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1415 | 2 | null | 973 | 2 | null | Prostate (gene expression array)
- k=2
- n=48+52
- p=6033
Available via (among other) R package [spls](http://cran.r-project.org/web/packages/spls/)
name of the dataset: prostate
error rate = 3/102 (see [here](http://www.stat.wisc.edu/%7Ekeles/Papers/C_SPLS.pdf)) also I think there are paper which show 1/102 ... | null | CC BY-SA 2.5 | null | 2010-08-08T19:02:55.487 | 2010-11-09T08:29:57.363 | 2010-11-09T08:29:57.363 | 223 | 223 | null |
1416 | 2 | null | 1413 | 3 | null | Douglas Bates addressed this on the sig-ME list a while back:
- using glmer with user-defined link function
I'm not aware of significant changes since, but his recommendation (using a quasi family with specified link and variance) might be of use. Hopefully this addresses your first and third questions. I'm not aw... | null | CC BY-SA 2.5 | null | 2010-08-08T19:26:40.020 | 2010-08-08T19:26:40.020 | null | null | 251 | null |
1417 | 2 | null | 485 | 6 | null | This site from Ecole normal Supérieure de Paris contains a lot of very interesting video
[http://www.diffusion.ens.fr/index.php?res=themes&idtheme=30](http://www.diffusion.ens.fr/index.php?res=themes&idtheme=30)
I greatly encourage you to visit this site !!
Among other you will find there all video presentation from ... | null | CC BY-SA 2.5 | null | 2010-08-08T19:59:34.217 | 2010-08-08T19:59:34.217 | null | null | 223 | null |
1418 | 2 | null | 1195 | 6 | null | The following paper describes a couple of approaches for imputing right censored data in the same domain (i.e. topcoded wage data). They use a truncated normal distribution and describe a single imputation model assuming homoscedasticity, and a multiple imputation model assuming heterscedasticity. Also a second paper... | null | CC BY-SA 2.5 | null | 2010-08-08T19:59:40.893 | 2010-08-08T19:59:40.893 | null | null | 251 | null |
1419 | 2 | null | 485 | 7 | null | The folks at SLAC put videos of their lecture series online. Given that their audience is mostly physicists, they tend to be fairly mathematical.
- SLUO Lecture Series (see the "Stat" links)
| null | CC BY-SA 2.5 | null | 2010-08-08T20:22:58.713 | 2010-08-08T20:22:58.713 | null | null | 251 | null |
1420 | 2 | null | 1202 | 4 | null | I think relative distribution methods are a good candidate for the question you pose.
Since you're comparing data based on binning, this is very similar to the method of constructing a probability-probability plot. Taking it a step further, you can can actually construct a relative CDF/PDF for two distributions base... | null | CC BY-SA 2.5 | null | 2010-08-08T20:38:09.240 | 2010-08-08T20:38:09.240 | null | null | 251 | null |
1421 | 2 | null | 1412 | 1 | null | I don't see how the question in your example is sensible. The slope of the values is the slope of the values. Using a logistic link function then you get the slope of the logit of the values. There's no under or overestimating.
The more interesting case in your (our) field is that of interactions in accuracy. You ... | null | CC BY-SA 3.0 | null | 2010-08-08T21:57:57.290 | 2017-12-21T02:09:02.167 | 2017-12-21T02:09:02.167 | 601 | 601 | null |
1423 | 2 | null | 726 | 119 | null | >
Prediction is very difficult, especially about the future.
-- Niels Bohr
| null | CC BY-SA 2.5 | null | 2010-08-08T23:05:17.700 | 2010-08-08T23:05:17.700 | null | null | 749 | null |
1424 | 1 | 1425 | null | 6 | 1553 | This definitely sounds like a homework, but I assure you that it's not. You're probably familiar with the [Risk](http://en.wikipedia.org/wiki/Risk_%28game%29) game. Now, friend of mine rolled 3 aces in one hand. I reckon that probability of such event is
$$C(n,k) = \frac{(n-1+k)!}{(n-1)!k!}$$
so that's $8!/(5!*3!) = 56... | The "Risk" game dice problem | CC BY-SA 3.0 | null | 2010-08-09T00:00:13.560 | 2016-08-17T17:37:49.293 | 2016-08-17T17:37:49.293 | 24669 | 1356 | [
"probability",
"games",
"dice"
] |
1425 | 2 | null | 1424 | 13 | null | You should not do a calculation of probability for an event deemed surprising post hoc as if it were an event specified before it was rolled (observed).
It's very difficult to to do a proper calculation of post hoc probability, because what other events would have been deemed at least as surprising depends on what the ... | null | CC BY-SA 3.0 | null | 2010-08-09T00:37:45.090 | 2013-12-20T07:46:37.133 | 2013-12-20T07:46:37.133 | 805 | 805 | null |
1426 | 2 | null | 726 | 64 | null | >
"It's easy to lie with statistics; it is easier to lie without them."
-- Frederick Mosteller
| null | CC BY-SA 3.0 | null | 2010-08-09T01:44:41.210 | 2015-03-06T04:35:44.930 | 2015-03-06T04:35:44.930 | 59319 | 319 | null |
1427 | 1 | 1428 | null | 2 | 705 | I'm exploring the use of changepoint detection or other methods (am slowly becoming aware of wavelet transformation, etc. but have tons to learn in this area) to identify key shifts in health care performance patterns over time. However, many of the metrics I'm seeking to analyze (e.g., health care quality metrics) are... | Time-series data pre-aggregated into non-stationary rolling 12-month periods: are there special considerations for modeling? | CC BY-SA 2.5 | null | 2010-08-09T03:57:50.097 | 2011-04-14T14:58:25.980 | 2011-04-14T14:58:25.980 | 919 | 394 | [
"time-series",
"modeling",
"change-point"
] |
1428 | 2 | null | 1427 | 5 | null | The 12-month rolling aggregation will remove seasonality which makes the task easier. For non-seasonal time series, the methods in the [strucchange](http://cran.r-project.org/package=strucchange) package for R are excellent.
