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The past decades have seen enormous improvements in computational inferencebased on statistical models, with continual enhancement in a wide range ofcomputational tools, in competition. In Bayesian inference, first and foremost,MCMC techniques continue to evolve, moving from random walk proposals toLangevin drift, to Hamiltonian Monte Carlo, and so on, with both theoreticaland algorithmic inputs opening wider access to practitioners. However, thisimpressive evolution in capacity is confronted by an even steeper increase inthe complexity of the models and datasets to be addressed. The difficulties ofmodelling and then handling ever more complex datasets most likely call for anew type of tool for computational inference that dramatically reduce thedimension and size of the raw data while capturing its essential aspects.Approximate models and algorithms may thus be at the core of the nextcomputational revolution.

Bayesian computation: a perspective on the current state, and sampling backwards and forwards