Monte Carlo Inference - STAT - EPFL

OutputPrior (black) and posterior (red) distributions of the number of changepoints; the prior is Poisson withmean 3, truncated to {0,1,... ,12}Density0.00 0.05 0.10 0.15 0.20 0.25 0.300 2 4 6 8 10 12kMonte Carlo Inference Spring 2009 – slide 214Discussion□ Many more quantities could be extracted from the output, such as– positions of changepoints, conditional on different values of k– heights of steps, conditional on different values of k– uncertainties for posterior mean/median of λ(u)□ RJMCMC algorithms are increasingly widely used for complex problems□ Pluses:– they provide a way to allow for model uncertainty as k varies– powerful generalisation of the Metropolis–Hastings algorithm□ Minuses:– can be difficult to invent good proposals (with high probabilities of acceptance) for thebirth/death moves– programming them is time-consuming and fiddleyMonte Carlo Inference Spring 2009 – slide 215206