The fifth afternoon meeting in Bayesian Methods, held at the University of Reading in October 2018, showcased presentations from postdoctoral researchers and two keynote speakers. This was a joint meeting of the RSS Computational Statistics and Machine Learning (CSML) network, the Reading Local Group of the RSS, and the Department of Mathematics and Statistics at the University of Reading.
Three external postdoctoral researchers from different backgrounds talked about their work in Bayesian computation. Matt Ludkin, from Lancaster University, presented a non-reversible MCMC method with links to bouncy particle samplers. An appealing aspect of this and other non-reversible methods is that they usually perform better than standard MCMC. David Hughes, from the University of Liverpool, discussed an application of variational methods to generalised linear models in clinical markers. This is motivated by the high computational complexity of MCMC methods for cases when the number of markers is large or even moderate. Tom Prescott, from the University of Oxford, talked about likelihood-free inference and the possibility of making early decisions (acceptance or rejection) without the need to complete the full simulation. As discussed, one needs to be cautious with the potential extra variance and bias introduced from these early decisions.
Mark Bell and Felipe Medina Aguayo, both from the University of Reading, also presented some of their research at the event. Mark talked about inference for networks using a particle Gibbs sampler, which performs split and merge moves in order to solve the clustering problem. The use of ancestor sampling to alleviate path degeneracy was also discussed. Medina Aguayo, discussed importance sampling when there are several proposal distributions indexed by a discrete label. When the number of labels is much larger than the number of importance points standard methods can become computationally expensive.
One of the keynote speakers was Chris Nemeth from Lancaster University, who gave an overview of several Monte Carlo approaches and their relevance in big data problems. For example, consensus Monte Carlo is useful for merging sub-posteriors, but it only performs well when these are close to a Gaussian distribution. Recent work on merging Gaussian processes instead may provide more flexibility and better results. A second scenario arises from data subsampling. The use of control variates within the stochastic gradient Langevin dynamics algorithm was discussed which may result in a more efficient method requiring a one-off expensive pre-processing step.
Finally, Professor Ruth King, from the University of Edinburgh and second keynote speaker, discussed Bayesian inference using semi-complete data likelihood for dealing with intractability with examples in Ecology. Numerical integration and data augmentations are the common approaches of choice when the likelihood cannot be expressed in closed form. The former Is usually feasible only in small dimensional spaces, whereas the latter can lead to poor mixing of the MCMC due to high correlation in the variables. The semi-complete approach is to combine the previous ideas within a Bayesian framework. Multiple specifications are possible, so it is important to identify useful variables for integration that will result in an efficient algorithm.