### ABC-Gibbs: componentwise approximate Bayesian computation

Statistics Seminar

28th February 2020, 3:00 pm – 3:45 pm

Fry Building, G. 13

Approximate Bayesian computation methods are useful for generative

models with intractable likelihoods. These methods are however sensitive

to the dimension of the parameter space, requiring exponentially

increasing resources as this dimension grows. To tackle this difficulty,

we explore a Gibbs version of the ABC approach that runs component-wise

approximate Bayesian computation steps aimed at the corresponding

conditional posterior distributions, and based on summary statistics of

reduced dimensions. While lacking the standard justifications for the

Gibbs sampler, the resulting Markov chain is shown to converge in

distribution under some partial independence conditions. The associated

stationary distribution can further be shown to be close to the true

posterior distribution and some hierarchical versions of the proposed

mechanism enjoy a closed form limiting distribution. Experiments also

demonstrate the gain in efficiency brought by the Gibbs version over the

standard solution. [Joint work with Grégoire Clarté, Robin Ryder and

Julien Stoehr, Paris Dauphine]

My slides will be close to

https://www.slideshare.net/xianblog/abcgibbs

and the paper is available as

https://arxiv.org/abs/1905.13599

*Organiser*: Henry Reeve

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