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Tags
list
5034
2
null
5025
9
null
You can test this hypothesis with a full versus reduced model test. Here is how you do this. First, fit the model $Z = aX + bY$ and get the residuals from that model. Square the residuals and sum them up. This is the sum of square error for the full model. Let's call this $SSE_f$. Next, calculate $Z - \hat{Z}$ where $\...
null
CC BY-SA 2.5
null
2010-11-30T17:14:08.923
2010-11-30T17:14:08.923
null
null
1934
null
5035
1
5036
null
1
267
I have a study which gives the hazard ratios for certain interventions like: - Intervention 1, HR: .9 - Intervention 2, HR: .8 - ... Is there any way in which I could predict the relative risk for e.g. someone who has intervention 1 and 2? I think if I assume that the interventions are independent, then the HR of...
Can covariates in a Cox Proportional Hazard model be combined in any meaningful way?
CC BY-SA 2.5
null
2010-11-30T19:19:28.500
2010-11-30T20:20:48.150
null
null
900
[ "survival", "hazard" ]
5036
2
null
5035
5
null
The HR of doing both is the product of the separate HRs if you assume that there's no [interaction](http://en.wikipedia.org/wiki/Interaction_%28statistics%29) between the two effects on the multiplicative scale. [Independence](http://en.wikipedia.org/wiki/Independence_%28probability_theory%29) is a separate issue from ...
null
CC BY-SA 2.5
null
2010-11-30T20:20:48.150
2010-11-30T20:20:48.150
null
null
449
null
5038
1
5039
null
8
1200
I'm experimenting with R and found that an anova() needs an object of type lm. But why should I continue with an anova after this: ``` > x <- data.frame(rand=rnorm(100), factor=sample(c("A","B","C"),100,replace=TRUE)) > head(x) rand factor 1 0.9640502 B 2 -0.5038238 C 3 -1.5699734 A 4 -0.842232...
What are the ANOVA's benefits over a normal linear model?
CC BY-SA 2.5
null
2010-11-30T21:01:07.213
2010-12-01T00:12:14.820
2010-12-01T00:12:14.820
null
2091
[ "r", "anova" ]
5039
2
null
5038
16
null
Let's look at what you get when you actually use the anova() function (the numbers are different than in your example, since I don't know what seed you used for generating the random numbers, but the point remains the same): ``` > anova(model) Analysis of Variance Table Response: x$rand Df Sum Sq Mean Sq F...
null
CC BY-SA 2.5
null
2010-11-30T21:46:50.907
2010-11-30T21:46:50.907
null
null
1934
null
5040
2
null
5004
4
null
The Unscented Kalman Filter is a type of non linear Kalman filter. (ie when the transition and observation functions are non linear) If these functions are differentiable, one can simply use the Extended Kalman Filter (EKF). But when the functions are highly non linear, one might need to use an Unscented Kalman Filter ...
null
CC BY-SA 3.0
null
2010-12-01T01:59:00.507
2015-03-16T04:57:20.763
2015-03-16T04:57:20.763
805
1709
null
5041
1
5066
null
7
346
For classification, what theoretical results are between cross-validation estimate of accuracy and generalisation accuracy? I particularly asking about results in a PAC-like framework where no assumptions are made that your function class contains the "true" function. I would love to know if there are theorems of the f...
Theoretical results for cross-validation estimation of classification accuracy?
CC BY-SA 2.5
null
2010-12-01T05:22:59.070
2017-04-08T15:35:36.667
2017-04-08T15:35:36.667
11887
2067
[ "classification", "cross-validation", "pac-learning" ]
5042
1
5044
null
10
11286
So, I have 16 trials in which I am trying to authenticate a person from a biometric trait using Hamming Distance. My threshold is set to 3.5. My data is below and only trial 1 is a True Positive: ``` Trial Hamming Distance 1 0.34 2 0.37 3 0.34 4 0.29 5 0.55 6 0.47 7 0.47 8 0.32 9 0.39 10 0.45 11 0...
Calculate ROC curve for data
CC BY-SA 2.5
null
2010-12-01T06:49:03.427
2015-12-03T16:48:07.387
null
null
1224
[ "mathematical-statistics", "roc" ]
5043
1
null
null
9
2305
I'm currently looking at the unconstrained primal form of the one-vs-all classifier $$\sum\limits_{i=1}^{N_I} \sum\limits_{k=1,\atop k \neq y_i}^{N_K} L(1+ \mathbf{w_k}\cdot\mathbf{x_i}-\mathbf{w_{y_i}}\cdot\mathbf{x_i})$$ where $N_I$ is the number of instances, $N_K$ is the number of classes, $N_F$ is the number of...
Hinge loss with one-vs-all classifier
CC BY-SA 3.0
null
2010-12-01T06:57:43.170
2012-06-02T22:12:56.977
2012-06-02T22:12:56.977
null
2023
[ "classification", "loss-functions" ]
5044
2
null
5042
7
null
I suggest [ROC Graphs: Notes and Practical Considerations for Reasearchers](http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.9777) by Tom Fawcett, really an excellent read. As far as I understand your question, you will find everything you need in this paper. Edit: Inspired by Adam I also want to recommend my ...
null
CC BY-SA 3.0
null
2010-12-01T07:32:11.380
2015-12-03T16:48:07.387
2015-12-03T16:48:07.387
264
264
null
5045
1
null
null
4
235
Consider a series like CPI (inflation), which I know is composed of a series of component prices (e.g. meat prices, grain prices, non-food prices, etc.), which in turn are also composed of a series of component prices (e.g. average meat prices are a combination of pork, beef, and chicken prices). If I wanted to use a r...
In a linear regression whose components can also be broken down, is it better to do multi-layered regression, or flatten to final components?
