SA 2.5 | null | 2010-11-27T19:42:14.197 | 2010-11-28T11:40:27.143 | 2010-11-27T19:51:05.120 | 1894 | 1894 | [
"regression",
"modeling",
"interaction"
] |
4965 | 2 | null | 4964 | 40 | null | Yes, why not? The same consideration as for categorical variables would apply in this case: The effect of $X_1$ on the outcome $Y$ is not the same depending on the value of $X_2$. To help visualize it, you can think of the values taken by $X_1$ when $X_2$ takes high or low values. Contrary to categorical variables, her... | null | CC BY-SA 2.5 | null | 2010-11-27T20:47:34.893 | 2010-11-28T11:40:27.143 | 2010-11-28T11:40:27.143 | 930 | 930 | null |
4966 | 2 | null | 4945 | 4 | null | If all your measurements are using the same units, then you've already addressed the scale problem; what's bugging you is degrees of freedom and precision of your estimates of standard deviation. If you recast your problem as comparing variances, then there are plenty of standard tests available.
For two independent... | null | CC BY-SA 2.5 | null | 2010-11-27T20:58:14.037 | 2010-11-27T20:58:14.037 | null | null | 5792 | null |
4967 | 2 | null | 134 | 6 | null | If you maintain a length-k window of data as a sorted doubly linked list then, by means of a binary search (to insert each new element as it gets shifted into the window) and a circular array of pointers (to immediately locate elements that need to be deleted), each shift of the window requires O(log(k)) effort for ins... | null | CC BY-SA 2.5 | null | 2010-11-27T21:45:52.897 | 2010-11-27T21:45:52.897 | null | null | 919 | null |
4968 | 2 | null | 423 | 116 | null | 
>
By the third trimester, there will be hundreds of babies inside you.
Also from [XKCD](http://xkcd.com/605/)
| null | CC BY-SA 2.5 | null | 2010-11-27T22:27:41.770 | 2010-11-29T14:53:40.757 | 2010-11-29T14:53:40.757 | 442 | 2166 | null |
4970 | 1 | null | null | 8 | 5694 | The matrix could be as large as $2500\times 2500$, what is the best algorithm to do that, is there some algorithm that is easy to write a program, is there any convenient packages for that?
| How to diagonalize a large sparse symmetric matrix, to get the eigen values and eigenvectors? | CC BY-SA 2.5 | null | 2010-11-28T04:38:02.957 | 2011-07-19T12:56:45.977 | 2010-11-28T11:55:30.167 | 930 | 2141 | [
"algorithms",
"matrix-decomposition"
] |
4971 | 2 | null | 4970 | 5 | null | I don't know much about eigenvalues or what they are applicable to, but R seems to have a built in function for this purpose named `eigen()`. Calculating the eigenvalues & eigenvectors for a 2500 * 2500 matrix took ~ 1 minute on my machine.
```
> sampData <- runif(6250000, 0, 2)
> x <- matrix(sampData, ncol = 2500, byr... | null | CC BY-SA 2.5 | null | 2010-11-28T05:09:44.260 | 2010-11-28T05:09:44.260 | 2017-05-23T12:39:26.167 | -1 | 696 | null |
4972 | 1 | 4973 | null | 6 | 623 | I am a novice in statistics so please correct me if I am doing something fundamentally wrong. After wrestling for a long time with R in trying to fit my data to a good distribution, I figured out that it fits the Cauchy distribution with the following parameters:
```
location scale
37.029894 18.678936
... | How to fit a model to self-reported number of friend interactions over a 20 day period? | CC BY-SA 3.0 | null | 2010-11-28T06:29:15.097 | 2011-10-07T02:15:16.517 | 2011-10-07T02:15:16.517 | 183 | 2164 | [
"r",
"distributions",
"dataset"
] |
4973 | 2 | null | 4972 | 12 | null | First off, your response variable is discrete. The Cauchy distribution is continuous. Second, your response variable is non-negative. The Cauchy distribution with the parameters you specified puts about 1/5 of its mass on negative values. Whatever you have been reading about the QQ norm plot is false. Points falling cl... | null | CC BY-SA 2.5 | null | 2010-11-28T07:13:23.237 | 2010-11-28T22:37:06.110 | 2010-11-28T22:37:06.110 | 2144 | 2144 | null |
4974 | 2 | null | 3856 | 2 | null | Typical measures of autocorrelation, such as Moran's I, are global estimates of clumpiness and could be masked by a trend or by "averaging" of clumpiness. There are two ways you could handle this:
1) Use a local measure of autocorrelation - but the drawback is you don't get a single number for clumpiness. An example o... | null | CC BY-SA 2.5 | null | 2010-11-28T08:03:09.037 | 2010-11-28T08:03:09.037 | null | null | 787 | null |
4975 | 2 | null | 4972 | 6 | null | Agree with HairyBeast (+1) that Cauchy is not appropriate here (it's symmetric for one thing) and that negative binomial might well be better.
