Delayed acceptance ABC-SMC

Approximate Bayesian computation (ABC) is now an established technique for statistical inference used in cases where the likelihood function is computationally expensive or not available. It relies on the use of a~model that is specified in the form of a~simulator, and approximates the likelihood at a~parameter value $\theta$ by simulating auxiliary data sets $x$ and evaluating the distance of $x$ from the true data $y$. However, ABC is not computationally feasible in cases where using the simulator for each $\theta$ is very expensive. This paper investigates this situation in cases where a~cheap, but approximate, simulator is available. The approach is to employ delayed acceptance Markov chain Monte Carlo (MCMC) within an ABC sequential Monte Carlo (SMC) sampler in order to, in a~first stage of the kernel, use the cheap simulator to rule out parts of the parameter space that are not worth exploring, so that the ``true'' simulator is only run (in the second stage of the kernel) where there is a~reasonable chance of accepting proposed values of $\theta$. We show that this approach can be used quite automatically, with few tuning parameters. Applications to stochastic differential equation models and latent doubly intractable distributions are presented

Sequential Monte Carlo with transformations

This paper examines methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. For this, we use sequential Monte Carlo samplers, introducing the innovation of using deterministic transformations to move particles effectively between target distributions with different dimensions. This approach, combined with adaptive methods, yields an extremely flexible and general algorithm for Bayesian model comparison that is suitable for use in applications where the acceptance rate in reversible jump Markov chain Monte Carlo is low. We use this approach on model comparison for mixture models, and for inferring coalescent trees sequentially, as data arrives

A statistical approach to the problem of restoring damaged and contaminated images

We address the problem of automatically identifying and restoring damaged and contaminated images. We suggest a novel approach based on a semi-parametric model. This has two components, a parametric component describing known physical characteristics and a more flexible non-parametric component. The latter avoids the need for a detailed model for the sensor, which is often costly to produce and lacking in robustness. We assess our approach using an analysis of electroencephalographic images contaminated by eye-blink artefacts and highly damaged photographs contaminated by non-uniform lighting. These experiments show that our approach provides an effective solution to problems of this type

Distribution in homology classes and discrete fractal dimension

In this note we examine the proportion of periodic orbits of Anosov flows that lie in an infinite zero density subset of the first homology group. We show that on a logarithmic scale we get convergence to a discrete fractal dimension.Comment: 8 page

Greenview : the gorilla in the library smart sensing and behaviour change

This paper provides a description and analysis of the Greenview project, an experiment in smart sensing leading to energy consumption behaviour change in building users. Greenview was an innovative app built on the back of the successful DUALL project (funded by JISC). Where DUALL created a simple web-based information-feedback tool that could report electrical consumption in specific university buildings back to users via a simple dashboard using Yahoo widgets; Greenview refined the ICT tool further into a sophisticated smart phone application which could connect staff and students in De Montfort University (DMU) to monitor the relative energy consumptions of their buildings. The developed iPhone ‘app’ visualised comparative energy use on the DMU campus through a narrative of improving or declining habitats for endangered species, represented by animated cartoon characters living as virtual mascots in each university building. Based on the emotive nature of the ‘Tamagochi’ concept, the app tested an engaging way to encourage care for the environment. When consumption levels exceeded those on the same day of the previous year, the visible well being of species would change. The app also provided real-time data through meter readings provided on a half-hourly basis, allowing the inclusion of graphical data options, appealing both to emotional identification with the building mascot and to the range of preferences individuals have for viewing and interpreting data.Funded by the Horizon 2020 Framework Programme of the European Union.peer-reviewe

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data