# Spring 2017

Date: 14 February 2017, CB 3.7, 14:15

Kate Button & Michelle St Clair (Bath) (Joint seminar)

(Kate Button) Personalising psychological care

Abstract: Depression and anxiety are leading causes of disability in the UK. Improving access to psychological therapies (IAPT) aims to reduce this disability by making ‘talking therapies’ available through the NHS. IAPT has been a success, providing therapy to those who would have otherwise not had access, and half of patients referred make a full recovery. However, we can still do better. The aim of this research is to use routinely collected IAPT data to identify optimal care regimes for a given patient. By providing evidence to tailor psychological care to the individual, we aim to further improve recovery rates.

(Michelle St Clair) Statistics and Human Development: Characterising developmental trajectories and (causal) pathways through childhood, adolescence and adulthood

Abstract: I will be giving a short overview of my research with regard using large scale longitudinal projects and/or longitudinal cohort databases to evaluate developmental trajectories using complex multivariate person centred and variable centred statistical techniques. I will also evaluate some work that is looking at possible causal pathways or relationships between experiences in early life and outcomes in later life using longitudinal cohort data.

Date: 17 Feb 2017, 4W 1.7, 15:15 (Landscapes seminar)

Adrian Bowman (Glasgow)

Surfaces, shapes and anatomy

Abstract: Three-dimensional surface imaging, through laser-scanning or stereo-photogrammetry, provides high-resolution data defining the surface shape of objects. In an anatomical setting this can provide invaluable quantitative information, for example on the success of surgery. Two particular applications are in the success of facial surgery and in developmental issues with associated facial shapes. An initial challenge is to extract suitable information from these images, to characterise the surface shape in an informative manner. Landmarks are traditionally used to good effect but these clearly do not adequately represent the very much richer information present in each digitised images.
Curves with clear anatomical meaning provide a good compromise between informative representations of shape and simplicity of structure, as well as providing guiding information for full surface representations. Some of the issues involved in analysing data of this type will be discussed and illustrated. Modelling issues include the measurement of asymmetry and longitudinal patterns of growth.

Date: 14 March 2017, CB 3.7, 13:15

Kari Heine (Bath)

TBA

Date: 28 March 2017, CB 3.7, 13:15

Paul Northrop (UCL)

Extreme value threshold selection

Abstract: A common form of extreme value modelling involves modelling excesses of a threshold by a generalised Pareto (GP) distribution. The GP model arises by considering the possible limiting distributions of excesses as the threshold increased. Selecting too low a threshold leads to bias from model mis-specification; raising the threshold increases the variance of estimators: a bias-variance trade-off. Many existing threshold selection methods do not address this trade-off directly, but rather aim to select the lowest threshold above which the GP model is judged to hold approximately. We use Bayesian cross-validation to address the trade-off by comparing thresholds based on predictive ability at extreme levels. Extremal inferences can be sensitive to the choice of a single threshold. We use Bayesian model averaging to combine inferences from many thresholds, thereby reducing sensitivity to the choice of a single threshold. The methodology is illustrated using significant wave height datasets from the North Sea and from the Gulf of Mexico.

Date: 25 April 2017, CB 3.7, 13:15

Heather Battey (Imperial)

Exploring and exploiting new structured classes of covariance and inverse covariance matrices

Abstract: Estimation of covariance and inverse covariance (precision) matrices is an essential ingredient to virtually every modern statistical procedure. When the dimension, p, of the covariance matrix is large relative to the sample size, the the sample covariance matrix is inconsistent in non-trivial matrix norms, and its non-invertibilty renders many techniques in multivariate analysis impossible. Structural assumptions are necessary in order to restrain the estimation error, even if this comes at the expense of some approximation error if the structural assumptions fail to hold. I will introduce new structured model classes for estimation of large covariance and precision matrices. These model classes result from imposing sparsity in the domain of the matrix logarithm. After studying the structure induced in the original and inverse domains, I will then introduce estimators of both the covariance and precision matrix that exploit this structure. I derive the convergence rates of these estimators and show that they achieve a new minimax lower bound over classes of covariance and precision matrices whose matrix logarithm is sparse. The implication of this result is that the estimators are efficient and the minimax lower bound is sharp.