For seasonal time series, you might look at the BFAST (Breaks For Additive Seasonal and Trend) ... | null | CC BY-SA 2.5 | null | 2010-08-09T04:05:27.520 | 2010-08-09T04:13:46.500 | 2010-08-09T04:13:46.500 | 159 | 159 | null |
1429 | 2 | null | 1268 | 1 | null | I'm somewhat confused by your example code, as it seems you drop the `V` variable from the computation of `newX`. Are you looking to model `X` as a reduced rank product, or are you interested in a reduced column space of `X`? in the latter case, I think an EM-PCA approach would work. you can find matlab code under the ... | null | CC BY-SA 2.5 | null | 2010-08-09T04:22:42.533 | 2010-08-09T04:22:42.533 | null | null | 795 | null |
1430 | 1 | 1431 | null | 11 | 4927 | Does anybody have a nice example of a stochastic process that is 2nd-order stationary, but is not strictly stationary?
| Example of a process that is 2nd order stationary but not strictly stationary | CC BY-SA 3.0 | null | 2010-08-09T06:50:42.803 | 2015-09-29T23:19:18.367 | 2015-09-29T23:19:18.367 | 22228 | 352 | [
"time-series",
"stochastic-processes",
"stationarity"
] |
1431 | 2 | null | 1430 | 7 | null | Take any process $(X_t)_t$ with independent components that has a constant first and second moment and put a varying third moment.
It is second order stationnary because $E[ X_t X_{t+h} ]=0$ and it is not strictly stationnary
because $P( X_t \geq x_t, X_{t+1} \geq x_{t+1})$ depends upon $t$
| null | CC BY-SA 2.5 | null | 2010-08-09T07:05:20.680 | 2010-08-09T08:29:24.173 | 2010-08-09T08:29:24.173 | 223 | 223 | null |
1432 | 1 | 1435 | null | 92 | 96453 | In answering [this](https://stats.stackexchange.com/questions/1412/consequences-of-an-improper-link-function-in-n-alternative-forced-choice-procedur) question John Christie suggested that the fit of logistic regression models should be assessed by evaluating the residuals. I'm familiar with how to interpret residuals ... | What do the residuals in a logistic regression mean? | CC BY-SA 4.0 | null | 2010-08-09T07:32:32.767 | 2020-09-04T09:39:43.583 | 2018-08-01T15:02:20.500 | 7290 | 196 | [
"r",
"logistic",
"generalized-linear-model",
"residuals",
"aic"
] |
1433 | 2 | null | 6 | 69 | null | What enforces more separation than there should be is each discipline's lexicon.
There are many instances where ML uses one term and Statistics uses a different term--but both refer to the same thing--fine, you would expect that, and it doesn't cause any permanent confusion (e.g., features/attributes versus expectatio... | null | CC BY-SA 3.0 | null | 2010-08-09T10:12:35.817 | 2016-08-16T18:12:10.847 | 2016-08-16T18:12:10.847 | 438 | 438 | null |
1434 | 2 | null | 421 | 4 | null | "[How to Tell the Liars from the Statisticians](http://rads.stackoverflow.com/amzn/click/0824718178)" by Hooke. I am fond of its way of explaining the concepts of statistics to laypersons.
As for explaining the motivations of statisticians, "The Lady Tasting Tea" is good reading.
| null | CC BY-SA 2.5 | null | 2010-08-09T10:23:41.673 | 2010-08-11T08:37:11.667 | 2010-08-11T08:37:11.667 | 509 | 830 | null |
1435 | 2 | null | 1432 | 47 | null | The easiest residuals to understand are the deviance residuals as when squared these sum to -2 times the log-likelihood. In its simplest terms logistic regression can be understood in terms of fitting the function $p = \text{logit}^{-1}(X\beta)$ for known $X$ in such a way as to minimise the total deviance, which is th... | null | CC BY-SA 3.0 | null | 2010-08-09T10:26:35.913 | 2014-03-28T13:31:33.143 | 2014-03-28T13:31:33.143 | 22311 | 521 | null |
1436 | 2 | null | 1337 | 72 | null | A mathematician, a physicist and a statistician went hunting for deer. When they chanced upon one buck lounging about, the mathematician fired first, missing the buck's nose by a few inches. The physicist then tried his hand, and missed the tail by a wee bit. The statistician started jumping up and down saying "We got ... | null | CC BY-SA 2.5 | null | 2010-08-09T10:29:38.373 | 2010-08-09T10:29:38.373 | null | null | 830 | null |
1437 | 1 | null | null | 1 | 1113 | Do you think it can be used instead of k means? I obtained a correlation with the first 2 components as they carry over 90% of the weight. Would you agree on the technique?
| Can Principal Component Analysis be used alone to infer major patterns within data instead of k means clustering? | CC BY-SA 2.5 | null | 2010-08-09T10:37:59.673 | 2010-08-09T12:45:05.153 | 2010-08-09T10:59:13.217 | 8 | null | [
"pca"
] |
1438 | 2 | null | 1437 | 2 | null | I think it depends on your data set and what you want to do with it. If you look at my answer to this [question](https://stats.stackexchange.com/questions/1289/visualizing-multiple-histograms/1291#1291), you will see that it indicates groups/differences. However, it certainly doesn't prove differences - it just gives y... | null | CC BY-SA 2.5 | null | 2010-08-09T10:47:18.197 | 2010-08-09T10:47:18.197 | 2017-04-13T12:44:44.530 | -1 | 8 | null |
1439 | 2 | null | 103 | 2 | null | I can't pick just one :)
Check out this great blog post by flowingdata: [37 Data-ish blogs you should know about](http://flowingdata.com/2009/05/06/37-data-ish-blogs-you-should-know-about/)
| null | CC BY-SA 2.5 | null | 2010-08-09T11:14:34.503 | 2010-08-09T11:14:34.503 | null | null | 665 | null |
1440 | 2 | null | 1437 | 0 | null | It's possible that my background in psychological research is disguising some understanding of the broader application of PCA and K-means, but I'd say the following:
- PCA is used to reduce a set of variables to a smaller number of dimensions
- k-means is used to group cases.