Disagree about QQ-plot though. You can do a QQ-plot for any distribution, not just normal. What you say about interpretation of a QQ-plot is correct, but note that 2 of your poi... | null | CC BY-SA 2.5 | null | 2010-11-28T08:50:51.503 | 2010-11-28T08:50:51.503 | null | null | 449 | null |
4976 | 2 | null | 4970 | 6 | null | Take a look at [A Survey of Software for Sparse Eigenvalue Problems](http://www.grycap.upv.es/slepc/documentation/reports/str6.pdf) by Hernández et al.
| null | CC BY-SA 2.5 | null | 2010-11-28T12:05:28.813 | 2010-11-28T15:40:35.627 | 2010-11-28T15:40:35.627 | 439 | 439 | null |
4977 | 2 | null | 4961 | 12 | null | Put in simple terms, regularization is about benefiting the solutions you'd expect to get. As you mention, for example you can benefit "simple" solutions, for some definition of simplicity. If your problem has rules, one definition can be fewer rules. But this is problem-dependent.
You're asking the right question, how... | null | CC BY-SA 2.5 | null | 2010-11-28T12:51:05.570 | 2010-11-28T12:51:05.570 | null | null | 1540 | null |
4978 | 1 | 4984 | null | 22 | 5000 | I'm in no way a statistician (I've had a course in mathematical statistics but nothing more than that), and recently, while studying information theory and statistical mechanics, I met this thing called "uncertainty measure"/"entropy". I read Khinchin derivation of it as a measure of uncertainty and it made sense to me... | Comparison between MaxEnt, ML, Bayes and other kind of statistical inference methods | CC BY-SA 2.5 | null | 2010-11-28T13:12:18.827 | 2011-02-17T16:03:19.943 | null | null | 2171 | [
"entropy",
"inference"
] |
4979 | 2 | null | 4978 | 19 | null | For an entertaining critique of maximum entropy methods, I'd recommend reading some old newsgroup posts on sci.stat.math and sci.stat.consult, particularly the ones by Radford Neal:
- How informative is the Maximum Entropy method? (1994)
- Maximum Entropy Imputation (2002)
- Explanation of Maximum Entropy (2004)
... | null | CC BY-SA 2.5 | null | 2010-11-28T15:27:54.147 | 2010-11-28T22:05:12.887 | 2010-11-28T22:05:12.887 | 495 | 495 | null |
4980 | 1 | null | null | 11 | 5877 | What open-source implementations -- in any language -- exist out there that can compute lasso regularisation paths for linear regression by coordinate descent?
So far I am aware of:
- glmnet
- scikits.learn
Anything else out there?
| Lasso fitting by coordinate descent: open-source implementations? | CC BY-SA 2.5 | null | 2010-11-28T15:34:13.590 | 2018-05-20T19:33:03.783 | null | null | 439 | [
"regression",
"lasso",
"regularization"
] |
4981 | 2 | null | 4766 | 5 | null | We have implemented this (along with a power iteration refinement) in the [scikit-learn](http://scikit-learn.sourceforge.net) python package.