Date: 2 May 2017, CB 3.7, 13:15

Anthony Lee (Warwick)

TBA

Date: 9 May 2017, CB 3.7, 13:15

Tiago de Paula Peixoto (Bath)

TBA

Date: 16 May 2017, CB 3.7, 13:15

Stats PhD students (Bath)

TBA

# Autumn 2016

Date: 11 October 2016, CB 5.8, 13:15

Daniel Falush (Bath)

The painting palettes of human ancestry

Abstract: Genomic technology is advancing at a remarkable pace and provide a great deal of information on our origins but requires new statistical technology to analyze. I will describe our chromosome painting approach to summarizing ancestry information (available from here). A Hidden Markov Model is used to fit each individual as a mosaic of the other individuals in the sample. A summary of this painting is used to subdivide the sample into populations with discrete ancestry profiles, using a merge-split sampler. I illustrate the application of this method to subdivide the British Isles into 17 regions with distinct ancestry profiles. Historical admixture events can be explored using mixture modelling. I show how Non Linear Least Squares and curve fitting can be used to estimate global admixture events in the last 3,000 years.

Date: 25 October 2016, CB 5.8, 13:15

Francisco Javier Rubio (LSHTM)

Tractable Bayesian variable selection: beyond normality

Abstract: Bayesian variable selection for continuous outcomes often assumes normality, and so do its theoretical studies. There are sound reasons behind this assumption, particularly for large $$p$$: ease of interpretation, analytical and computational convenience. More flexible frameworks exist, including semi- or non-parametric models, often at the cost of losing some computational or theoretical tractability. We propose a simple extension of the Normal model that allows for skewness and thicker-than-normal tails but preserves its tractability. We show that a classical strategy to induce asymmetric Normal and Laplace errors via two-piece distributions leads to easy interpretation and a log-concave likelihood that greatly facilitates optimization and integration. We also characterize asymptotically its maximum likelihood estimator and Bayes factor rates under model misspecification. Our work focuses on the likelihood and can thus be combined with any likelihood penalty or prior, but here we adopt non-local priors, a family that induces extra sparsity and which we characterize under misspecification for the first time. Under suitable conditions Bayes factor rates are of the same order as those that would be obtained under the correct model, but we point out a potential loss of sensitivity to detect truly active covariates. Our examples show how a novel approach to infer the error distribution leads to substantial gains in sensitivity, thus warranting the effort to go beyond normality, whereas for near-normal data one can get substantial speedups relative to assuming unnecessarily flexible models.

The methodology is available as part of R package mombf.

Joint work with David Rossell.

Date: 1 November 2016, CB 5.8, 13:15

Keming Yu (Brunel)

Data Adaptive Tail-index Regression

Abstract: Tail-index is an important measure to gauge the heavy-tailed behavior of a distribution. The problem of estimation of a Tail-index from various types of data has become rather important. Tail-index regression is introduced when covariate information is available. Inference of Tail-index regression may face two challenges: small sample bias with the analysis of small to moderate size data and the problem of storage and computational efficiency with dealing with massive data. In this paper we derive new statistical inference for Tail-index regression based on Pareto-type of distributions and Burr-XII distributions.

Date: 15 November 2016, CB 5.8, 13:15

Theresa Smith (Bath)

Age-period-cohort models for cancer incidence

Abstract: Age-period-cohort models have been used to examine and forecast cancer incidence and mortality for over three decades. However, the fitting and interpretation of these models requires great care because of the well-known identifiability problem that exists; given any two of age, period, and cohort, the third is determined.

In this talk I introduce APC models and the identifiability problem. I examine proposed ‘’solutions’’ to this problem and approaches based on an identifiable parameterization. I conclude with an analyis of cancer incidence data from Washington State and a discussion of future research directions.

Date: 21 November 2016, CB 3.16, 13:15 (Note different time and venue)

Adam Johansen (Warwick)

Search and Jump Algorithm for Markov Chain Monte Carlo Sampling

Abstract: We present an offline, iterated particle filter to facilitate statistical inference in general state space hidden Markov models. Given a model and a sequence of observations, the associated marginal likelihood L is central to likelihood-based inference for unknown statistical parameters. We define a class of “twisted” models: each member is specified by a sequence of positive functions psi and has an associated psi-auxiliary particle filter that provides unbiased estimates of L. We identify a sequence psi* that is optimal in the sense that the psi-auxiliary particle filter’s estimate of L has zero variance. In practical applications, psi is unknown so the psi-auxiliary particle filter cannot straightforwardly be implemented. We use an iterative scheme to approximate psi, and demonstrate empirically that the resulting iterated auxiliary particle filter significantly outperforms the bootstrap particle filter in challenging settings. Applications include parameter estimation using a particle Markov chain Monte Carlo algorithm and approximation of conditioned diffusion sample paths. [arxiv: 1511.06286]

Joint work with Pieralberto Guarniero and Anthony Lee

Date: 22 November 2016, CB 5.8, 13:15

Chris Jennison (Bath)

Search and Jump Algorithm for Markov Chain Monte Carlo Sampling

Abstract: MCMC sampling is now established as a fundamental tool in statistical inference but there are still problems to solve. MCMC samplers can mix slowly when the target distribution has multiple modes. A more insidious problem arises when sampling a distribution that is concentrated on a thin sub-region of a high-dimensional sample space. I shall present a new approach to mode-jumping and show how this can be used to sample from some challenging “thin” distributions.