For example, take a study of 1000 parti... | null | CC BY-SA 2.5 | null | 2010-08-09T12:45:05.153 | 2010-08-09T12:45:05.153 | null | null | 183 | null |
1441 | 1 | 337429 | null | 10 | 1983 | This question follows from [my previous question](https://stats.stackexchange.com/questions/1430/example-of-a-2nd-order-stationary-but-not-strictly-stationary-process), where Robin answered the question in the case of weak stationary processes. Here, I am asking a similar question for (strong?) stationary processes. ... | Example of a stochastic process that is 1st and 2nd order stationary, but not strictly stationary (Round 2) | CC BY-SA 3.0 | null | 2010-08-09T12:50:55.720 | 2018-03-29T15:33:21.537 | 2018-03-29T15:33:21.537 | 161461 | 352 | [
"time-series",
"stochastic-processes",
"stationarity",
"example"
] |
1442 | 2 | null | 173 | 15 | null | To assess the historical trend, I'd use a gam with trend and seasonal components. For example
```
require(mgcv)
require(forecast)
x <- ts(rpois(100,1+sin(seq(0,3*pi,l=100))),f=12)
tt <- 1:100
season <- seasonaldummy(x)
fit <- gam(x ~ s(tt,k=5) + season, family="poisson")
plot(fit)
```
Then `summary(fit)` will give you... | null | CC BY-SA 2.5 | null | 2010-08-09T13:36:43.330 | 2010-08-13T13:01:56.437 | 2010-08-13T13:01:56.437 | 159 | 159 | null |
1443 | 2 | null | 6 | 15 | null | Ideally one should have a thorough knowledge of both statsitics and machine learning before attempting to answer his question. I am very much a neophyte to ML, so forgive me if wat I say is naive.
I have limited experience in SVMs and regression trees. What strikes me as lacking in ML from a stats point of view is a we... | null | CC BY-SA 2.5 | null | 2010-08-09T13:51:29.007 | 2010-08-09T13:56:39.603 | 2010-08-09T13:56:39.603 | 521 | 521 | null |
1444 | 1 | 1446 | null | 236 | 196934 | If I have highly skewed positive data I often take logs. But what should I do with highly skewed non-negative data that include zeros? I have seen two transformations used:
- $\log(x+1)$ which has the neat feature that 0 maps to 0.
- $\log(x+c)$ where c is either estimated or set to be some very small positive value.... | How should I transform non-negative data including zeros? | CC BY-SA 3.0 | null | 2010-08-09T13:57:51.753 | 2022-10-20T16:28:12.010 | 2015-08-11T08:45:22.567 | 49647 | 159 | [
"data-transformation",
"large-data"
] |
1445 | 2 | null | 1444 | 11 | null | I assume you have continuous data.
If the data include zeros this means you have a spike on zero which may be due to some particular aspect of your data. It appears for example in wind energy, wind below 2 m/s produce zero power (it is called cut in) and wind over (something around) 25 m/s also produce zero power (for... | null | CC BY-SA 3.0 | null | 2010-08-09T14:05:50.187 | 2013-05-28T21:09:50.753 | 2013-05-28T21:09:50.753 | 22047 | 223 | null |
1446 | 2 | null | 1444 | 67 | null | It seems to me that the most appropriate choice of transformation is contingent on the model and the context.
The '0' point can arise from several different reasons each of which may have to be treated differently:
- Truncation (as in Robin's example): Use appropriate models (e.g., mixtures, survival models etc)
- M... | null | CC BY-SA 2.5 | null | 2010-08-09T14:22:11.460 | 2010-08-09T14:22:11.460 | null | null | null | null |
1447 | 1 | 1450 | null | 24 | 13547 | I want to fully grasp the notion of $r^2$ describing the amount of variation between variables. Every web explanation is a bit mechanical and obtuse. I want to "get" the concept, not just mechanically use the numbers.
E.g.: Hours studied vs. test score
$r$ = .8
$r^2$ = .64
- So, what does this mean?
- 64% of the vari... | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation | CC BY-SA 3.0 | null | 2010-08-09T14:52:42.430 | 2017-04-19T18:33:23.947 | 2016-03-04T16:01:26.207 | 485 | 6967 | [
"regression",
"correlation",
"variance"
] |
1448 | 2 | null | 1447 | 6 | null | A mathematical demonstration of the relationship between the two is here: [Pearson's correlation and least squares regression analysis](http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient#Pearson.27s_correlation_and_least_squares_regression_analysis).
I am not sure if there is a geometric or any... | null | CC BY-SA 2.5 | null | 2010-08-09T15:09:34.683 | 2010-08-09T19:58:51.157 | 2010-08-09T19:58:51.157 | null | null | null |
1449 | 2 | null | 726 | 56 | null | >
My greatest concern was what to call
it. I thought of calling it
'information,' but the word was overly
used, so I decided to call it
'uncertainty.' When I discussed it
with John von Neumann, he had a better
idea. Von Neumann told me, 'You should
call it entropy, for two reasons. In
the first place y... | null | CC BY-SA 2.5 | null | 2010-08-09T15:36:26.553 | 2010-08-09T15:36:26.553 | null | null | 223 | null |
1450 | 2 | null | 1447 | 31 | null | Start with the basic idea of variation. Your beginning model is the sum of the squared deviations from the mean. The R^2 value is the proportion of that variation that is accounted for by using an alternative model. For example, R-squared tells you how much of the variation in Y you can get rid of by summing up the ... | null | CC BY-SA 3.0 | null | 2010-08-09T15:44:50.163 | 2017-04-19T18:33:23.947 | 2017-04-19T18:33:23.947 | 485 | 485 | null |
1451 | 2 | null | 942 | 19 | null | The list in the presentation that you reference seems fairly arbitrary to me, and the technique that would be used will really depend on the specific problem. You will note however that it also includes [Kalman filters](http://en.wikipedia.org/wiki/Kalman_filter), so I suspect that the intended usage is as a filtering... | null | CC BY-SA 2.5 | null | 2010-08-09T15:51:47.087 | 2010-08-09T15:51:47.087 | null | null | 5 | null |
1452 | 2 | null | 1444 | 43 | null | The log transforms with shifts are special cases of the [Box-Cox transformations](http://en.wikipedia.org/wiki/Box-Cox_transformation):
$y(\lambda_{1}, \lambda_{2}) =
\begin{cases}
\frac {(y+\lambda_{2})^{\lambda_1} - 1} {\lambda_{1}} & \mbox{when } \lambda_{1} \neq 0 \\ \log (y + \lambda_{2}) & \mbox{when } \lambda... | null | CC BY-SA 2.5 | null | 2010-08-09T16:43:48.870 | 2010-08-10T01:59:44.693 | 2010-08-10T01:59:44.693 | 251 | 251 | null |
1453 | 2 | null | 1447 | 3 | null | The [Regression By Eye](http://onlinestatbook.com/stat_sim/reg_by_eye/index.html) applet could be of use if you're trying to develop some intuition.