Our [implementation](https://github.com/scikit-learn/scikit-learn/blob/master/scikits/learn/utils/extmath.py#L97) is able to find the exact same singular values and vectors if k ... | null | CC BY-SA 2.5 | null | 2010-11-28T15:54:33.683 | 2010-11-28T16:01:55.277 | 2010-11-28T16:01:55.277 | 2150 | 2150 | null |
4982 | 2 | null | 4970 | 4 | null | 2500x2500 is not such a large problem. Even without leveraging the sparsity the SVD implementation of scipy.linalg is able to decompose it in less than a minute. See [my answer](https://stats.stackexchange.com/questions/4766/randomized-svd-and-singular-values/4981#4981) to a related questions for more details.
For larg... | null | CC BY-SA 2.5 | null | 2010-11-28T16:10:35.137 | 2010-11-28T16:10:35.137 | 2017-04-13T12:44:40.807 | -1 | 2150 | null |
4983 | 1 | 5053 | null | 3 | 1914 | I am using [SVM-light](http://svmlight.joachims.org/) with Matlab, for linear SVM. I would like to understand the output model, but I cannot find any documentation or help about it.
Here is the output:
```
sv_num: 639
upper_bound: 547
b: 1.4023
totwords: 576
totdoc: 2000
loo_e... | Output of linear SVM model in Matlab using SVM-light | CC BY-SA 2.5 | null | 2010-11-28T16:13:12.200 | 2012-11-23T15:08:49.377 | 2012-11-23T15:08:49.377 | 919 | 1351 | [
"svm",
"matlab"
] |
4984 | 2 | null | 4978 | 19 | null | MaxEnt and Bayesian inference methods correspond to different ways of incorporating information into your modeling procedure. Both can be put on axiomatic ground (John Skilling's ["Axioms of Maximum Entropy"](http://yaroslavvb.com/papers/skilling-axioms.pdf) and Cox's ["Algebra of Probable Inference"](http://yaroslavvb... | null | CC BY-SA 2.5 | null | 2010-11-28T22:05:16.413 | 2010-11-29T02:32:55.783 | 2010-11-29T02:32:55.783 | 511 | 511 | null |
4985 | 2 | null | 4908 | 1 | null | I may be misunderstanding your question (and falling into the same misunderstanding as fRed despite your explanation), in which case I apologize. It seems to me like you are saying you already know the various P_A, P_B, and P_C values for each context. I assume P_A + P_B + P_C = 1? Given those priors and the actual o... | null | CC BY-SA 2.5 | null | 2010-11-28T23:09:43.057 | 2010-11-28T23:09:43.057 | null | null | 196 | null |
4986 | 2 | null | 4980 | 5 | null | I have a MATLAB and C/C++ implementation [here](http://www.emakalic.org/blog/?page_id=7).
Let me know if you find it useful.
| null | CC BY-SA 2.5 | null | 2010-11-29T00:23:57.847 | 2010-11-29T00:23:57.847 | null | null | 530 | null |
4987 | 1 | 4990 | null | 3 | 4671 | I must have generated at least 5 Q-Q plots until now when trying to fit my data into a known distribution but I just noticed something that I could not understand. In the figure shown below, from what I've read from the wiki, X-axis is supposed to read "Negative Binomial Theoretical Quantiles" and Y-axis is supposed to... | Understanding a Quantile-Quantile Plot | CC BY-SA 2.5 | 0 | 2010-11-29T01:02:22.203 | 2017-11-12T17:22:04.010 | 2017-11-12T17:22:04.010 | 11887 | 2164 | [
"r",
"distributions",
"quantiles",
"qq-plot"
] |
4988 | 1 | null | null | 5 | 270 | Suppose we have a distribution for $\mathbf{x}\in \{-1,1\}^n$ and are interested in representing $p(\mathbf{x})$ as a linear exponential family with sufficient statistics of the form $1,x_1,x_2,\ldots,x_1 x_2,\ldots,x_1 x_2 \cdots x_n$
Suppose we know that entropy some measure of complexity of target distribution is b... | Asymmetry between high order and low order interaction terms | CC BY-SA 4.0 | null | 2010-11-29T02:08:24.257 | 2019-01-14T23:15:12.813 | 2019-01-14T23:15:12.813 | 79696 | 511 | [
"model-selection",
"entropy",
"graphical-model"
] |
4989 | 1 | 5248 | null | 4 | 2784 | My data consists of individual level observations nested within countries over time. I would like to use multilevel models along with some sort of selection model.
