Random dive MH

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A new Metropolis-Hastings algorithm that I would call “universal” was posted by Somak Dutta yesterday on arXiv. Multiplicative random walk Metropolis-Hastings on the real line contains a different Metropolis-Hastings algorithm called the random dive. The proposed new value x’ given the current value x is defined by

begin{cases} xepsilon &text{with probability } 1/2\ x/epsilon &text{with probability } 1/2end{cases}

when epsilon is a random variable on (-1,1). Thus, at each iteration, the current value is either shrunk or expanded by a random amount. When I read the paper in the Paris metro, while appreciating that this algorithm could be geometrically ergodic as opposed to the classical random walk algorithm, I was not convinced by the practical impact of the method, as I thought that the special role of zero in the proposal was not always reflected in the target. Especially when considering that the proposal is parameter-free. However, after running the following R program on a target centred away from zero, I found the proposal quite efficient.

for (t in 2:Nsim){
if (runif(1) }

Obviously, it is difficult to believe that this extension will keep working similarly well when the dimension increases but this is an interesting way of creating a heavy tail proposal.

Filed under: R, Statistics Tagged: geometric ergodicity, Metropolis-Hastings, R, random walk, randomness

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