CC BY-SA 2.5
null
2010-12-01T07:50:58.993
2011-01-10T16:46:43.897
2010-12-01T09:39:25.810
1195
1195
[ "time-series", "regression" ]
5046
2
null
4556
-1
null
find steady state gain of transfer function H(s), we let s=0. since z=exp(sT), to find steady state gain of H(z), let z=exp(0)=1.
null
CC BY-SA 2.5
null
2010-12-01T08:04:02.930
2010-12-01T08:04:02.930
null
null
null
null
5047
2
null
5042
4
null
Why do you want to make an ROC curve? Do you want to graph the curve for your dependent variables, or are you looking to use it as a test statistic in order to gauge the accuracy of your probability predictions (in which case you're looking for the AUC [area under the curve]). If you're familiar with R, the verificatio...
null
CC BY-SA 2.5
null
2010-12-01T08:46:39.030
2010-12-01T08:46:39.030
null
null
2166
null
5048
1
5091
null
2
1257
I have a time serie that I want to analyse through a wavelet decomposition. I am using the R package WaveThres. I am interested in the wavelet autocorrelation, but I struggle to understand what does it mean precisely. I have from the book [Wavelet Methods in Statistics with R](http://www.springer.com/statistics/stati...
Wavelet auto correlation
CC BY-SA 2.5
null
2010-12-01T10:05:09.643
2010-12-02T22:25:41.843
2010-12-01T10:18:28.720
930
1709
[ "correlation", "autocorrelation", "wavelet" ]
5049
1
null
null
8
610
Let $A$ be a finite set and suppose we want to compute the size of some subset $X$. Motivation: If we can generate elements $x$ of $A$ uniformly at random, then we can estimate the size of $A$ by random sampling. That is, we take $n$ random samples from $A$, if $m$ of them belong to $X$, then $|X|/|A| \approx m/n$. U...
Can we estimate the size of a subset X of a set A, by randomly sampling subsets of A?
CC BY-SA 2.5
null
2010-12-01T11:28:41.573
2010-12-01T16:29:30.777
2010-12-01T12:25:50.300
386
386
[ "estimation" ]
5050
2
null
5049
3
null
OK, try reading the wikipedia page for [Monte Carlo integration](http://en.wikipedia.org/wiki/Monte_Carlo_integration). You'll see they mention a stratified version. Stratification is the technical term in statistics for what you attempt: subdividing in subsets (subsamples). I guess the references can help you further....
null
CC BY-SA 2.5
null
2010-12-01T12:23:22.067
2010-12-01T12:23:22.067
null
null
2036
null
5051
2
null
5049
2
null
I assume your measure is finite. WLOG it can be a probability. The first procedure you mention is the good old empirical probability estimate: $\hat{P}(Y\in X)= | \{ x_i \in X\} | /n $ (there montecarlo estimate of an inetgral is a good interpretation also). In high dimension it does not work since $\{x_i\in X\}$ is...
null
CC BY-SA 2.5
null
2010-12-01T12:34:07.033
2010-12-01T16:08:12.340
2010-12-01T16:08:12.340
223
223
null
5052
2
null
4892
1
null
The answer is 6. See the edits above for details.
null
CC BY-SA 2.5
null
2010-12-01T13:10:35.207
2010-12-01T13:10:35.207
null
null
1351
null
5053
2
null
4983
0
null
``` sv_num: one added to the number of support vectors b: offset alpha: 0, then "a" corresponding to the support vectors, then only zeros index: link index between "a" and alpha, "x" and supvec supvec: 0, then "x" corresponding to the support vectors a: weights_i (between 0 and C) times y_i ```
null
CC BY-SA 2.5
null
2010-12-01T13:23:03.733
2010-12-01T13:23:03.733
null
null
1351
null
5054
1
null
null
4
290
Say we are studying Twitter hashtags over time. We monitor how popular they are day to day. Some hashtags may be volatile (i.e. "lunch", "Celtics", "Friday"). Their popularity rises and falls frequently. Some hashtags may be in the process of becoming unpopular (i.e. "Gulf oil spill", "Transformers 2", "Christine O'...
Is there a mathematical model that distinguishes between volatility and trend?
CC BY-SA 2.5
null
2010-12-01T16:14:58.283
2011-05-12T20:00:40.270
null
null
null
[ "volatility-forecasting" ]
5055
2
null
5049
3
null
For any subset $Y$ of $A$, let $\pi(Y)$ be the probability you will select it in your sampling. You have described a random variable $$f(Y) = |Y \cap X|.$$ The total of $f$ in the population of subsets of $A$ is $$\tau(X) = \sum_{Y \subset A}|Y \cap X| = 2^{|A|-1}|X|.$$ From a sample (with replacement) of subsets of...
null
CC BY-SA 2.5
null
2010-12-01T16:29:30.777
2010-12-01T16:29:30.777
null
null
919
null
5056
1
5080
null
21
22620
Given the support vectors of a linear SVM, how can I compute the equation of the decision boundary?
Computing the decision boundary of a linear SVM model
CC BY-SA 2.5
null
2010-12-01T18:25:03.223
2017-11-08T12:10:41.377
2010-12-03T08:06:06.830
930
2221
[ "machine-learning", "svm" ]
5057
2
null
5056
4
null
It's a linear combination of the support vectors where the coefficients are given by the Lagrange multipliers corresponding to these support vectors.
null
CC BY-SA 2.5
null
2010-12-01T20:04:56.970
2010-12-01T20:04:56.970
null
null
881
null
5058
1
null
null
6
1583
In a social experiment that I was conducting, I was trying to count the number of people each user contacted in a period of 10 days. The population size was 100 for the experiment. Based on the values that I calculated, I fit a negative binomial distribution to the data (the Q-Q plot is given below). Conventional wisdo...
Is there any relation between Power Law and Negative Binomial distribution?