I have three related questions.
1) Are there any issues or concerns with using a Heckman selection model twice?
I have a model with two selection stages.... | Multi-stage selection model with panel data in R | CC BY-SA 2.5 | null | 2010-11-29T02:23:14.403 | 2010-12-08T10:22:15.833 | 2010-11-29T12:42:38.483 | null | 2050 | [
"r",
"panel-data",
"multilevel-analysis"
] |
4990 | 2 | null | 4987 | 5 | null | I think R is doing perfectly what you want it to do.
You are plotting:
>
x = qnbinom(ppoints(data),
size=2.3539444, mu=50.7752809)
which is:
>
[1] 3 5 7 9 10 11 12 13
14 15 16 17 18 19 20 [16] 21
21 22 23 24 25 25 26 27 28 28
29 30 31 31 [31] 32 33 34 35
35 36 37 3... | null | CC BY-SA 2.5 | null | 2010-11-29T06:04:07.037 | 2010-11-29T06:15:40.893 | 2010-11-29T06:15:40.893 | 1307 | 1307 | null |
4991 | 1 | null | null | 12 | 3130 | I want to implement (in R) the following very simple Dynamic Linear Model for which I have 2 unknown time varying parameters (the variance of the observation error $\epsilon^1_t$ and the variance of the state error $\epsilon^2_t$).
$
\begin{matrix}
Y_t & = & \theta_t + \epsilon^1_t\\
\theta_{t+1} & = & \theta_... | Estimating parameters of a dynamic linear model | CC BY-SA 3.0 | null | 2010-11-29T07:43:32.537 | 2015-04-27T06:02:33.610 | 2015-04-27T06:02:33.610 | 8336 | 1709 | [
"r",
"markov-chain-montecarlo",
"dlm",
"particle-filter"
] |
4993 | 2 | null | 4961 | 27 | null | Suppose you perform learning via empirical risk minimization.
More precisely:
- you have got your non-negative loss function $L(\text{actual value},\text{ predicted value})$ which characterize how bad your predictions are
- you want to fit your model in a such way that its predictions minimize mean of loss function... | null | CC BY-SA 3.0 | null | 2010-11-29T10:32:29.997 | 2011-11-22T13:41:56.597 | 2011-11-22T13:41:56.597 | null | 1725 | null |
4995 | 2 | null | 4945 | 0 | null | Harvey:
You're absolutely right that the F and Bartlett's tests won't work to compare raw data with smoothed data! Once the data has been smoothed, there's all manner of autocorrelation in there, and the testing becomes much more complicated. Better to compare separate--and hopefully independent--sequences.
| null | CC BY-SA 2.5 | null | 2010-11-29T15:19:15.583 | 2010-11-29T16:53:58.290 | 2010-11-29T16:53:58.290 | 8 | 5792 | null |
4996 | 2 | null | 4988 | 3 | null | Under these assumptions any permutation of the monomials leads to exactly the same results, implying there is no inherent distinction between the low order terms and other terms.
---
If this doesn't seem convincing, let's look at a simple example. Pick any one of the monomials and set $f(\mathbf{x}, \theta)$ propor... | null | CC BY-SA 2.5 | null | 2010-11-29T15:51:33.780 | 2010-11-29T16:19:52.817 | 2010-11-29T16:19:52.817 | 919 | 919 | null |
4997 | 1 | 5003 | null | 38 | 15682 | I'm using AIC (Akaike's Information Criterion) to compare non-linear models in R. Is it valid to compare the AICs of different types of model? Specifically, I'm comparing a model fitted by glm versus a model with a random effect term fitted by glmer (lme4).
