Asymptotic behaviour of the posterior distribution in approximate Bayesian computation

On the Asymptotic Efficiency of Approximate Bayesian Computation Estimators

Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian inference in such cases. We present results on the asymptotic variance of estimators obtained using approximate Bayesian computation in a large-data limit. Our key...

Asymptotic behaviour of the posterior distribution in overfitted mixture models

M ay 2 01 1 ASYMPTOTIC BEHAVIOUR OF APPROXIMATE BAYESIAN

Although approximate Bayesian computation (ABC) has become a popular technique for performing parameter estimation when the likelihood functions are analytically intractable there has not as yet been a complete investigation of the theoretical properties of the resulting estimators. In this paper we give a theoretical analysis of the asymptotic properties of ABC based parameter estimators for h...

Piecewise Approximate Bayesian Computation: fast inference for discretely observed Markov models using a factorised posterior distribution

Many modern statistical applications involve inference for complicated stochastic models for which the likelihood function is difficult or even impossible to calculate, and hence conventional likelihood-based inferential techniques cannot be used. In such settings, Bayesian inference can be performed using Approximate Bayesian Computation (ABC). However, in spite of many recent developments to ...

Approximate Bayesian Computation

Just when you thought it was safe to go back into the water, I’m going to complicate things even further. The Nielsen-Wakely-Hey [5, 3, 4] approach is very flexible and very powerful, but even it doesn’t cover all possible scenarios. It allows for non-equilibrium scenarios in which the populations from which we sampled diverged from one another at different times, but suppose that we think our ...