CC BY-SA 2.5
null
2010-12-01T20:16:27.117
2010-12-02T04:00:56.167
null
null
2164
[ "r", "distributions", "probability", "modeling" ]
5059
2
null
4551
43
null
interpreting `Probability(data | hypothesis)` as `Probability(hypothesis | data)` without the application of Bayes' theorem.
null
CC BY-SA 2.5
null
2010-12-01T20:17:08.233
2010-12-01T20:17:08.233
null
null
961
null
5060
2
null
4551
6
null
Probably not as applicable to psych stats (or is it? I'm not sure) but failing to account for a split plot design in an analysis of an experiment. I've seem way too many people do this.
null
CC BY-SA 2.5
null
2010-12-01T21:09:50.050
2010-12-01T21:09:50.050
null
null
1028
null
5061
2
null
5026
9
null
I'd add some observations to what's been said... AI is a very broad term for anything that has to do with machines doing reasoning-like or sentient-appearing activities, ranging from planning a task or cooperating with other entities, to learning to operate limbs to walk. A pithy definition is that AI is anything compu...
null
CC BY-SA 2.5
null
2010-12-01T21:17:22.760
2010-12-01T21:17:22.760
null
null
1764
null
5062
1
5063
null
1
3114
I have data points from a half circle and I already know the radius. I want to find the circle which best fits the points using a fixed radius. How can I do this? If I solve the problem using a typical circle fit algorithm the radius is too unstable due to "noise".
Geometric circle fitting with known radius
CC BY-SA 2.5
null
2010-12-01T21:43:00.990
2010-12-01T22:06:55.510
null
null
2223
[ "nonlinear-regression" ]
5063
2
null
5062
3
null
It depends on how the points might depart from the circle. If they do so through measurement error, a natural model is that their locations are binormally distributed with the coordinates $x$ and $y$ uncorrelated, of equal variances. This leads to a difficult model to fit, but if the errors are not too great compared...
null
CC BY-SA 2.5
null
2010-12-01T22:06:55.510
2010-12-01T22:06:55.510
null
null
919
null
5064
2
null
5026
16
null
I'm most familiar with the machine-learning - data mining axis - so I'll concentrate on that: Machine learning tends to be interested in inference in non-standard situations, for instance non-i.i.d. data, active learning, semi-supervised learning, learning with structured data (for instance strings or graphs). ML also...
null
CC BY-SA 2.5
null
2010-12-01T23:57:48.737
2010-12-01T23:57:48.737
null
null
887
null
5065
1
5067
null
2
2287
I want to find $\theta$ such that $ \theta = argmin_{\theta} \left( \left|\left| Y - \sum_{i=1}^k \theta_i X_i \right|\right| \right) $ where $X_i$ and $Y$ are N x N matrices and $\theta$ is a weight vector that specifies how to linearly combine the $k$ $X$'s to approximate Y. This smells like a linear optimization pr...
How can I find the best linear combination of a set of matrices to approximate a target matrix?
CC BY-SA 2.5
null
2010-12-02T01:24:18.253
2010-12-17T07:57:59.127
2010-12-17T07:57:59.127
223
2224
[ "regression", "optimization", "matrix" ]
5066
2
null
5041
3
null
I don't know much about these kinds of proofs, but I think John Langford's thesis might be a good reference. Here's a relevant page: [http://hunch.net/~jl/projects/prediction_bounds/prediction_bounds.html](http://hunch.net/~jl/projects/prediction_bounds/prediction_bounds.html) and the probably relevant section of the t...
null
CC BY-SA 2.5
null
2010-12-02T02:45:59.310
2010-12-02T02:45:59.310
null
null
2077
null
5067
2
null
5065
5
null
$\theta = argmin_{\theta} (Y - \sum_{i=1}^k \theta_i X_i)$ would be an affine function in $\theta$ and hence an unconstrained linear program. But $\theta = argmin_{\theta} || Y - \sum_{i=1}^k \theta_i X_i ||$ has an arbitrary norm. Fortunately, norms are convex and convexity is preserved under compositions with affin...
null
CC BY-SA 2.5
null
2010-12-02T03:39:19.017
2010-12-02T03:47:30.290
2010-12-02T03:47:30.290
1815
1815
null
5069
2
null
5058
2
null
There are many power-law distributions, so you have a lot of possible models. You might start by trying to fit a [log-series distribution](http://en.wikipedia.org/wiki/Logarithmic_distribution), which is a limiting case of the negative binomial. Don't think a priori that you have a mixture distribution as suggested ...
null
CC BY-SA 2.5
null
2010-12-02T04:00:56.167
2010-12-02T04:00:56.167
null
null
5792
null
5070
1
5072
null
4
1134
If we have a loaded coin that plays out 75% heads, 25% tails, what would be the best way to bet on the outcome of each of $n$ trials? How could we maximize our probability of winning? Is it possible to generalize for a coin that's loaded $n:(100-n)$?
Maximizing probability of winning on loaded coin
CC BY-SA 2.5
null
2010-12-02T04:20:55.457
2013-01-02T18:51:39.693
2010-12-02T09:29:43.640
930
2226
[ "probability", "dice" ]
5071
2
null
5070
6
null
1/ do you already know the bias n? 2/ if yes (actually you need only to know which side of the coin is heavier) then you cannot do better than always bet on this side. In the long term, you'll have a n % success ratio. You cannot do better because the trials are independent.
null
CC BY-SA 2.5
null
2010-12-02T04:54:20.090
2010-12-02T04:54:20.090
null
null
1709
null
5072
2
null
5070
9
null
In what follows, I will assume you mean someone gives you 1:1 odds on the loaded coin. You are looking for the [Kelly criterion](http://en.wikipedia.org/wiki/Kelly_criterion), which states: $$ f^* = \frac{ b p - q }{ b } $$ where (just copying from wikipedia) $f^*$ is the fraction of your bank roll, $b$ is the fractio...
null
CC BY-SA 2.5
null
2010-12-02T05:34:57.873
2010-12-02T15:02:08.493
2010-12-02T15:02:08.493
2168
2168
null
5073
1
5075
null
7
7179
I have a data-frame whose first column is the name of an item and the second column is the frequency of that item in the dataset. ``` names freq 1 tomato 7 2 potato 4 3 cabbage 5 4 sukuma-wiki 8 5 terere 20 ``` I would like to have a stacked bar column that depi...