If not, is there a way such a comparison can be done? Or is th... | Can AIC compare across different types of model? | CC BY-SA 2.5 | null | 2010-11-29T16:08:13.153 | 2022-03-19T09:26:30.813 | 2019-02-19T07:50:34.397 | 128677 | 2182 | [
"lme4-nlme",
"model-selection",
"aic"
] |
4999 | 1 | 7276 | null | 6 | 657 | I recently came across the following paper: "[Stochastic Methods for $\ell_1$ Regularized Loss Minimization](http://www.cs.huji.ac.il/~shais/papers/ShalevTewari09.pdf)" by Shai Shalev-Shwartz and Ambuj Tewari, ICML 2009.
In the paper, the authors propose a modification of the coordinate descent algorithm for the LASSO... | Stochastic coordinate descent for $\ell_1$ regularization | CC BY-SA 2.5 | null | 2010-11-29T17:26:43.070 | 2014-12-31T05:33:49.130 | 2010-11-29T23:35:42.850 | 439 | 439 | [
"regression",
"lasso",
"regularization"
] |
5000 | 2 | null | 4698 | 0 | null | Model evidence $P(D|M_i)$ can be viewed as an expectation of $P(D|w, M_i)$ with respect to distribution $P(w|M_i)$. You can then use Monte-Carlo methods to estimate it with required precision.
Other suitable options include using Laplace Approximation and then finding closed-form solution for evidence (as they do in RV... | null | CC BY-SA 2.5 | null | 2010-11-29T17:30:31.260 | 2010-11-29T17:30:31.260 | null | null | null | null |
5001 | 2 | null | 212 | 3 | null | The Sclite tool from [NIST](http://www.itl.nist.gov/iad/mig//tools/) offers a statistical test to compare two ASR systems on the same test set (http://www.itl.nist.gov/iad/mig//tools/).
For the test you described several of the test offered would be suitable (including the sign test) but not all are equally powerful.
| null | CC BY-SA 2.5 | null | 2010-11-29T17:49:27.980 | 2010-11-29T18:25:11.713 | 2010-11-29T18:25:11.713 | 919 | null | null |
5003 | 2 | null | 4997 | 20 | null | It depends. AIC is a function of the log likelihood. If both types of model compute the log likelihood the same way (i.e. include the same constant) then yes you can, if the models are nested.
I'm reasonably certain that `glm()` and `lmer()` don't use comparable log likelihoods.
The point about nested models is also up... | null | CC BY-SA 2.5 | null | 2010-11-29T18:01:09.517 | 2010-11-29T20:43:10.753 | 2010-11-29T20:43:10.753 | 1390 | 1390 | null |
5004 | 1 | 5040 | null | 3 | 2587 | What is the Unscented Kalman Filter and when is it used in preference to other types of filters?
edit: I find the Wikipedia explanation a bit too technical to be readily understood.
| What is the Unscented Kalman Filter? | CC BY-SA 2.5 | null | 2010-11-29T19:08:24.390 | 2022-09-03T19:15:12.147 | 2010-11-29T20:22:17.710 | 439 | 439 | [
"kalman-filter"
] |
5005 | 1 | null | null | 3 | 397 | The following piece of Perl code randomly maps a set of ranges onto a circumference of a circle. In the example, the circumference is of length 1000 and legal ranges are e.g. (0,8)=0,1,2,...,8 and (995,2)=995,996,...,999,0,1,2 (i.e. zero-based coordinates; both start and end are inclusive).
I take some arbitrary positi... | Unexpected under-dispersion in Perl simulations of Poisson RV | CC BY-SA 2.5 | null | 2010-11-29T20:35:43.210 | 2010-11-30T07:01:38.970 | 2010-11-30T07:01:38.970 | 634 | 634 | [
"distributions",
"binomial-distribution",
"random-variable",
"poisson-distribution",
"simulation"
] |
5006 | 2 | null | 423 | 39 | null | [Here](http://phd.kt.pri.ee/2009/08/11/captain-statistics-episode-1/)'s a somewhat more technical one.