It lets you generate data then guess a value for R, which you can then compare with the actual value.
| null | CC BY-SA 2.5 | null | 2010-08-09T16:49:45.147 | 2010-08-09T16:49:45.147 | null | null | 251 | null |
1454 | 1 | 1457 | null | 2 | 125 | I have a data set that contains two types of points. The first type of points come from an N(0,1) distribution. The second type of points come from an N(m,v) distribution for some real m and some positive, real v. The objective is to classify each point as type 1 or type 2, and to identify m & v. We have no apriori inf... | How to identify points and an unknown distribution in a two type clustering problem? | CC BY-SA 2.5 | null | 2010-08-09T17:43:33.807 | 2011-04-29T00:21:42.403 | 2011-04-29T00:21:42.403 | 3911 | 247 | [
"clustering",
"mixture-distribution"
] |
1455 | 1 | 1456 | null | 17 | 15364 | I have a bunch of articles presenting "OR" with a- 95% CI (confidence intervals).
I want to estimate from the articles the P value for the observed OR. For that, I need an assumption regarding the OR distribution. What distribution can I safely assume/use?
| What is the distribution of OR (odds ratio)? | CC BY-SA 2.5 | null | 2010-08-09T17:47:12.227 | 2014-03-31T16:41:03.707 | 2011-04-29T00:22:12.450 | 3911 | 253 | [
"distributions",
"odds-ratio"
] |
1456 | 2 | null | 1455 | 13 | null | The log odds ratio has a Normal asymptotic distribution :
$\log(\hat{OR}) \sim N(\log(OR), \sigma_{\log(OR)}^2)$
with $\sigma$ estimated from the contingency table. See, for example, page 6 of the notes:
- Asymptotic Theory for Parametric Models
| null | CC BY-SA 2.5 | null | 2010-08-09T18:00:24.507 | 2010-08-13T06:44:20.513 | 2010-08-13T06:44:20.513 | 251 | 251 | null |
1457 | 2 | null | 1454 | 1 | null | You could use a [mixture model](http://en.wikipedia.org/wiki/Mixture_model) to separate out the components. The data generating process can be represented as follows:
Let:
$z_i$: be the type (1 or 2) for the $i^{th}$ observation,
$y_i$ be the $i^{th}$ observation.
Then you have:
$f(y_i|z_i=1) \sim N(0,1)$
$f(y_i|z_i=2... | null | CC BY-SA 2.5 | null | 2010-08-09T18:03:31.257 | 2010-08-09T18:36:17.977 | 2010-08-09T18:36:17.977 | null | null | null |
1458 | 1 | null | null | 46 | 6887 | I find it hard to understand what really is the issue with multiple comparisons. With a simple analogy, it is said that a person who will make many decisions will make many mistakes. So very conservative precaution is applied, like Bonferroni correction, so as to make the probability that, this person will make any mi... | Why is multiple comparison a problem? | CC BY-SA 2.5 | null | 2010-08-09T18:03:54.360 | 2020-02-08T06:34:30.300 | 2010-12-17T07:48:12.923 | 223 | 148 | [
"hypothesis-testing",
"multiple-comparisons"
] |
1459 | 1 | null | null | 9 | 9312 | I am trying to build a time series regression forecasting model for an outcome variable, in dollar amount, in terms of other predictors/input variables and autocorrelated errors. This kind of model is also called dynamic regression model. I need to learn how to identify transfer functions for each predictor and would... | How to identify transfer functions in a time series regression forecasting model? | CC BY-SA 2.5 | null | 2010-08-09T18:10:39.633 | 2013-08-28T17:05:23.470 | 2010-08-13T13:04:38.100 | 159 | 833 | [
"time-series",
"forecasting",
"dynamic-regression"
] |
1460 | 1 | 1994 | null | 2 | 1571 | I am trying to figure out the best transformation of my consumption variable. I am running a probit regression to look at whether or not a household enrolls in health insurance. Consumption per capita is an independent variable and in my current model I use both consumption and consumption squared (two separate variab... | Ideal transformation for consumption variable in a probit model | CC BY-SA 2.5 | null | 2010-08-09T18:16:21.917 | 2010-09-16T14:17:36.323 | 2010-09-16T06:56:30.077 | null | 834 | [
"data-transformation",
"econometrics"
] |
1461 | 2 | null | 1460 | 0 | null | It seems to me that you already have a 'partial' statistics answer (better $R^2$ as to the decision as to what to choose: log vs quadratic). You could use other data-driven metrics (e.g., out-of-sample hit rates, whether the parameters are reasonable etc) to judge which model structure is 'better'.
PS: By the way, are... | null | CC BY-SA 2.5 | null | 2010-08-09T18:27:59.960 | 2010-08-09T18:27:59.960 | null | null | null | null |
1462 | 1 | 1467 | null | 4 | 3795 | Let's say I want to make a football simulator based on real-life data.
Say I have a player who averages 5.3 yards per carry with a SD of 1.7 yards.
I'd like to generate a random variable that simulates the next few plays.
eg: 5.7, 4.9, 5.3, etc.
What stats terms to I need to look up to pursue this idea? Density funct... | Using Std.Dev and Mean to generate hypothetical/additional data points? | CC BY-SA 2.5 | null | 2010-08-09T18:53:30.313 | 2010-08-13T16:15:41.417 | null | null | 6967 | [
"standard-deviation"
] |
1463 | 2 | null | 1458 | 41 | null | You've stated something that is a classic counter argument to Bonferroni corrections. Shouldn't I adjust my alpha criterion based on every test I will ever make? This kind of ad absurdum implication is why some people do not believe in Bonferroni style corrections at all. Sometimes the kind of data one deals with in... | null | CC BY-SA 3.0 | null | 2010-08-09T18:55:55.957 | 2016-03-10T00:06:53.230 | 2016-03-10T00:06:53.230 | 601 | 601 | null |
1464 | 2 | null | 1462 | 4 | null | You need a random number generator for the standard normal. Either you can supply mean and standard deviation as arguments to the function, or you simply scale yourself by multiplying with the latter for the variability and adding the former for for the central location.
