Metropolis Algorithm Matlab practice Matlab code taken from Professor Joo-Ho Choi He applied it to p x 0.3exp 0.2 x 0.7 exp 0.2 x 10 with proposal distribution N(x,10). Matlab code for that give in the notes. Here applied to the triangular distribution with U(x0.25,x+0.25) 2 2 Metropolis-Hastings algorithm Metropolis algorithm A proposal distribution q(x*|x) is symmetric w.r.t x* and x. Then the ratio p x q x | x is simplified. p x * * * A x, x min 1, min 1, * p x q x | x p x * Example: normal pdf at x* with mean at x equals to the vice versa. Practice with matlab Generate samples of this distribution using a proposal pdf
2 p x 0.3exp 0.2 x 2 0.7 exp 0.2 x 10 q x* | x N x,10 As the random walk progresses, the number of samples are increased, and the distribution converges to the target distribution. 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 -15 -10 -5 0 5
0 0.1 0.2 0.3 0.4 0.5 x 0.6 0.7 0.8 0.9 1 practice problems 1. Try triangular distribution with with a normal proposal distribution with different mean and standard deviations. 2. Do Professor Chois example with different starting points. Source: Smithsonian Institution Number: 2004-57325
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