| null | CC BY-SA 2.5 | null | 2010-11-29T20:45:50.423 | 2010-11-29T23:10:51.197 | 2010-11-29T23:10:51.197 | 930 | null | null |
5007 | 1 | 34252 | null | 59 | 127292 | I have a plot I'm making in ggplot2 to summarize data that are from a 2 x 4 x 3 celled dataset. I have been able to make panels for the 2-leveled variable using `facet_grid(. ~ Age)` and to set the x and y axes using `aes(x=4leveledVariable, y=DV)`. I used `aes(group=3leveledvariable, lty=3leveledvariable)` to produc... | How can I change the title of a legend in ggplot2? | CC BY-SA 3.0 | null | 2010-11-29T20:54:10.447 | 2013-08-04T15:52:12.873 | 2013-08-04T15:52:12.873 | 7290 | 196 | [
"r",
"data-visualization",
"ggplot2"
] |
5009 | 2 | null | 5007 | 39 | null | You can change the title of the legend by modifying the scale for that legend. Here's an example using the CO2 dataset
```
library(ggplot2)
p <- qplot(conc, uptake, data = CO2, colour = Type) + scale_colour_discrete(name = "Fancy Title")
p <- p + facet_grid(. ~ Treatment)
p
```
EDIT:
Using the example data from abov... | null | CC BY-SA 2.5 | null | 2010-11-29T21:08:00.030 | 2010-11-29T22:54:18.910 | 2010-11-29T22:54:18.910 | 696 | 696 | null |
5010 | 2 | null | 4997 | 4 | null | This is a great question that I've been curious about for a while.
For models in the same family (ie. auto-regressive models of order k or polynomials) AIC/BIC makes a lot of sense. In other cases it's less clear. Computing the log-likelihood exactly (with the constant terms) should work, but using more complicated mod... | null | CC BY-SA 2.5 | null | 2010-11-29T21:48:11.017 | 2010-11-29T21:48:11.017 | null | null | 2077 | null |
5011 | 1 | 5137 | null | 8 | 1791 | Kernel density estimator is given by
$$\hat{f}(x,h)=\frac{1}{nh}\sum_{i=1}^{n}K(\frac{x-X_{i}}{h})$$
where $X_1,...X_n$ i.i.d with some unknown density $f$, $h$ - bandwith,
$K$ - kernel function (
$\int_{-\infty}^{\infty}K(x)dx=1$,
$\int_{-\infty}^{\infty}K(x)xdx=0$,
$\int_{-\infty}^{\infty}K(x)x^2dx<\infty$).
Th... | Bias for kernel density estimator (periodic case) | CC BY-SA 2.5 | null | 2010-11-29T22:35:10.797 | 2015-04-23T05:53:56.053 | 2015-04-23T05:53:56.053 | 9964 | 2189 | [
"kernel-smoothing"
] |
5012 | 2 | null | 5005 | 3 | null | If I understood correctly, a "range" of length $k$ (such as $k=100$) within a circumference of length $n$ (such as $n = 1000$) has a chance of $(2k+1)/n$ of covering a given point on the circumference, and all the chances in a simulation are independent. Therefore in a simulation of $N$ trials (such as $N=1000$) the c... | null | CC BY-SA 2.5 | null | 2010-11-29T23:23:02.660 | 2010-11-29T23:23:02.660 | null | null | 919 | null |
5013 | 1 | 5030 | null | 6 | 3447 | 
N=2762
I've been exploring a data set that seems to give rise to this kind of plot rather frequently. Would you say this is one population with a different than normal population? Or are two populations confounding the normal distribution?
It used matplotlib and scipy.stat... | Quantile-Quantile Plot with Unknown Distribution? | CC BY-SA 2.5 | null | 2010-11-29T23:53:09.483 | 2010-12-03T03:44:23.953 | null | null | 2191 | [
"distributions"
] |
5014 | 2 | null | 5013 | -1 | null | You may want to take a look at the [Anderson-Darling](http://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test#Test_for_Normality) test for normality which empirically tests whether or not your data comes from a given distribution. @chl recommends looking at the `scipy` toolkit, specifically `anderson()` in `morest... | null | CC BY-SA 2.5 | null | 2010-11-30T02:33:35.903 | 2010-12-03T03:44:23.953 | 2010-12-03T03:44:23.953 | 696 | 696 | null |
5015 | 1 | 25081 | null | 19 | 29920 | I am interested in learning (and implementing) an alternative to polynomial interpolation.
