Approximate Bayesian computation for finite mixture models

Adaptive approximate Bayesian computation for complex models

Approximate Bayesian Computation for Smoothing

We consider a method for approximate inference in hidden Markov models (HMMs). The method circumvents the need to evaluate conditional densities of observations given the hidden states. It may be considered an instance of Approximate Bayesian Computation (ABC) and it involves the introduction of auxiliary variables valued in the same space as the observations. The quality of the approximation m...

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is wellsuited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior densi...

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 ...

Adaptive approximate Bayesian computation

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.’s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine im...