Compute Probability of a Multivariate Normal Distribution over Polytope

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Michael Fink
Michael Fink on 29 Jun 2022
Commented: Torsten on 4 Jul 2022
I have a Multivariate Normal Distribution with the mean vector and the covariance matrix given as
Now, I want to compute the probability that a realization of lies in a given polytopic set of the form
where the matrix and the vector describes m half-spaces and therefore a convex set.
The probability which I want to compute is given as
How can I compute/approximate this integration numerically in MATLAB for a given mean μ, a given covariance Σ, and a given set 𝒫. In my problem, the variable x has around 10 to 100 dimensions.
Edit: ->
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Answers (1)

Paul
Paul on 30 Jun 2022
Hi Michael,
If A is nonsingular, perhaps a change of coordinates will work
% z = A*x
muz = A*mux;
Sigmaz = A*Sigmax*A.';
ProbAxLTb = mvncdf(-inf+b,b,muz,Sigmaz);
See the doc page for mvncdf for examples, info, options, etc.
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Torsten
Torsten on 4 Jul 2022
It was only an example.
Of course, you can directly use your values for sigma, mu, A and b in Paul's code instead of the randomly created.

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