Stacked bar plot
CC BY-SA 3.0
null
2010-12-02T06:09:21.087
2015-02-09T13:34:20.480
2011-11-21T22:34:57.970
930
18462
[ "r", "data-visualization", "barplot" ]
5074
2
null
5073
6
null
For the coloring, either you specify a list of colors or you generate them. In the latter, I suggest you execute this code ``` n = 32; main.name = paste("color palettes; n=",n) ch.col = c("rainbow(n, start=.7, end=.1)", "heat.colors(n)", "terrain.colors(n)", "topo.colors(n)", "cm.colors(n)"); nt <- length(c...
null
CC BY-SA 2.5
null
2010-12-02T06:27:26.500
2010-12-02T07:33:43.230
2010-12-02T07:33:43.230
1709
1709
null
5075
2
null
5073
13
null
With 60 distinct categories, I feel you may have a hard time making that an effective graphic. You may want to consider a regular bar-chart that is sorted in ascending or descending order. Whether or not these are counts or percentages is up to you. Maybe something like this: ``` library(ggplot2) df$names <- reorder(df...
null
CC BY-SA 2.5
null
2010-12-02T07:26:52.260
2010-12-02T07:56:40.507
2010-12-02T07:56:40.507
696
696
null
5076
2
null
5073
7
null
I doubt you fill find a suitable range of distinct colours with so much categories. Anyway, here are some ideas: - For stacked barchart, you need barplot() with beside=FALSE (which is the default) -- this is in base R (@Chase's solution with ggplot2 is good too) - For generating a color ramp, you can use the RColorBr...
null
CC BY-SA 2.5
null
2010-12-02T07:35:19.660
2010-12-02T07:35:19.660
null
null
930
null
5077
1
null
null
17
2386
I'm trying to implement the hit and run MCMC algorithm, but I'm having a bit of trouble understanding how to go about it. The general idea, is as follows: > To generate a proposal jump in MH, we: Generate a direction $d$ from a distribution on the surface of the unit sphere $\mathcal{O}$ Generate a signed di...
Hit and run MCMC
CC BY-SA 2.5
null
2010-12-02T10:31:27.627
2017-04-24T07:45:30.210
2010-12-02T11:21:44.393
8
null
[ "r", "bayesian", "markov-chain-montecarlo" ]
5078
1
5085
null
3
5622
Sorry for a possibly ignorant question. I have fit a mixed-effects model using the lmer function from the lme4 package, and the main fixed effect (a factor with three levels) in the model was significant according to a run with pvals.fnc (from the languageR package). To illustrate the effect in an appealing way, I woul...
Confidence-intervals for conditions tested with a mixed-effects model
CC BY-SA 2.5
null
2010-12-02T10:32:07.580
2013-06-27T08:51:47.620
2017-04-13T12:44:24.947
-1
2228
[ "r", "confidence-interval", "mixed-model" ]
5079
1
5084
null
6
2162
I have some data which describe residential units for people with learning disability, variables like how nice the furnishings are, the level of psychiatric symptomology on the unit, how happy the staff are, stuff like that. I want to check to see if we are measuring the right things- e.g. do units with happier staff h...
Compare rank orders of population members across different variables
CC BY-SA 2.5
null
2010-12-02T10:33:12.123
2010-12-02T12:44:04.133
2010-12-02T11:07:53.903
930
199
[ "ranks" ]
5080
2
null
5056
30
null
The [Elements of Statistical Learning](https://web.stanford.edu/~hastie/ElemStatLearn/), from Hastie et al., has a complete chapter on support vector classifiers and SVMs (in your case, start page 418 on the 2nd edition). Another good tutorial is [Support Vector Machines in R](http://www.ci.tuwien.ac.at/~meyer/svm/fina...
null
CC BY-SA 3.0
null
2010-12-02T10:37:22.867
2017-11-08T12:10:41.377
2017-11-08T12:10:41.377
132810
930
null
5081
1
null
null
1
3609
As the headline suggest, I am looking for a java library for learning and inference of Bayesian Networks. I have already found some, but I am hoping for a recommendation. Requirements in a quick overview: - written in Java (my overlord tells me that this is no point of discussion) - configuration is possible via code...
Java library for Bayesian Networks
CC BY-SA 3.0
null
2010-12-02T11:17:13.693
2017-11-22T14:24:28.683
2017-11-22T14:24:28.683
11887
264
[ "bayesian", "bayesian-network", "software", "java" ]
5082
2
null
5081
2
null
See the [packages](http://weka.sourceforge.net/doc.dev/overview-summary.html) of the open source project Weka, which is a collection of machine learning algorithms for data mining tasks. The algorithms can either be applied directly to a dataset or called from your own Java code. This is the class for [Bayes Network l...
null
CC BY-SA 2.5
null
2010-12-02T11:30:28.597
2010-12-02T11:30:28.597
null
null
339
null
5083
1
null
null
6
743
The signal to noise ratio is simple, and is usually defined in the context of simple Gaussian local-level models. In the cause of non-gaussian signal or noise models, do people do things more complicated then the ratio of the variances of the two distributions?
