## 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 Tuesday 19 April 2016, 12:30-18:15, at the University of Reading, Nike Lecture Theatre, Agriculture Building.

Schedule:

 12:30-13:00 Sam Livingstone, University of Bristol 13:00-13:30 Ingmar Schuster, Université Paris-Dauphine 13:30-14:00 Francois-Xavier Briol, University of Warwick 14:00-14:30 Jack Baker, University of Lancaster 14:30-15:00 Alexander Mihailov, University of Reading 15:00-15:45 Coffee Break (Room AGRIC 1L14) 15:45-16:30 Arnaud Doucet, University of Oxford 16:30-17:00 Philip Maybank, University of Reading 17:00-17:30 Elske van der Vaart, University of Reading 17:30-18:00 Reham Badawy, Aston University 18:15 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 in the Nike Lecture Theatre, Agriculture Building, which is building number 59 on the map at http://goo.gl/AtV6rU. The university is easily accessed by bus from the railway station (see http://www.reading.ac.uk/15/about/find/about-findcoach.aspx 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: Dr Sam Livingstone
Title: TBC
Abstract: TBC

Speaker: Dr Ingmar Schuster
Title: On the geometric ergodicity of Hamiltonian Monte Carlo
Abstract: Hamiltonian/Hybrid Monte Carlo (HMC) is a sampling method which has existed for almost 30 years, and recently has become very popular among statisticians, primarily because general purpose software for its implementation is now available. In this talk I'll then discuss recent work in which we establish fairly general \pi-irreducibility and geometric ergodicity criteria for the method, giving some basic guidelines on when it should 'work well' for estimating expectations of interest. The results also shed light on how to tune some of the free parameters. If time permits I may also mention some ongoing work on non-quadratic choices for the kinetic energy, and how this can either positively or negatively impact performance.

Speaker: Francois-Xavier Briol
Title: Probabilistic Numerics Approaches to Integration
Abstract: Probabilistic numerical methods aim to model numerical error as a source of epistemic uncertainty that is subject to probabilistic analysis and reasoning, enabling the principled propagation of numerical uncertainty through a computational pipeline. This talk will present probabilistic numerical integrators based on Markov chain and Quasi Monte Carlo methods and provide asymptotic results on the coverage of the associated probability models for numerical integration error. The performance of probabilistic integrators is guaranteed to be no worse than non-probabilistic integrators and is, in many cases, asymptotically superior. These probabilistic integrators therefore enjoy the "best of both worlds", leveraging the sampling efficiency of advanced Monte Carlo methods whilst being equipped with valid probabilistic models for uncertainty quantification, which will be shown to be essential in cases with expensive integrands.

Speaker: Jack Baker
Title: A Comparison of MCMC for Big Data
Abstract: https://www.dropbox.com/s/7pimk973qgu11sy/abstract.pdf?dl=0

Speaker: Dr Alexander Mihailov
Title: What Do Latin American Inflation Targeters Care About? A Comparative Bayesian Estimation of Central Bank Preferences
Abstract: This paper aims to reveal and compare the central bank preferences of the big five Latin American inflation targeting (LAIT) countries: Brazil, Chile, Colombia, Mexico, and Peru. Using a small open economy New Keynesian model with incomplete asset markets and incomplete exchange-rate pass-through, we estimate by Bayesian methods the loss function parameters for each central bank. Our results suggest a significant degree of heterogeneity in central bank objectives across the region. While Brazil and Peru placed priority on minimizing the volatility of nominal interest rate changes, Chile, Colombia and Mexico were more concerned about stabilizing inflation. Out of the five countries, only Brazil assigned a sizeable weight to output gap stabilization, whereas only Mexico assigned a significant weight to stabilizing the real exchange rate.

Speaker: Arnaud Doucet
Title: On a novel class of pseudo-marginal algorithms
Abstract: The pseudo-marginal algorithm is a popular variant of the Metropolis--Hastings scheme which allows us to sample asymptotically from a target probability density when we are only able to estimate unbiasedly an unnormalized version of this target. It has found numerous applications in Bayesian statistics as there are many scenarios where the likelihood function is intractable but can be estimated unbiasedly using Monte Carlo samples. For a fixed computing time, it has been shown in several recent contributions that an efficient implementation of the pseudo-marginal method requires the variance of the log-likelihood ratio estimator appearing in the acceptance probability of the algorithm to be of order 1, which in turn usually requires scaling the number N of Monte Carlo samples linearly with the number T of data points. We propose two novel pseudo-marginal algorithms which are based on low-variance estimators of the log-likelihood ratio appearing in Metropolis-Hastings. We show that the parameters of these schemes can be selected such that the variance of these estimators is of order 1 as $N,T\rightarrow\infty$ whenever $N/T\rightarrow0$; e.g. N=log(T). In our numerical examples, the efficiency of computations is increased relative to the standard pseudo-marginal algorithm by several order of magnitude for large data sets.

Speaker: Philip Maybank
Title: MCMC for Inverse Problems in Brain Imaging
Abstract: In Neuroscience, mean-field models are nonlinear dynamical systems that are used to describe the evolution of mean neural population activity, within a given brain region such as the cortex. Mean-field models typically contain 10-100 unknown parameters, and receive high-dimensional noisy input from other brain regions. Here we present preliminary results on inferring mechanistic parameters in the differential equations.

Speaker: Elske van der Vaart
Title: Using Approximate Bayesian Computation with Repeated Measures Data: Assessing and Improving Accuracy
Abstract: Approximate Bayesian Computation (ABC) is an increasingly popular technique for calibrating and evaluating complex simulation models. Originally developed within population genetics, it is now widely applied across a variety of fields, but ensuring the accuracy of its estimates remains difficult. In this paper, we offer an improved approach to evaluation for cases where the empirical data consists of repeated measures of the same quantity - such as a time series. As ABC can give exact results under the assumption of model and / or measurement error, an accurate estimate of this error should make it possible to produce accurate posteriors. Our key insight is that for repeated measures data, the error can be estimated from the discrepancy between the observations and the model at its best-fitting parameter values, as would routinely be done in classical statistics. Using this approach, we derive the correct acceptance probabilities for a probabilistic rejection algorithm and apply it to both a toy example and a realistic ecological case study. A comparison with exact methods and an updated coverage test suggest that our approach produces accurate posteriors for both models. At the same time, we reach new conclusions about the interpretation of coverage tests more generally.

Title: MCMC-ABC for neurobiological modelling of smartphone data

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