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Next: David Brillinger - Some Up: Probability Theory / Théorie Previous: Siva Athreya - Existence

Claude Belisle - The Hit-and-run sampler



CLAUDE BELISLE, Département de mathématiques et statistique, Université de Laval, Montréal, Québec  G1K 7P4, Canada
The Hit-and-run sampler


The hit-and-run sampler is a Markov Chain Monte Carlo method for simulating probability measures.

Let $\pi$ be an absolutely continuous probability measure on ${\bbd R}^d$. Let $\nu$ be a full dimensional probability measure on the surface S of the d-dimensional unit ball centered at the origin. Given a current point $X_n \in {\bbd R}^d$, the hit-and-run sampler chooses a next point Xn+1 according to the conditionalization of $\pi$ on the line through Xn and $X_n +
\Theta_{n+1}$. The directions $\Theta_1, \Theta_2,
\Theta_3,\dots$ are independent and identically distributed on S, with distribution $\nu$. Under an appropriate irreducibility condition, the Markov chain $(X_n; n \ge 0)$ converges in total variation towards the target distribution $\pi$. In this talk, I will discuss the convergence properties of this Markov chain. Related Markov Chain Monte Carlo methods, including the Gibbs sampler, will also be discussed.


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Next: David Brillinger - Some Up: Probability Theory / Théorie Previous: Siva Athreya - Existence
 

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