Generalization of the Signal-Noise ratio for non-Gaussian processes
CC BY-SA 2.5
null
2010-12-02T11:33:03.493
2012-05-03T16:17:11.510
null
null
996
[ "mixed-model", "signal-processing" ]
5084
2
null
5079
7
null
I don't know how useful the following approach is, but one might conceptualize the situation slightly differently: imagine the different variables are raters who simply order the units from "best" to "worst". You expect that the rank order will be similar among "raters". This seems to be an application for Kendall's co...
null
CC BY-SA 2.5
null
2010-12-02T11:48:46.770
2010-12-02T12:44:04.133
2010-12-02T12:44:04.133
1909
1909
null
5085
2
null
5078
3
null
The [DRAFT r-sig-mixed-models FAQ](http://glmm.wikidot.com/faq) details (in the "Predictions and/or confidence (or prediction) intervals on predictions" section) how to obtain predictions and confidence intervals for cells in the design of a mixed effects model. The ezPredict() function in the ez package wraps the code...
null
CC BY-SA 2.5
null
2010-12-02T12:27:31.840
2010-12-02T12:27:31.840
null
null
364
null
5086
2
null
5081
3
null
You can easily accomplish this with R though rJava ([JRI](http://rosuda.org/JRI/), to be precise). You should tell your overlord that you want to use the best tool for the job.
null
CC BY-SA 2.5
null
2010-12-02T14:46:14.977
2010-12-02T14:46:14.977
null
null
5
null
5087
1
5088
null
7
1642
There are numerous procedures for functional data clustering based on orthonormal basis functions. I have a series of models built with the GAMM models, using the `gamm()` from the mgcv package in R. For fitting a long-term trend, I use a thin plate regression spline. Next to that, I introduce a CAR1 model in the rando...
Use coefficients of thin plate regression splines in a clustering method
CC BY-SA 2.5
null
2010-12-02T15:18:04.343
2010-12-03T09:12:20.757
null
null
1124
[ "r", "clustering", "mgcv" ]
5088
2
null
5087
4
null
If I understand correctly, I think you want the coefficients from the `$gam` component: ``` > coef(test$gam) (Intercept) s(x1).1 s(x1).2 s(x1).3 s(x1).4 s(x1).5 21.8323526 9.2169405 15.7504889 -3.4709907 16.9314057 -19.4909343 s(x1).6 s(x1).7 s(x1).8 s(x1).9 s(x2).1 s...
null
CC BY-SA 2.5
null
2010-12-02T15:49:45.877
2010-12-03T09:12:20.757
2010-12-03T09:12:20.757
1390
1390
null
5089
2
null
5065
3
null
If your norm is a hilbert space norm (for example root mean square error, also called hilbert schmidt norm in the case of matrices or l^2 norm if you take them as vectors) then obtaining the solution is a first year calculous exercise if you rephrase things using: $c=(\langle Y,X_i \rangle)_{i=1,\dots,k}$ and $A=(\lan...
null
CC BY-SA 2.5
null
2010-12-02T16:19:17.053
2010-12-02T16:19:17.053
null
null
223
null
5090
1
5641
null
8
1933
The R package [dlm](http://cran.r-project.org/web/packages/dlm/index.html) implements filtering and smoothing (`dlmFilter` and `dlmSmooth`) for models with regression effects, but forecasting is not (yet) available for these models: ``` mod <- dlmModSeas(4)+dlmModReg(cbind(rnorm(100),rnorm(100))) fi <- dlmFilter(rnorm(...
Gaussian state space forecasting with regression effects
CC BY-SA 2.5
null
2010-12-02T21:44:09.290
2016-05-23T08:16:00.953
2010-12-02T22:55:07.853
159
null
[ "r", "forecasting", "dlm" ]
5091
2
null
5048
1
null
The correlation coefficient of two sets of values is one number. The auto-correlation of one set of values is a function (see e.g. [http://en.wikipedia.org/wiki/Autocorrelation](http://en.wikipedia.org/wiki/Autocorrelation) ). Let's call the argument of the function `t` (looks like it's the $\tau$ in your question), t...
null
CC BY-SA 2.5
null
2010-12-02T22:25:41.843
2010-12-02T22:25:41.843
null
null
961
null
5092
1
null
null
9
2119
I am a stats newbie, so apologies in advance if I'm asking a braindead question. I have searched for answers to my question, but I find that many of the topics are either too specific, or quickly go beyond what I currently comprehend. I have some simulation work that includes large datasets which become infeasible to s...
How to calculate sample size for simulation in order to assert some level of goodness in my results?
CC BY-SA 3.0
null
2010-12-02T23:24:13.180
2011-10-04T23:33:55.633
2011-10-04T23:33:55.633
183
2246
[ "distributions", "sample-size", "experiment-design", "sampling" ]
5093
1
5095
null
6
1120
I am currently working on a RandomForest based prediction method using protein sequence data. I have generated two models first model (NF) using standard set of features and the second model (HF) using hybrid features. I have done Mathews Correlation Coefficient (MCC) and Accuracy calculation and the following are my r...