Here is a quick example of the former approach:... | null | CC BY-SA 2.5 | null | 2010-08-09T19:02:57.657 | 2010-08-09T19:02:57.657 | null | null | 334 | null |
1465 | 2 | null | 1460 | 3 | null | I am not sure I understand your interpretation: a log-transformed predictor would imply that the effect is increasing with diminishing returns, while a quadratic function as a predictor would imply the existance of a peak in the effect (for ax^2+bx+c the peak is at -b/(2a)). I would assume the latter is less realistic ... | null | CC BY-SA 2.5 | null | 2010-08-09T19:13:45.493 | 2010-08-09T19:13:45.493 | null | null | 279 | null |
1466 | 2 | null | 1462 | 5 | null | If you want a realistic simulation you need to find a distribution that describes the real process good enough (a model).
When a real player makes a move he will on average (e.g.) throw `X` yards, with a standard deviation of `Y`. This does however not mean that the distribution of throws is a normal distribution. You ... | null | CC BY-SA 2.5 | null | 2010-08-09T19:13:48.053 | 2010-08-10T06:53:15.300 | 2010-08-10T06:53:15.300 | 56 | 56 | null |
1467 | 2 | null | 1462 | 8 | null | Of course you can use rnorm() in R, but it may be easier to understand how drawing from a pdf works by using the [probability integral transform](http://en.wikipedia.org/wiki/Normal_distribution#Generating_values_from_normal_distribution).
Basically, once we specify the structure of the pdf, we can transform this into ... | null | CC BY-SA 2.5 | null | 2010-08-09T19:53:30.360 | 2010-08-09T20:28:40.977 | 2010-08-09T20:28:40.977 | 291 | 291 | null |
1468 | 2 | null | 1458 | 10 | null | To fix ideas: I will take the case when you obverse, $n$ independent random variables $(X_i)_{i=1,\dots,n}$ such that for $i=1,\dots,n$ $X_i$ is drawn from $\mathcal{N}(\theta_i,1)$. I assume that you want to know which one have non zero mean, formally you want to test:
$H_{0i} : \theta_i=0$ Vs $H_{1i} : \theta_i\neq ... | null | CC BY-SA 2.5 | null | 2010-08-09T21:18:01.033 | 2010-08-10T05:10:38.933 | 2020-06-11T14:32:37.003 | -1 | 223 | null |
1469 | 1 | 2084 | null | 5 | 249 | Can someone recommend a text with derivations of classical estimator efficiency results? I'm particularly interested in likelihood and pseudo-likelihood estimators for multi-variate discrete models
| A Primer on Estimator Efficiency? | CC BY-SA 2.5 | null | 2010-08-09T21:55:08.393 | 2022-11-29T18:35:55.963 | 2019-01-28T08:02:44.497 | 11887 | 511 | [
"estimation",
"references",
"efficiency"
] |
1470 | 2 | null | 1458 | 13 | null | Related to the comment earlier, what the fMRI researcher should remember is that clinically-important outcomes are what matter, not the density shift of a single pixel on a fMRI of the brain. If it doesn't result in a clinical improvement/detriment, it doesn't matter. That is one way of reducing the concern about multi... | null | CC BY-SA 2.5 | null | 2010-08-09T22:18:22.997 | 2010-08-09T22:18:22.997 | null | null | 561 | null |
1471 | 1 | 1473 | null | 13 | 35087 | I need to analyze with R the data from a medical survey (with 100+ coded columns) that comes in a CSV. I will use [rattle](http://rattle.togaware.com/) for some initial analysis but behind the scenes it's still R.
If I read.csv() the file, columns with numerical codes are treated as numerical data. I'm aware I could cr... | Is it possible to directly read CSV columns as categorical data? | CC BY-SA 2.5 | null | 2010-08-09T22:25:11.207 | 2010-08-10T00:25:34.777 | null | null | 840 | [
"r",
"categorical-data",
"data-transformation"
] |
1472 | 2 | null | 1459 | 7 | null | The classic approach, described in [Box, Jenkins & Reinsell (4th ed, 2008)](http://rads.stackoverflow.com/amzn/click/0470272848) involves looking at the cross-correlation function and the various auto-correlation functions, and making a lot of subjective decisions about the orders and lags for the various terms. The ap... | null | CC BY-SA 2.5 | null | 2010-08-09T22:27:53.513 | 2010-08-09T22:27:53.513 | null | null | 159 | null |
1473 | 2 | null | 1471 | 17 | null | You can use the `colClasses` argument to specify the classes of your data columns. For example:
```
data <- read.csv('foo.csv', colClasses=c('numeric', 'factor', 'factor'))
```
will assign numeric to the first column, factor to the second and third. Since you have so many columns, a shortcut might be:
```
data <- re... | null | CC BY-SA 2.5 | null | 2010-08-09T22:31:23.070 | 2010-08-10T00:25:34.777 | 2010-08-10T00:25:34.777 | 251 | 251 | null |
1474 | 2 | null | 1471 | 3 | null | or just do it after you read the data
```
dat <- read.csv("kdfjdkf")
apply(dat, 2, factor)
```
though this type of Q is probably more fit for [Stack Overflow](https://stackoverflow.com/questions/tagged/r).
edit: see below.
| null | CC BY-SA 2.5 | null | 2010-08-09T22:33:37.870 | 2010-08-09T23:48:44.260 | 2017-05-23T12:39:26.523 | -1 | 291 | null |
1475 | 1 | 1491 | null | 14 | 11365 | I want to cluster ~22000 points. Many clustering algorithms work better with higher quality initial guesses. What tools exist that can give me a good idea of the rough shape of the data?
I do want to be able to choose my own distance metric, so a program I can feed a list of pairwise distances to would be just fine. I ... | Visualization software for clustering | CC BY-SA 2.5 | null | 2010-08-09T22:33:40.163 | 2015-07-31T02:31:24.627 | 2010-11-13T20:32:11.607 | 930 | null | [
"data-visualization",
"clustering",
"software"
] |
1476 | 2 | null | 1458 | 26 | null | Well-respected statisticians have taken a wide variety of positions on multiple comparisons. It's a subtle subject. If someone thinks it's simple, I'd wonder how much they've thought about it.