However, I am having trouble finding a good description of how these methods work, how they relate, and how they compare.
I would appreciate your input on the pros/cons/conditions under which these methods or alternatives would ... | What are the advantages / disadvantages of using splines, smoothed splines, and gaussian process emulators? | CC BY-SA 3.0 | null | 2010-11-30T02:36:57.163 | 2018-06-14T03:20:00.983 | 2012-03-22T16:30:04.380 | 1381 | 1381 | [
"interpolation",
"splines"
] |
5016 | 1 | null | null | 4 | 619 | I'm trying to compute some p-values for samples from a distribution of sums of ~1000 random variables. The exact distribution of these random variables isn't known, but I have empirical estimates that I think are pretty accurate.
So far I've been using the central limit theorem to produce a normal approximation for thi... | Central Limit Theorem Tails | CC BY-SA 2.5 | null | 2010-11-30T04:34:16.530 | 2010-11-30T05:21:01.157 | null | null | 2111 | [
"normal-distribution",
"approximation",
"central-limit-theorem"
] |
5017 | 2 | null | 5016 | 3 | null | $n=1000$ gets you actually extremely close to normal if you do not go to the extreme tails ($n=10$ is often close enough to normal in the central region), but if you need to go there, estimating a PDF might well be impossible.
To get an event very far out in the tails, extreme fluctuations in your sumands need to happe... | null | CC BY-SA 2.5 | null | 2010-11-30T05:21:01.157 | 2010-11-30T05:21:01.157 | null | null | 56 | null |
5018 | 2 | null | 4551 | 12 | null | My old stats prof had a "rule of thumb" for dealing with outliers: If you see an outlier on your scatterplot, cover it up with your thumb :)
| null | CC BY-SA 2.5 | null | 2010-11-30T06:18:04.063 | 2010-11-30T06:18:04.063 | null | null | 74 | null |
5019 | 2 | null | 4551 | 65 | null | Reporting p-values when you did data-mining (hypothesis discovery) instead of statistics (hypothesis testing).
| null | CC BY-SA 3.0 | null | 2010-11-30T06:19:58.040 | 2012-08-02T03:12:36.993 | 2012-08-02T03:12:36.993 | 74 | 74 | null |
5020 | 2 | null | 4551 | 48 | null | A few mistakes that bother me:
- Assuming unbiased estimators are always better than biased estimators.
- Assuming that a high $R^2$ implies a good model, low $R^2$ implies a bad model.
- Incorrectly interpreting/applying correlation.
- Reporting point estimates without standard error.
- Using methods which assume... | null | CC BY-SA 3.0 | null | 2010-11-30T06:54:37.230 | 2011-09-22T15:01:04.260 | 2011-09-22T15:01:04.260 | 919 | 2144 | null |
5022 | 2 | null | 4551 | 29 | null | Being exploratory but pretending to be confirmatory. This can happen when one is modifying the analysis strategy (i.e. model fitting, variable selection and so on) data driven or result driven but not stating this openly and then only reporting the "best" (i.e. with smallest p-values) results as if it had been the only... | null | CC BY-SA 2.5 | null | 2010-11-30T08:02:28.100 | 2010-12-01T15:50:26.957 | 2010-12-01T15:50:26.957 | 1573 | 1573 | null |
5023 | 1 | null | null | 4 | 317 | Is there any comprehensive reference on (or introduction to) how people have tried to model non-independent random variables? I already know about mixing processes, which express in various ways according to various coefficients how "future" events depend on "past" events, but that's about it...
| Modelling dependence between random variables | CC BY-SA 2.5 | null | 2010-11-30T08:37:51.447 | 2010-11-30T16:00:56.360 | null | null | 2197 | [
"random-variable",
"non-independent"
] |
5024 | 2 | null | 4698 | 2 | null | Yes, you can do that. However, your I'd like to play with your formulas a little bit.