Statistical validation of RandomForest models
CC BY-SA 2.5
null
2010-12-03T00:12:49.363
2010-12-03T00:53:44.013
2010-12-03T00:35:31.087
null
529
[ "machine-learning", "cross-validation", "random-forest" ]
5094
2
null
5093
4
null
It just seems those two variants are equivalent; yet some better test should be made to confirm this, at least cross validation. Also if this NF and HF sets have some attributes in common, it may suggest that only this common part is useful -- I would invest some time in making feature selection.
null
CC BY-SA 2.5
null
2010-12-03T00:34:34.147
2010-12-03T00:34:34.147
null
null
null
null
5095
2
null
5093
8
null
I like the idea of parsimony- the smaller the number of variables in the model, the better. Unless you are driven theoretically of course. Feature selection refers to the process of choosing which variables to use in the model (getting the best combination of variables). There are lots of different options for feature ...
null
CC BY-SA 2.5
null
2010-12-03T00:53:44.013
2010-12-03T00:53:44.013
null
null
2238
null
5096
2
null
4904
0
null
I will repost the answer I gave on math.stackexchange: Your question needs some more information: How is their score generated (what kind of game is it)? What should your non-cheating data look like? How do people cheat? How will their score be different (in a statistical sense) when they are not cheating? Do you know ...
null
CC BY-SA 2.5
null
2010-12-03T04:58:22.370
2010-12-03T04:58:22.370
null
null
1146
null
5097
1
5099
null
4
3063
This is a follow-up of the question I posted [earlier](https://stats.stackexchange.com/questions/5093/statistical-validation-of-randomforest-models). I am assessing the two RF models which are generated using two different set of features > NF - Test_Accuracy > Training accuracy (500 features) HF - Test_Accuracy < Tra...
How to assess overfitting?
CC BY-SA 2.5
null
2010-12-03T05:23:38.833
2016-04-25T20:50:50.197
2020-06-11T14:32:37.003
-1
529
[ "machine-learning", "random-forest" ]
5098
2
null
5092
6
null
I think the answer to your question is a couple other questions: how rare does a given test outcome need to be before you don't care about it? How certain do you want to be that you'll actually find at least test that comes out that way if it occurs right at the threshold where you've stopped caring about it. Given t...
null
CC BY-SA 2.5
null
2010-12-03T05:41:03.173
2010-12-03T05:41:03.173
null
null
196
null
5099
2
null
5097
9
null
This result does not mean that you have overfitting. First of all, CV is more reliable than test set -- you can have (bad) luck in selecting test, what results in (pessimistic) optimistic bias with respect to true accuracy. CV effectively smooths this problem by repeating the procedure of selecting test. What's worse f...
null
CC BY-SA 2.5
null
2010-12-03T09:36:39.130
2010-12-03T09:36:39.130
null
null
null
null
5100
1
5103
null
2
444
this is my first question on this site, so please be patient with me. I am doing a random walk, where I build a timeseries curve. I do that a preset number of times ( let's say 100 times ). Now I was wondering what should I do with all the generated curves. Eventually I want to have 1 curve that is the best representat...
Random walk data post processing
CC BY-SA 2.5
null
2010-12-03T12:32:23.160
2010-12-03T14:00:26.023
null
null
2218
[ "random-variable" ]
5102
2
null
5100
2
null
Plotting the mean or median for each timepoint sounds a sensible start. You could also plot a [reference range](http://en.wikipedia.org/wiki/Reference_range) for each timepoint to show the variability across curves at each timepoint. You could also add a few (perhaps 5 or 10) randomly-chosen curves to illustrate the va...
null
CC BY-SA 2.5
null
2010-12-03T13:22:49.450
2010-12-03T13:22:49.450
null
null
449
null
5103
2
null
5100
5
null
I'm somewhat confused - if these are random walks, isn't the expectation a flat, uninteresting line? ``` set.seed(123) nWalks <- 1000 nTimes <- 100 mat <- matrix(c(rep(0, nWalks), rnorm(nWalks*(nTimes-1))), ncol = nTimes) rwalks <- apply(mat, 1, cumsum) matplot(rwalks, type = "l") ## Stack the data for fi...
null
CC BY-SA 2.5
null
2010-12-03T13:55:13.343
2010-12-03T13:55:13.343
null
null
1390
null
5104
2
null
5100
1
null
If you're simply looking for a way of representing a process for readers, look up "diffusion modelling" in the psychological literature and you'll find how those folks typically attempt to represent a stochastic process and typical exemplar.
null
CC BY-SA 2.5
null
2010-12-03T14:00:26.023
2010-12-03T14:00:26.023
null
null
364
null
5105
2
null
4259
1
null
The best introductory Bayesian book I have found is [Data Analysis - A Bayesian Tutorial](http://rads.stackoverflow.com/amzn/click/0198518897). It is quite practical.
null
CC BY-SA 2.5
null
2010-12-03T16:23:28.423
2010-12-03T16:23:28.423
null
null
1146
null
5107
1
5183
null
4
1436
Say I have a set of sample points generated by a multivariate normal distribution D whose parameters I don't know. I want to be able to measure the distance from an arbitrary point to the distribution D. One way of doing this would be to get an estimate of the parameters of D, and use it to get the manalanobis distance...
(Mahalanobis) distance to a multivariate distribution of which I have few sample points
CC BY-SA 2.5
null
2010-12-03T17:40:07.863
2011-08-30T12:25:24.120
2010-12-03T20:47:09.717
930
1737
[ "classification", "multivariate-analysis", "distance-functions" ]
5109
1
5113
null
6
4099
When minimizing a function by general Metropolis-Hastings algorithms, the function is viewed as an unnormalized density of some distribution. (1) As density functions are required to be nonnegative, I was wondering if there is some restriction on functions that can be minimized by Metropolis-Hastings algorithms? (2) T...
Minimization of a function by Metropolis-Hastings algorithms
CC BY-SA 2.5
null
2010-12-03T20:34:20.547
2020-05-02T08:38:51.247
2010-12-05T00:35:31.170
1005
1005
[ "self-study", "optimization", "monte-carlo", "metropolis-hastings" ]
5110
2
null
726
6
null
> “Statistics is much like a streetlight. Not very enlightening, but nice for supporting you” [Storm P](https://secure.wikimedia.org/wikipedia/en/wiki/Robert_Storm_Petersen#Quotes)
null
CC BY-SA 2.5
null
2010-12-03T21:05:59.607
2010-12-03T21:05:59.607
null
null
2247
null
5111
1
null
null
6
431
I have a question regarding the sign test when the individual measurements may be correlated. Let me start off with some background. Suppose we have 4 Organisms (a,b,c,d),and we make measurements in two separate ways, say A and B. Our data may look as follows a = 3 for measurement A and 1 for measurement B b = 4 for me...