Here's an interesting Bayesian perspective on multiple testing from Andrew Gelman: [Why we don't (usually) worry about multipl... | null | CC BY-SA 2.5 | null | 2010-08-09T23:39:55.867 | 2010-08-09T23:39:55.867 | 2020-06-11T14:32:37.003 | -1 | 319 | null |
1477 | 2 | null | 1385 | 1 | null | If you have a reasonable hunch about the data generating process that is responsible for the data in question then you could use bayesian ideas to estimate the missing data. Under the bayesian approach you would simply assume that the missing data are also random variables and construct the posterior for the missing da... | null | CC BY-SA 2.5 | null | 2010-08-10T00:32:44.947 | 2010-08-10T00:32:44.947 | null | null | null | null |
1478 | 1 | 1479 | null | 3 | 1410 | I am trying to write unit tests for a whole mess of statistics code. Some of the unit tests take the form: generate a sample following a null hypothesis, use code to get a p-value under that null, repeat hundreds of times, then look at all the p-values: if they are reasonably uniform, then the code passes. I usually ch... | Testing implementation of Anderson-Darling test for uniform RV | CC BY-SA 2.5 | null | 2010-08-10T00:33:26.960 | 2018-08-27T08:44:52.570 | 2018-08-27T08:44:52.570 | 11887 | 795 | [
"hypothesis-testing",
"uniform-distribution"
] |
1479 | 2 | null | 1478 | 1 | null | You could test your Anderson-Darling code using data that is generated from an external library. However, you then run into the issue of how to test/trust the external library. At some point you have to trust that well established libraries are error free and that their output can be relied on.
Once you have the Ander... | null | CC BY-SA 2.5 | null | 2010-08-10T00:41:01.463 | 2010-08-10T00:41:01.463 | null | null | null | null |
1480 | 2 | null | 1385 | 2 | null | I might be a little unorthodox here, but what the heck. Please note: this line of thought comes from my own philosophy for classification, which is that I use it when my purpose is squarely on pure prediction -- not explanation, conceptual coherence, etc. Thus, what I'm saying here contradicts how I'd approach building... | null | CC BY-SA 2.5 | null | 2010-08-10T00:43:08.527 | 2010-08-10T00:43:08.527 | null | null | 394 | null |
1481 | 2 | null | 1462 | 1 | null | If you have all the relevant data rather than just summary data such as mean, SD etc. you could create your own distribution model from the real life data you have. Sort the data (y values) from lowest to highest and equally space them between 0 and 1 (x values). Then solve to find the coefficients of an nth order poly... | null | CC BY-SA 2.5 | null | 2010-08-10T01:20:52.150 | 2010-08-10T01:20:52.150 | null | null | 226 | null |
1482 | 2 | null | 1475 | 1 | null | Take a look at [Cluster 3.0](http://bonsai.hgc.jp/~mdehoon/software/cluster/). I'm not sure if it will do all you want, but it's pretty well documented and lets you choose from a few distance metrics. The visualization piece is through a separate program called [Java TreeView](http://jtreeview.sourceforge.net/) ([scr... | null | CC BY-SA 2.5 | null | 2010-08-10T02:54:09.990 | 2010-08-10T02:54:09.990 | null | null | 251 | null |
1483 | 2 | null | 1405 | 10 | null | Assuming the odds ratios are independent, you can proceed as you would in general with any estimate, only you have to look at the log odds.
Take the difference of the log odds, $\delta$. The standard error of $\delta$ is $\sqrt{SE_{1}^2 + SE_{2}^2}$. Then you can obtain a p-value for the ratio $z = \delta/SE(\delta)$... | null | CC BY-SA 2.5 | null | 2010-08-10T04:19:05.090 | 2010-08-17T18:56:31.063 | 2010-08-17T18:56:31.063 | 251 | 251 | null |
1484 | 2 | null | 1475 | 5 | null | Exploring clustering results in high dimensions can be done in [R](http://www.r-project.org/) using the packages [clusterfly](http://had.co.nz/model-vis/) and [gcExplorer](http://cran.r-project.org/web/packages/gcExplorer/index.html). Look for more [here](http://cran.r-project.org/web/views/Cluster.html).
| null | CC BY-SA 2.5 | null | 2010-08-10T06:19:14.900 | 2010-08-10T06:19:14.900 | null | null | 339 | null |
1485 | 1 | 1732 | null | 6 | 1100 | In a particular application I was in need of machine learning (I know the things I studied in my undergraduate course). I used Support Vector Machines and got the problem solved. Its working fine.
Now I need to improve the system. Problems here are
- I get additional training examples every week. Right now the system ... | Few machine learning problems | CC BY-SA 2.5 | null | 2010-08-10T06:41:06.993 | 2010-08-16T12:54:51.460 | 2010-08-16T12:54:51.460 | null | 851 | [
"machine-learning",
"svm"
] |
1486 | 2 | null | 97 | 14 | null | Conventional practice is to use the non-parametric statistics rank sum and mean rank to describe ordinal data.
Here's how they work:
Rank Sum
- assign a rank to each member in each
group;
- e.g., suppose you are looking at goals for each
player on two opposing football
teams then rank each member on
both teams from f... | null | CC BY-SA 3.0 | null | 2010-08-10T06:42:10.703 | 2012-03-19T12:02:50.270 | 2012-03-19T12:02:50.270 | 1036 | 438 | null |
1487 | 1 | 1489 | null | 1 | 161 | We have performed a microarray screening of about 200 samples. In each sample we measure about 100 different variables. For technical reasons the screening of these 200 samples was divided into two batches with a couple of weeks interval between them. When all the data has been collected, I have performed principle com... | Correcting experiment results | CC BY-SA 2.5 | null | 2010-08-10T06:55:21.597 | 2010-09-16T10:02:46.633 | 2010-09-16T09:41:11.077 | 8 | 213 | [
"pca",
"experiment-design",
"normalization",
"microarray"
] |
1488 | 2 | null | 1475 | 1 | null | [Weka](http://www.cs.waikato.ac.nz/ml/weka/) is an open source program for data mining (wirtten and extensible in Java), [Orange](http://www.ailab.si/orange/) is an open source program and library for data mining and machine learning (written in Python). They both allow convenient and efficient visual exploration of mu... | null | CC BY-SA 3.0 | null | 2010-08-10T06:59:13.557 | 2011-12-06T09:35:54.143 | 2011-12-06T09:35:54.143 | 930 | 213 | null |
1489 | 2 | null | 1487 | 2 | null | I would think that the first step would be to examine the component loadings and the actual variables to see if you can identify why the two batches yielded discernible differences. Depending on the reasons for the differences you may or may not be able to use a statistical control to "correct" the results.
