Metropolis-Hastings algorithm independent candidate density

In Chapter 7 we develop a method for finding a Markov chain that has good mixing properties. We will use the Metropolis-Hastings algorithm with heavy-tailed independent candidate density. We then discuss the problem of statistical inference on the sample from the Markov chain. We want to base our inferences on an approximately random sample from the posterior. This requires that we determine... 

In Section 6.1 we show how the Metropolis-Hastings algorithm can be used to find a Markov chain that has the posterior as its long-run distribution in the case of a single parameter. There are two kinds of candidate densities we can use, random-walk candidate densities, or independent candidate densities. We see how the chain... 

In the computational Bayesian approach, we want to draw a sample from the actual posterior, not its approximation. As we noted before, we know its shape. Our approach will be to use the Metropolis-Hastings algorithm with an independent candidate density. We want a candidate density that is as close as possible to the posterior so many candidates will be accepted. We want the candidate density to have heavier tails than the posterior, so we move around the parameter space quickly. That will let us have shorter burn-in and use less thinning. We use the maximum likelihood vector 0ml matched curvature covariance matrix Vj fz, as the... 

A sample from the true posterior can be found using the Metropolis-Hastings algorithm with an independent candidate density having the same mean vector and correlation structure as the approximate posterior, but with heavier tails that come from using Student s t with low degrees of freedom instead of normal. 

A mixture of two normal distributions. The macros NormMixMHRW. mac and NormMixMHInd.mac use the Metropolis-Hastings algorithm to draw a sample from a univariate target distribution that is a mixture of two normal distributions using an independent Normal candidate density and a random-walk normal candidate density, respectively. Table A.6 shows the Minitab commands to set up and run these two macros. 

By default, normMixMH samples from an independent candidate density and uses 1,000 steps in the Metropolis-Hastings algorithm. Therefore to sample using an independent iV(0,3 ) candidate density we type... 

A correlated bivariate normal distribution. The function blvnormMH can use the Metropolis-Hastings algorithm to draw a sample from a correlated bivariate normal target density using either an independent candidate density or a random-walk candidate density when we are drawing both parameters in a single draw. Also,... 

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