Nonparametric sign test for correlated variables
CC BY-SA 2.5
null
2010-12-03T22:19:21.333
2010-12-21T18:22:10.200
2010-12-20T19:28:26.343
919
null
[ "hypothesis-testing", "nonparametric" ]
5112
2
null
5109
3
null
If you want to find the global minimum of a function, [simulated annealing](http://en.wikipedia.org/wiki/Simulated_annealing) would be the algorithm to look at, in which case there is no need to view the function as an unnormalised density of any kind and no need to transform the function.
null
CC BY-SA 2.5
null
2010-12-03T23:45:11.203
2010-12-03T23:45:11.203
null
null
887
null
5113
2
null
5109
7
null
You are rather looking for a simulated annealing, which is easier to understand when formulated in the original, physics way: Having - $x$ is a state of the system - $f(x)$ is an energy of the system; energy is defined up to addition of a constant, so there is no problem with it being negative or positive -- the only...
null
CC BY-SA 2.5
null
2010-12-03T23:50:56.123
2010-12-04T12:44:09.460
2010-12-04T12:44:09.460
null
null
null
5114
1
5411
null
8
320
I am trying to state a prior distribution for a Bayesian meta-analysis. I have the following information about a random variable: - Two observations: 3.0, 3.6 - a scientist who studies the variable has told me that $P(X<2)=P(X>8)=0$, and that values as high as 6 have nonzero probability. I have used the following ...
Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints?
CC BY-SA 2.5
null
2010-12-03T23:57:59.227
2010-12-15T17:34:52.937
2010-12-15T17:34:52.937
1381
1381
[ "r", "distributions", "probability", "bayesian", "optimization" ]
5115
1
5124
null
64
10822
What are the most important statisticians, and what is it that made them famous? (Reply just one scientist per answer please.)
Most famous statisticians
CC BY-SA 3.0
null
2010-12-04T00:08:23.027
2022-10-08T18:09:33.393
2014-04-06T02:40:34.817
32036
1808
[ "methodology", "history" ]
5116
2
null
5115
38
null
[Pierre-Simon Laplace](http://en.wikipedia.org/wiki/Laplace) for work on fundamentals of (Bayesian) probability.
null
CC BY-SA 2.5
null
2010-12-04T00:18:06.090
2010-12-04T00:18:06.090
null
null
887
null
5117
2
null
5115
94
null
[Ronald Fisher](http://en.wikipedia.org/wiki/Ronald_Fisher) for his fundamental contributions to the way we analyze data, whether it be the analysis of variance framework, maximum likelihood, permutation tests, or any number of other ground-breaking discoveries.
null
CC BY-SA 2.5
null
2010-12-04T00:36:08.460
2010-12-04T00:36:08.460
null
null
1118
null
5118
2
null
5115
52
null
[Karl Pearson](http://en.wikipedia.org/wiki/Karl_Pearson) for his work on mathematical statistics. Pearson correlation, Chi-square test, and principal components analysis are just a few of the incredibly important ideas that stem from his works.
null
CC BY-SA 2.5
null
2010-12-04T01:32:33.420
2010-12-04T01:32:33.420
null
null
1028
null
5119
1
5120
null
4
2485
I asked this question on mathoverflow yesterday and got a suggestion to try it here. I apologize if this is an easy question, but I can't seem to find an answer anywhere. I'm trying to duplicate a macroeconomic paper that uses MCMC analysis to derive time series and parameter values. For the variance of a white noise t...
Square root of inverse gamma distribution?
CC BY-SA 2.5
null
2010-12-04T02:13:27.347
2014-04-05T09:29:54.803
null
null
2251
[ "distributions", "probability", "bayesian" ]
5120
2
null
5119
5
null
You need not worry about the square root of the error variance. Instead, sample the error variance directly conditional on everything else. The posterior of the error variance will also be an inverse gamma given your model assumptions. So, I am not sure why you want to know the square root of the inverse-gamma. Edit: ...
null
CC BY-SA 2.5
null
2010-12-04T02:51:18.860
2010-12-04T03:10:39.210
2010-12-04T03:10:39.210
null
null
null
5121
2
null
22
51
null
Just a little bit of fun... # A Bayesian is one who, vaguely expecting a horse, and catching a glimpse of a donkey, strongly believes he has seen a mule. From this site: [http://www2.isye.gatech.edu/~brani/isyebayes/jokes.html](http://www2.isye.gatech.edu/~brani/isyebayes/jokes.html) and from the same site, a nice e...
null
CC BY-SA 2.5
null
2010-12-04T03:06:00.983
2010-12-04T03:12:36.393
2010-12-04T03:12:36.393
485
485
null
5122
2
null
5115
32
null
[Francis Galton](http://en.wikipedia.org/wiki/Francis_Galton) for discovering statistical correlation and promoting regression.
null
CC BY-SA 3.0
null
2010-12-04T03:37:32.367
2011-08-09T17:17:42.100
2011-08-09T17:17:42.100
74
74
null
5123
2
null
5115
30
null
[Andrey Markov](http://en.wikipedia.org/wiki/Andrey_Markov) for stochastic processes and markov chains.
null
CC BY-SA 2.5
null
2010-12-04T03:38:44.393
2010-12-04T03:38:44.393
null
null
74
null
5124
2
null
5115
56
null
Reverend [Thomas Bayes](http://en.wikipedia.org/wiki/Thomas_Bayes) for discovering Bayes' theorem
null
CC BY-SA 3.0
null
2010-12-04T03:46:20.583
2012-08-02T03:09:39.773
2012-08-02T03:09:39.773
74
74
null
5125
2
null
5115
50
null
[Carl Gauss](http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss) for least squares estimation.