However, ... | null | CC BY-SA 2.5 | null | 2010-08-10T07:02:57.383 | 2010-08-10T15:31:41.193 | 2010-08-10T15:31:41.193 | 196 | 196 | null |
1491 | 2 | null | 1475 | 11 | null | GGobi (http://www.ggobi.org/), along with the R package rggobi, is perfectly suited to this task.
See the related presentation for examples: [http://www.ggobi.org/book/2007-infovis/05-clustering.pdf](http://www.ggobi.org/book/2007-infovis/05-clustering.pdf)
| null | CC BY-SA 2.5 | null | 2010-08-10T07:15:35.670 | 2010-08-10T07:15:35.670 | null | null | 5 | null |
1492 | 2 | null | 1149 | 36 | null | I was eating sushi once and thought that it might make a good intuitive demonstration of ill-conditioned problems. Suppose you wanted to show someone a plane using two sticks touching at their bases.
You'd probably hold the sticks orthogonal to each other. The effect of any kind of shakiness of your hands on the pla... | null | CC BY-SA 2.5 | null | 2010-08-10T08:04:22.340 | 2010-08-10T08:04:22.340 | null | null | 167 | null |
1493 | 1 | null | null | 4 | 275 | $\chi^n_k=\sum_{i=1}^kx_i^n$ where $x_i$ are Gaussian variables and $n>2$?
| What is the distribution of $\chi^n_k$? | CC BY-SA 2.5 | null | 2010-08-10T08:45:44.720 | 2011-04-29T00:22:23.557 | 2011-04-29T00:22:23.557 | 3911 | 852 | [
"distributions",
"probability",
"stochastic-processes"
] |
1494 | 2 | null | 1487 | 5 | null | How did you normalise your microarray data? Standard ways are:
- Robust Multichip Average (RMA)
- Genechip RMA - this can be a bit slow for lots of samples.
This [presentation](http://www.ogic.ca/projects/SCNcourse/course_units/unit1/lecture/Introduction%20to%20Affymetrix%20Microarrays.ppt) gives a good overview of... | null | CC BY-SA 2.5 | null | 2010-08-10T08:50:49.683 | 2010-08-10T08:50:49.683 | null | null | 8 | null |
1495 | 1 | 1504 | null | 13 | 412 | Does anyone know of research which investigates the effectiveness (understandability?) of different visualization techniques?
For example, how quickly do people understand one form of visualization over another? Does interactivity with the visualization help people recall the data? Anything along those lines. An examp... | Cognitive processing/interpretation of data visualizations techniques | CC BY-SA 2.5 | null | 2010-08-10T09:02:02.700 | 2021-02-03T15:11:14.310 | 2021-02-03T15:11:14.310 | 101426 | 665 | [
"data-visualization",
"presentation"
] |
1496 | 2 | null | 1444 | 22 | null | I'm presuming that zero != missing data, as that's an entirely different question.
When thinking about how to handle zeros in multiple linear regression, I tend to consider how many zeros do we actually have?
Only a couple of zeros
If I have a single zero in a reasonably large data set, I tend to:
- Remove the point, ... | null | CC BY-SA 4.0 | null | 2010-08-10T09:29:15.230 | 2019-09-19T15:35:09.693 | 2019-09-19T15:35:09.693 | 22047 | 8 | null |
1497 | 2 | null | 1495 | 8 | null | Cleveland reports on a lot of this research in his 1994 book [The Elements of Graphing Data](http://rads.stackoverflow.com/amzn/click/0963488414) (2nd ed). It is very readable and extremely useful.
| null | CC BY-SA 2.5 | null | 2010-08-10T10:24:28.057 | 2010-08-10T10:24:28.057 | null | null | 159 | null |
1498 | 2 | null | 1142 | 2 | null | what I do is group the measurements by hour and day of week and compare standard deviations of that. Still doesn't correct for things like holidays and summer/winter seasonality but its correct most of the time.
The downside is that you really need to collect a year or so of data to have enough so that stddev starts ma... | null | CC BY-SA 2.5 | null | 2010-08-10T10:54:56.550 | 2010-08-10T10:54:56.550 | null | null | 94 | null |
1499 | 2 | null | 1495 | 4 | null | Couple of thoughts:
- I think Bertin's Semiology of Graphics is a classic position in this area.
- As Rob pointed out, Cleveland has done some interesting work in the area, example here.
- Some examples of poor design from Stephen Few.
- Recently I stumbled upon interesting [and quite provocative, especially for T... | null | CC BY-SA 2.5 | null | 2010-08-10T10:58:52.050 | 2010-08-10T10:58:52.050 | 2017-04-13T12:44:41.493 | -1 | 22 | null |
1500 | 2 | null | 1475 | 2 | null | I've had good experience with [KNIME](http://www.knime.org/) during one of my project. It 's an excellent solution for quick exploratory mining and graphing. On top of that it provides R and Weka modules seamless integration.
| null | CC BY-SA 2.5 | null | 2010-08-10T11:06:46.970 | 2010-08-10T11:06:46.970 | null | null | 22 | null |
1501 | 1 | 1503 | null | 4 | 301 | I'm interested in the process of testing or validating a particular implementation of a statistical method, and what datasets and/or published analysis exist that could be used to do this in practice.
For instance, if I write an algorithm to implement a simple linear regression, I might feed in some numbers and check t... | What resources/methods exist for testing/validation or evaluation of Statistical Methods | CC BY-SA 3.0 | null | 2010-08-10T13:47:10.963 | 2013-09-11T19:15:32.583 | 2013-09-11T19:15:32.583 | 22311 | 114 | [
"dataset",
"validation",
"hypothesis-testing"
] |
1502 | 2 | null | 1475 | 1 | null | GGobi does look interesting for this. Another approach could be to treat your similarity/inverse distance matrices as network adjacency matrices and feeding that into a network analysis routine (e.g., either igraph in R or perhaps Pajek). With this approach I would experiment with cutting the cutting the node distances... | null | CC BY-SA 2.5 | null | 2010-08-10T14:02:22.253 | 2010-08-10T14:02:22.253 | null | null | 394 | null |
1503 | 2 | null | 1501 | 2 | null | See the stackoverflow question on this subject: [Datasets for Running Statistical Analysis on](https://stackoverflow.com/questions/2252144/datasets-for-running-statistical-analysis-on/).