If the model is determined by the parameters, than $P(D|M_i)=\int P(D|w,M_i)P(M_i|w)*P(w)dw$ should be more appropriate. Since I guess the model is determined by the parameters in a deterministic (instead of stochastic) way, the formu... | null | CC BY-SA 2.5 | null | 2010-11-30T09:33:50.900 | 2010-11-30T09:33:50.900 | null | null | 264 | null |
5025 | 1 | 5032 | null | 10 | 1794 | Suppose we have a simple linear regression model $Z = aX + bY$ and would like to test the null hypothesis $H_0: a=b=\frac{1}{2}$ against the general alternative.
I think one can use the estimate of $\hat{a}$ and $SE(\hat{a})$ and further apply a $Z$-test to get the confidence interval around $\frac{1}{2}$. Is this ok?... | How to test if the slopes in the linear model are equal to a fixed value? | CC BY-SA 2.5 | null | 2010-11-30T10:07:53.553 | 2010-11-30T19:25:30.990 | 2010-11-30T16:45:51.890 | 8 | 1215 | [
"hypothesis-testing",
"regression"
] |
5026 | 1 | null | null | 222 | 202047 | What is the difference between data mining, statistics, machine learning and AI?
Would it be accurate to say that they are 4 fields attempting to solve very similar problems but with different approaches? What exactly do they have in common and where do they differ? If there is some kind of hierarchy between them, what... | What is the difference between data mining, statistics, machine learning and AI? | CC BY-SA 2.5 | null | 2010-11-30T11:26:15.473 | 2019-10-23T17:27:44.153 | 2017-04-13T12:44:33.550 | -1 | 2199 | [
"machine-learning",
"data-mining"
] |
5028 | 2 | null | 5026 | 22 | null | We can say that they are all related, but they are all different things.
Although you can have things in common among them, such as that in statistics and data mining you use clustering methods.
Let me try to briefly define each:
- Statistics is a very old discipline mainly based on classical mathematical methods, w... | null | CC BY-SA 3.0 | null | 2010-11-30T12:05:06.173 | 2013-10-23T15:54:59.260 | 2013-10-23T15:54:59.260 | 28740 | 1808 | null |
5030 | 2 | null | 5013 | 7 | null | There are a variety of different possibilities. For example, a chi-square distribution with degrees of freedom in the range of 30-40 would give rise to such a qq-plot. In R:
```
x <- rchisq(10000, df=35)
qqnorm(x)
qqline(x)
```
looks like this:
A mixture of two normals ... | null | CC BY-SA 2.5 | null | 2010-11-30T15:35:14.227 | 2010-11-30T15:35:14.227 | null | null | 1934 | null |
5031 | 2 | null | 5023 | 2 | null | OK, I think in what exists now, what comes closest to what you are looking for is the coalescent theory. [Quoting from wikipedia](http://en.wikipedia.org/wiki/Coalescence_%28genetics%29):
>
In genetics, coalescent theory is a retrospective model of population genetics. It employs a sample of individuals from a populat... | null | CC BY-SA 2.5 | null | 2010-11-30T16:00:56.360 | 2010-11-30T16:00:56.360 | null | null | 2036 | null |
5032 | 2 | null | 5025 | 8 | null | In linear regression the assumption is that $X$ and $Y$ are not random variables. Therefore, the model
$$Z = a X + b Y + \epsilon$$
is algebraically the same as
$$Z - \frac{1}{2} X - \frac{1}{2} Y = (a - \frac{1}{2})X + (b - \frac{1}{2})Y + \epsilon = \alpha X + \beta Y + \epsilon.$$
Here, $\alpha = a - \frac{1}{2... | null | CC BY-SA 2.5 | null | 2010-11-30T16:25:00.833 | 2010-11-30T19:25:30.990 | 2010-11-30T19:25:30.990 | 919 | 919 | null |
5033 | 2 | null | 5013 | 5 | null | Your dataset clearly is not normal. (With this much data, any goodness of fit test will tell you that.) But you can read much more than that from the normal probability plot:
- The generally smooth curvature does not hint at a mixture structure.
- The upper tail is too stretched out (values too high compared to the... | null | CC BY-SA 2.5 | null | 2010-11-30T17:08:52.140 | 2010-11-30T17:08:52.140 | null | null | 919 | null |
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