null
CC BY-SA 3.0
null
2010-12-04T03:48:36.697
2012-08-02T03:11:50.300
2012-08-02T03:11:50.300
74
74
null
5126
2
null
22
31
null
The Bayesian is asked to make bets, which may include anything from which fly will crawl up a wall faster to which medicine will save most lives, or which prisoners should go to jail. He has a big box with a handle. He knows that if he puts absolutely everything he knows into the box, including his personal opinion, an...
null
CC BY-SA 2.5
null
2010-12-04T06:54:30.117
2010-12-04T06:54:30.117
null
null
1789
null
5128
1
5130
null
8
411
We are preparing a manuscript and the editor asked us to convert a figure with a boxplot into a table "because of the more exact data content". While I think boxplots are pretty decent in revealing something about the data, I was wondering what you guys think about this? Do you (often) opt for tables over boxplots for ...
Boxplots as tables
CC BY-SA 2.5
null
2010-12-04T09:05:32.740
2010-12-04T15:54:10.600
2010-12-04T15:54:10.600
null
144
[ "data-visualization", "boxplot", "tables" ]
5129
2
null
5128
3
null
It depends on your objective, if it is a quick visualization I will stick with boxplot but if it is a more detailed examination I would stay with the data
null
CC BY-SA 2.5
null
2010-12-04T09:22:22.180
2010-12-04T09:22:22.180
null
null
1808
null
5130
2
null
5128
13
null
I tend to think that boxplots will convey more effective information if there are numerous empirical distributions that you want to summarize into a single figure. If you only have two or three groups, editors may ask you to provide numerical summaries instead, either because it is more suitable for the journal policy,...
null
CC BY-SA 2.5
null
2010-12-04T09:23:44.360
2010-12-04T09:50:30.397
2010-12-04T09:50:30.397
930
930
null
5131
2
null
5115
24
null
[Edwin Thompson Jaynes](http://en.wikipedia.org/wiki/Edwin_Thompson_Jaynes) for work on objective Bayesian methods, particularly MaxEnt and transformation groups.
null
CC BY-SA 2.5
null
2010-12-04T10:52:07.720
2010-12-04T10:52:07.720
null
null
887
null
5132
2
null
5115
25
null
[Harold Jeffreys](http://en.wikipedia.org/wiki/Harold_Jeffreys) for revival of Bayesian interpretation of probability.
null
CC BY-SA 2.5
null
2010-12-04T10:54:08.763
2010-12-04T10:54:08.763
null
null
887
null
5133
2
null
5115
46
null
[Bradley Efron](http://en.wikipedia.org/wiki/Bradley_Efron) for the [Bootstrap](http://en.wikipedia.org/wiki/Bootstrapping_%28statistics%29) - one of the most useful techniques in computational statistics.
null
CC BY-SA 2.5
null
2010-12-04T11:07:26.660
2010-12-04T11:07:26.660
null
null
887
null
5134
2
null
4451
2
null
Just found this: [476 million Twitter tweets](http://snap.stanford.edu/data/twitter7.html) (via [@yarapavan](https://twitter.com/#!/yarapavan)).
null
CC BY-SA 2.5
null
2010-12-04T11:27:56.983
2010-12-04T11:27:56.983
null
null
930
null
5135
1
5138
null
278
227335
The help pages in R assume I know what those numbers mean, but I don't. I'm trying to really intuitively understand every number here. I will just post the output and comment on what I found out. There might (will) be mistakes, as I'll just write what I assume. Mainly I'd like to know what the t-value in the coefficien...
Interpretation of R's lm() output
CC BY-SA 3.0
null
2010-12-04T11:28:14.300
2021-09-16T13:03:26.477
2016-11-10T13:37:43.810
7290
2091
[ "r", "regression", "interpretation" ]
5136
1
5163
null
8
3102
The problem is to define when a variable might be considered as a latent variable. I am interested in how to describe a latent variable, and what are the properties of latent variables. My twofold question is: - When you try to explain what a latent variable is, what do you consider as the main differences between a ...
When do you consider a variable is a latent variable?
CC BY-SA 2.5
null
2010-12-04T11:41:22.610
2010-12-05T12:21:37.620
2010-12-04T20:14:58.293
930
1154
[ "psychometrics", "latent-variable" ]
5137
2
null
5011
5
null
A quick google brings up this, which indicates that when working with circular data you'll need a different definition of 'bias' for a start: > However, when using data on the circle, we cannot use distance in Euclidean space, so all differences θ − θi should be replaced by considering the angle between two vectors: $...
null
CC BY-SA 2.5
null
2010-12-04T12:13:36.183
2010-12-04T12:13:36.183
2020-06-11T14:32:37.003
-1
449
null
5138
2
null
5135
240
null
## Five point summary yes, the idea is to give a quick summary of the distribution. It should be roughly symmetrical about mean, the median should be close to 0, the 1Q and 3Q values should ideally be roughly similar values. ## Coefficients and $\hat{\beta_i}s$ Each coefficient in the model is a Gaussian (Normal)...
null
CC BY-SA 4.0
null
2010-12-04T12:59:27.017
2019-04-03T15:11:20.927
2019-04-03T15:11:20.927
28740
1390
null
5139
2
null
5136
3
null
That is a modeling decision. One way to look at it can be illustrated by the following example. A couple of hundreds electrodes are attached to the head to measure brain activity. Electricity, blood flow, whatever and you get lots of signals. These measurements that you get are observables. They are mixed in probably ...
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CC BY-SA 2.5
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2010-12-04T15:12:21.650
2010-12-04T15:12:21.650
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2084
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