# Tagged Questions

Questions about performing probabilistic calculations, especially those concerned with the Mathematica commands Probability, Expectation and the various functions related to distributions such as NormalDistribution, CDF, PDF etc.

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### Speeding up the non-negativity algorithm for multilinear function with interval probabilities?

The algorithm is a branch-and-bound algorithm that calculates the non-negativity of a multilinear function with interval probabilities. The lines 9-11 has an optimization that is explained on the ...
188 views

### Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
208 views

### Calculating probabilities symbolically

Is there a way to solve for statistical quantities analytically/symbolically in Mathematica? example 1: Lets say that I want to do a calculation that requires Bayes theorem. I know p(a), p(b) and ...
86 views

### Converting problem into form involving Probability

I want to solve the following problem symbolically, using Probability: What is the probability of the first random variate of a set to be present more than ...
117 views

### What can I do to improve the performance of my calculations?

I'm trying to express a simple probability problem in Mathematica, but am having trouble getting my calculations to execute at a reasonable speed. I have an object whose unknown location is modeled ...
224 views

### Markov Chain for combined events?

I was wondering how to apply Markov steady-state chains to a simple case in genetics, eye colour. Assuming the probabilities of being brown, green or blue eyed, given your parents were a certain ...
110 views

### ProbabilityDistribution PDF on boundary points

I would like to evaluate the PDF of a custom ProbabilityDistribution at the min and max values. However, PDF[...] returns 0 at ...
47 views

### Optimization of custom probability distibutions?

Consider the two tests: Timing[Do[RandomVariate[NormalDistribution[0.5, 0.3]], {200}]] {0.001188, Null} ...
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### Computational Bayesian analysis in Mathematica: Any plans to develop MCMC?

Does anyone know if there are any plans to develop an MCMC capability in Mathematica? My reasoning for asking is that as it stands, I can't seem to find any 'out-of-the-box' functions/capabilities ...
69 views

### Belief Network, Bayesian network

There is already a question about simulating Bayesian networks with Mathematica (Mathematica Package for Bayesian Networks). However, are there any packages or approaches which help in computing the ...
78 views

### Simulating Dynamic Priority Queues

I have found several examples of static priority queue implementations: there are two classes of items, with the exponential interarrival times. The service times are also exponential. The first-class ...
107 views

### How to include confidence intervals into ProbabilityScalePlot?

I use ProbabilityScalePlot[data, "Weibull"] to plot measured data and ...
681 views

### Calculate variance of random walk?

How can I symbolically calculate the variance of the following random walk in Mathematica? Given several discrete random variables such that $p(Z_i=1-2k)=p$, where $k$ is a small real number, and ...
84 views

### Extrapolation of area for a 2D integration

I have a set of points distributed almost uniformly in a certain area of a 2D plane as follow: An example of data points (orange) data = {{0.919443, 1.68921*10^-22}, {0.262277, ...
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### Help with Multivariate ProbabilityDistribution

I wish to obtain numbers from ...
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### Why is Plot3D applied to TransformedDistribution in 2 random variables so slow?

I am trying to plot 3D, the pdf of a TransformedDistribution made up of random variables. So I can see the pdf in 3D, similar to this answer here Visualizing a 2-dimensional PDF But it seems to take ...
322 views

### Slow mixture fitting when having ill-conditioned covariance matrices. How to make it faster?

I'm using Mathematica 9.0 to fit multidimensional observations with a gaussian mixture. To do so I first adapted these steps to ensure that the mixture parameters are well defined (see ...
397 views

### When are If, Piecewise, Switch, and Which interchangeable and when are they not?

Experimenting with joint dependent distributions via the TransformedDistribution function, I used the following to derive a distribution where the second variate is ...
45 views

### How to Fit a Generalized Pareto Distribution to data in Mathematica

I'd like to know how to fit a Generalized Pareto distribution in Mathematica to implement the Peak Over Threshold method for tail estimation of operational risk losses. Does anybody have a toy example ...
76 views

### Von Neumann's method to generate points uniformly distributed on a region of a n-sphere surface

I am trying to generate points uniformly distributed on a region of a single n-sphere surface (all angles in hyperspheric coordinates are between 0 and Pi/2). I decided to use von Neumann's method ...
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### Constrained Nonlinear Optimization with expectations functions in the constraints

I am modeling an optimal compensation contract with a CRRA utility function : ...
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### Mixture / Hierarchical Distribution from Conditional

How does Mathematica handle Hierarchical distributions. For example, if I have X|Y ~ Poisson(Z) Y ~ Exp(lambda) Z ~ Normal(0,1) First, of all, the distribution of X is only given conditionally and ...
85 views

### How to be faster at making a frequency list of increasing steps

I want to find propabilities of having a sequence in a list, by using frequencies. The case is that you will bet on an increase when the last event had an increased and bet on derease when the last ...
56 views

### Expectation taking unusually long to evaluate

I am trying to evaluate an expectation, but it is taking an extremely long time although the expression itself should not be too complicated. My code is ...
52 views

### Symbolic manipulation of the moments of an unknown distribution

I'm curious as to whether it's possible to get Mathematica to simplify/manipulate/expand basic expectations, conditional expectations, sums of random variables, etc. A simple example might be: ...