I would reiterate [my answer](https://stackoverflow.com/questions/2252144/datasets-for-running-statistical-analysis-on/2252450#225245... | null | CC BY-SA 2.5 | null | 2010-08-10T14:59:06.187 | 2010-08-10T14:59:06.187 | 2017-05-23T12:39:26.593 | -1 | 5 | null |
1504 | 2 | null | 1495 | 5 | null | This subject matter is often discussed under the discipline of HCI ([human-computer interaction](http://en.wikipedia.org/wiki/Human%E2%80%93computer_interaction)) which has [it's own journal](http://www.informaworld.com/smpp/title~db=all~content=t775653648).
There is a lot of great work being done on this at Stanford u... | null | CC BY-SA 2.5 | null | 2010-08-10T15:11:18.593 | 2010-08-10T15:25:14.560 | 2010-08-10T15:25:14.560 | 5 | 5 | null |
1505 | 2 | null | 1495 | 2 | null | Stephen Kosslyn studies human visual processing, and has written a book called [Graph Design for the Eye and Mind](http://rads.stackoverflow.com/amzn/click/0195306627). There's useful stuff in there, but he also suggests funny things sometimes. For example, he suggests truncating the y-axis on bar graphs at some point,... | null | CC BY-SA 2.5 | null | 2010-08-10T15:29:25.843 | 2010-08-10T15:29:25.843 | null | null | 287 | null |
1506 | 2 | null | 1495 | 2 | null | Specifically on color and perception, I liked the papers below by Bergman, Rogowitz and Treinish.
- Why Should Engineers and Scientists Be Worried About Color?
- A Rule-based Tool for Assisting Colormap Selection
- How NOT to Lie with Visualization
- Lloyd Treinish's home page (for links to related work)
| null | CC BY-SA 2.5 | null | 2010-08-10T15:33:16.217 | 2010-08-10T15:33:16.217 | null | null | 251 | null |
1507 | 1 | 1545 | null | 1 | 1821 | Q: Is my approach correct?
Event: You toss 5 coins at once.
A student of mine claimed he got 4T & 1H in 39 out of 40 trials (!!)
I decided to calc the odds of this...
First, P(4T & 1H) = 5C4 * (1/2)^4 * (1/2)^1 = .16
I did this 2 ways:
---
1) Binomial Probability
n = 40
r = 39
p = .16
q = .84
P(Exactly 39) = 40... | Example of using binomial distribution | CC BY-SA 2.5 | null | 2010-08-10T16:03:57.047 | 2010-08-11T14:06:35.990 | null | null | 6967 | [
"binomial-distribution"
] |
1508 | 2 | null | 1507 | 0 | null | Technically, your case 1 and 2 calculations are not correct as they are not independent trials. You are tossing the same 5 coins 40 times. So, those events are dependent.
If you ignore the above issue then the above seems ok.
On some more reflection I think you can ignore the issue of dependency. Here is my reasoning: ... | null | CC BY-SA 2.5 | null | 2010-08-10T16:23:37.183 | 2010-08-10T17:08:25.473 | 2010-08-10T17:08:25.473 | null | null | null |
1509 | 2 | null | 1207 | 4 | null | You could use the Hilbert Transformation from DSP theory to measure the instantaneous frequency of your data. The site [http://ta-lib.org/](http://ta-lib.org/) has open source code for measuring the dominant cycle period of financial data; the relevant function is called HT_DCPERIOD; you might be able to use this or ad... | null | CC BY-SA 2.5 | null | 2010-08-10T17:29:28.280 | 2010-08-10T17:29:28.280 | null | null | 226 | null |
1510 | 2 | null | 1478 | 1 | null | >
I can q-q plot them, but I'm more interested in an automatic unit test I can run.
If a visual inspection of a q-q plot would suffice, then you could calculate an entropy measure such as the [Gini coefficient](http://en.wikipedia.org/wiki/Gini_coefficient) and accept the test after allowing for some tolerance for d... | null | CC BY-SA 2.5 | null | 2010-08-10T17:51:38.350 | 2010-08-10T17:51:38.350 | null | null | 251 | null |
1511 | 2 | null | 1507 | 5 | null | The probability of observing 4 heads and 1 tail 39 times out of 40 after observing 4 heads and 1 tail 39 times out of 40 is 1.0.
:)
| null | CC BY-SA 2.5 | null | 2010-08-10T18:25:52.837 | 2010-08-10T18:25:52.837 | null | null | 601 | null |
1512 | 2 | null | 1207 | 10 | null | If you expect the process to be stationary -- the periodicity/seasonality will not change over time -- then something like a Chi-square periodogram (see e.g. Sokolove and Bushell, 1978) might be a good choice. It's commonly used in analysis of circadian data which can have extremely large amounts of noise in it, but i... | null | CC BY-SA 3.0 | null | 2010-08-10T18:41:10.997 | 2016-08-01T19:09:59.097 | 2016-08-01T19:09:59.097 | 53690 | 61 | null |
1513 | 2 | null | 1462 | 2 | null | if you decide to generate your distribution from the data you have observed, your model will never spit out a "tail value", ie, something outside the range of what you have observed.
your example data:
average 5.3 yards per carry with a SD of 1.7 yards
will have a max and a min, say 10 and 2. in that case, your cal... | null | CC BY-SA 2.5 | null | 2010-08-10T20:20:04.203 | 2010-08-10T20:20:04.203 | null | null | 125 | null |
1514 | 2 | null | 1444 | 17 | null | If you want something quick and dirty why not use the square root?
| null | CC BY-SA 2.5 | null | 2010-08-10T20:48:11.953 | 2010-08-10T20:48:11.953 | null | null | 856 | null |
1515 | 2 | null | 1493 | 2 | null | well, as a bound, if $n$ is even, $\chi_k^n$ will be bounded from below by a Chi-square, and $(\chi_k^n)^{1/n}$ should be bounded from above by the maximum of $k$ half-normals, or thereabouts.
| null | CC BY-SA 2.5 | null | 2010-08-10T21:34:55.513 | 2010-08-10T21:34:55.513 | null | null | 795 | null |
1516 | 2 | null | 118 | 69 | null | The reason that we calculate standard deviation instead of absolute error is that we are assuming error to be normally distributed. It's a part of the model.
Suppose you were measuring very small lengths with a ruler, then standard deviation is a bad metric for error because you know you will never accidentally measur... | null | CC BY-SA 3.0 | null | 2010-08-10T22:34:01.363 | 2016-01-27T22:28:06.527 | 2016-01-27T22:28:06.527 | 858 | 858 | null |
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