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

By Peter J. Green, K. Latuszy'nski, Marcelo Pereyra, Christian P. Robert. 2015

22 citations recorded by the source corpus.

The past decades have seen enormous im-provements in computational inference based on sta-tistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC techniques con-tinue to evolve, moving from random walk proposals to Langevin drift, to Hamiltonian Monte Carlo, and so on, with both theoretical and algorithmic inputs opening wider access to practitioners. However, this impressive evolution in capacity is confronted by an even steeper increase in the complexity of the models and datasets to be addressed. The difficulties of modelling and then handling ever more complex datasets most likely call for a new type of tool for computational inference that dramatically reduce the dimension and size of the raw data while capturing its essential aspects. Approximate models and algorithms may thus be at the core of the next computational revolution.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, background): “…(e.g. Heinrich (1995), Giles (2013) and Giles and Szpruch, 2014), (h) Bayesian Monte Carlo (BMC) methods (O’Hagan, 1991; Rasmussen and Ghahramani, 2003; Briol et al., 2016a,b) and (i) a plethora of sophisticated Markov chain Monte Carlo (MCMC) sampling schemes (La- tuszyński et al., 2015).”
Proximal Algorithms in Statistics and Machine Learning (2015, background): “…[Geman and Reynolds, 1992, Geman and Yang, 1995, Rudin et al., 1992], nonlinear curve ﬁtting [Tibshirani, 2014], Bayesian MAP inference [Polson and Scott, 2012], multiple hypothesis testing [Tansey et al., 2014] and shrinkage/sparsity-inducing prior regularisation problems [Green et al., 2015].”
On the properties of variational approximations of Gibbs posteriors (2015, methodology): “…Tsybakov, 2012, Alquier and Biau, 2013, Guedj and Alquier, 2013] is to sample from a Gibbs posterior using MCMC [Markov chain Monte Carlo, see e.g. Green et al., 2015]; but constructing an efficient MCMC sampler is often difficult, and even efficient implementations are often too slow for…”