4 research outputs found
Exact Bayesian inference for diffusion driven Cox processes
In this paper we present a novel methodology to perform Bayesian inference
for Cox processes in which the intensity function is driven by a diffusion
process. The novelty lies on the fact that no discretisation error is involved,
despite the non-tractability of both the likelihood function and the transition
density of the diffusion. The methodology is based on an MCMC algorithm and its
exactness is built on retrospective sampling techniques. The efficiency of the
methodology is investigated in some simulated examples and its applicability is
illustrated in some real data analyses
CLTs and asymptotic variance of time-sampled Markov chains
For a Markov transition kernel P and a probability distribution
μ on nonnegative integers, a time-sampled Markov chain evolves according
to the transition kernel Pμ = Σkμ(k)Pk. In this note we obtain CLT
conditions for time-sampled Markov chains and derive a spectral formula
for the asymptotic variance. Using these results we compare efficiency of
Barker's and Metropolis algorithms in terms of asymptotic variance
Bayesian computation: a summary of the current state, and samples backwards and forwards
CLTs and asymptotic variance of time-sampled Markov chains
For a Markov transition kernel P and a probability distribution μ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel Pμ = ∑k μ(k)Pk. In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker's and Metropolis algorithms in terms of asymptotic variance