Afternoon Meeting on Bayesian Computation

This is a joint meeting of the RSS Reading Local Group and the University of Reading and takes place on Wednesday 21 January 2015, 13:00-18:00, at the University of Reading, Palmer Building, Room 103.

Schedule:

13:00-13:45  Prof Christian Robert (Universit√© Paris-Dauphine and University of Warwick) 
13:50-14:20  Dr Dennis Prangle (University of Reading) 
14:20-14:50  Dr John Hemmings (Wessex Environmental Associates) 
14:50-15:20  Luke Kelly (University of Oxford) 
15:20-16:00  Coffee and posters 
16:00-16:45  Prof Christophe Andrieu (University of Bristol) 
16:50-17:20  Dr Marcelo Pereyra (University of Bristol)
17:20-17:50  Dr Richard Everitt (University of Reading) 
17:50 onwards Pub and food (Senior Common Room, University of Reading campus)

Description:
The Bayesian approach to statistical inference has seen major successes in the past twenty years, finding application in many areas of science, engineering, finance and elsewhere. The main drivers of these successes were developments in Monte Carlo methods and the wide availability of desktop computers. More recently, the use of standard Monte Carlo methods has become infeasible due the size and complexity of data now available. This has been countered by the development of next-generation Monte Carlo techniques, which are the topic of this meeting.

Registration:
The event is open to all, and there is no registration fee.

Directions:
The meeting is on the first floor of the Palmer Building, which is building number 26 on the map at http://goo.gl/AtV6rU. The university is easily accessed by bus from the railway station (see http://goo.gl/Ybe9AB for further details). Parking is limited on campus - please contact Richard Everitt (r.g.everitt@reading.ac.uk) if you require a parking permit.

Titles and abstracts:

Speaker: Prof Christian Robert
Title: Reliable ABC model choice via random forests
Abstract: Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior probabilities are poorly evaluated by ABC. We propose a novel approach based on a machine learning tool named random forests to conduct selection among the highly complex models covered by ABC algorithms. We strongly shift the way Bayesian model selection is both understood and operated, since we replace the evidential use of model posterior probabilities by predicting the model that best fits the data with random forests and computing an associated posterior error rate. Compared with past implementations of ABC model choice, the ABC random forest approach offers several improvements: (i) it has a larger discriminative power among the competing models, (ii) it is robust to the number and choice of statistics summarizing the data, (iii) the computing effort is drastically reduced, and (iv) it includes an embedded and cost-free error evaluation conditional on the actual analyzed dataset. Random forest will undoubtedly extend the range of size of datasets and complexity of models that ABC can handle. We illustrate the power of the ABC random forest methodology by analyzing controlled experiments as well as real population genetics datasets.

Speaker: Dr Dennis Prangle
Title: Lazy ABC
Abstract: Approximate Bayesian computation (ABC) performs approximate statistical inference for otherwise intractable probability models by accepting parameter proposals when corresponding simulated datasets are sufficiently close to the observations. This involves producing a large number of model simulations, which demands considerable computing time. However, it is often clear before a simulation ends that it is unpromising: it is likely to produce a poor match or require excessive time. This talk is on "lazy ABC", an ABC algorithm which saves time by abandoning some such simulations. This is accomplished in such a way as to leave the target distribution unchanged from that of standard ABC i.e. no further approximation is introduced.

Speaker: Dr Marcelo Pereyra
Title: Proximal Markov chain Monte Carlo: stochastic simulation meets convex optimisation
Abstract: Convex optimisation and stochastic simulation are two powerful computational methodologies for performing statistical inference in high-dimensional inverse problems. It is widely acknowledged that these methodologies can complement each other very well, yet they are generally studied and used separately. This talk presents a new Langevin Markov chain Monte Carlo method that uses elements of convex analysis and proximal optimisation to simulate efficiently from high-dimensional densities that are log-concave, a class of probability distributions that is widely used in modern high-dimensional statistics and data analysis. The method is based on a new first-order approximation for Langevin diffusions that uses Moreau-Yoshida approximations and proximity mappings to capture the log-concavity of the target density and construct Markov chains with favourable convergence properties. This approximation is closely related to Moreau-Yoshida regularisations for convex functions and uses proximity mappings instead of gradient mappings to approximate the continuous-time process. The proposed method complements existing Langevin algorithms in two ways. First, the method is shown to have very robust stability properties and to converge geometrically for many target densities for which other algorithms are not geometric, or only if the time step is sufficiently small. Second, the method can be applied to high-dimensional target densities that are not continuously differentiable, a class of distributions that is increasingly used in image processing and machine learning and that is beyond the scope of existing Langevin and Hamiltonian Monte Carlo algorithms. The proposed methodology is demonstrated on three challenging high-dimensional and non-differentiable models related to image resolution enhancement, audio compressive sensing, and low-rank matrix estimation that are not well addressed by existing MCMC methodology.

Speaker: Luke Kelly
Title: Lateral transfer on phylogenetic trees
Abstract: https://www.dropbox.com/s/aqaemnjllrevm7e/Kelly_Nicholls_abstract.pdf?dl=0

Speaker: Prof Christophe Andrieu
Title: Some applications of asymmetric Metropolis-Hastings updates in the context of exact approximate algorithms
Abstract: There has recently been some interest in approximating MH updates in situations where quantities required for their implementation are not tractable. This is often the case for the acceptance ratio involved in the MH accept/reject mechanism, for examples in situations where the target density is not tractable. In this scenario one can for example resort to pseudo-marginal strategies which exploit the possibility to unbiasedly estimate a function proportional to the target density. Other more general strategies are however available, cover more scenarios, and the aim of the talk is to review such scenarios and show how "asymmetric" M-H updates can be useful, and in particular allow for the reduction of the variability of these approximations and improve performance at virtually no cost on a parallel computer.

Speaker: Dr John Hemmings
Title: Site-based Emulation of an Ocean Biogeochemical Model for Practical Parameter Estimation
Abstract: Reliable representation of ocean biogeochemistry in Earth system models is important for understanding and predicting global change. Key outputs of biogeochemical models are sensitive to many adjustable parameters with weakly constrained prior distributions. Application of Monte-Carlo techniques to evaluate posterior distributions with reference to ocean data is highly desirable but inhibited by the computational demands of global 3-D simulations. 1-D site-based simulators describing representative vertical water columns can capture much of the biogeochemical dynamics using a small fraction of the computer resources. We investigate their potential as tools for making inferences about 3-D model parameters. It is shown that an array of site-based simulators combined with a scheme for predicting spatio-temporal variations in simulator uncertainty can act as a robust emulator of 3-D model output for comparison with satellite ocean colour observations. The efficiency and flexibility of this mechanistic emulation method will enable the practical generation of ensemble data that can be combined with fast statistical emulators for comprehensive investigation of large parameter spaces.

Speaker: Dr Richard Everitt
Title: Exact and inexact sequential Monte Carlo for inference and model selection in Markov random fields
Abstract: Markov random field models are used widely in computer science, statistical physics and spatial statistics and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to an intractable likelihood function. This talk examines the use of random weight sequential Monte Carlo (SMC) methods for performing parameter inference and evidence estimation in these models and explores the possibility of using importance samplers with biased weights, examining the advantages and drawbacks of this approach.

                                

 

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