Joint work with Adriana Ibrahim, University of Malasya.

Date: 6 December 2016, CB 5.8, 13:15

Sam Livingstone (Bristol)

Some recent advances in dynamics-based Markov chain Monte Carlo

Abstract: Markov chain Monte Carlo methods based on continuous-time dynamics such as Langevin diffusions and Hamiltonian flow are among the state of the art when performing inference for challenging models in many application areas. I will talk about some statistical models which Markov chains produced by these methods can explore well, and others for which they often struggle to do so. I’ll discuss some existing and new algorithms that use gradient information and/or exploit the geometry of the space through an appropriate Riemannian metric, and how these inputs can both positively and negatively affect exploration, using the notion of geometric ergodicity for Markov chains.

Date: 13 December 2016, CB 5.8, 13:15

Ilaria Prosdocimi (Bath)

A statistician’s wander into flood hydrology

Abstract: In the design and maintenance of structures such as dams or drainage networks, it is essential to be able to obtain reliable estimates of the magnitude and frequency of extreme events such as high river flow and rainfall totals. This talk will discuss methods to perform such estimation, focusing on similarities and differences of the different approaches developed by statisticians and civil engineers. Rather than presenting final results, the talk will focus on discussing the open challenges in the statistical methods for flood frequency estimation and will suggest possible future research avenues.

# Spring 2016

Date: 19 April 2016, CB 5.1, 14:15

Nick Whiteley (Bristol)

Variance estimation in the particle filter

Abstract: Particle filters provide sampling based approximations of marginal likelihoods and filtering expectations in hidden Markov models. However, estimating the Monte Carlo variance of these approximations, without generating multiple independent realizations of the approximations themselves, is not straightforward. We present an unbiased estimator of the variance of the marginal likelihood approximation, and consistent estimators of the asymptotic variance of the approximations of the marginal likelihood and filtering expectations. These estimators are byproducts of a single run of a particle filter and have no added computational complexity or storage requirements. With additional storage requirements, one can also consistently estimate higher-order terms in the non-asymptotic variance. This is information can be used to approximate the variance-optimal allocation of particle numbers.

Joint work with Anthony Lee, University of Warwick

Date: 26 April 2016, CB 5.1, 14:15

Statistical shape analysis in a Bayesian framework for shapes in two and three dimensions

Thomai Tsiftsi (Bath)

Abstract: Shape analysis is an integral part of object classification and has been used as a tool by many branches of science such as computer vision, pattern recognition and shape classification. In this talk I will present a novel shape classification method which is embedded in the Bayesian paradigm and utilises the efficacy of geometrical statistics as well as differential geometry. I will focus on the statistical classification of planar shapes by using techniques which replace some previous approximate results by analytic calculations in a closed form. This gives rise to a new Bayesian shape classification algorithm of which the efficiency was tested on available shape databases. Finally, I will conclude by demonstrating the extension of the proposed classification algorithm for shapes in three-dimensions.

Date: 3 May 2016, CB 5.1, 14:15

Hilbertian Fourth Order Blind Identification

Germain Van Bever (Open University)

Abstract: In the classical Independent Component (IC) model, the observations $$X_1,\cdots,X_n$$ are assumed to satisfy $$X_i=\Omega Z_i$$, $$i=1,\dots,n$$, where the $$Z_i$$’s are i.i.d random vectors with independent marginals and $$\Omega$$ is the mixing matrix. Independent component analysis (ICA) encompasses the set of all methods aiming at $$X=(X_1,\dots,X_n)$$, that is estimating a (non unique) unmixing matrix $$\Gamma$$ such that $$\Gamma X_i$$, $$i=1,\dots,n$$, has independent components. Cardoso (1989) introduced the celebrated Fourth Order Blind Identification (FOBI) procedure, in which an estimate of $$\Gamma$$ is provided, based on the regular covariance matrix and a scatter matrix based on fourth moments. Building on robustness considerations and generalizing FOBI, Invariant Coordinate Selection (ICS, 2009) was originally introduced as an exploratory tool generating an affine invariant coordinate system. The obtained coordinates, however, are proved to be independent in most IC models.

Nowadays, functional data (FD) are occurring more and more often in practice, and only little statistical techniques have been developed to analyze this type of data (see, for example Ramsay and Silverman 2006). Functional PCA is one such technique which only aims at dimension reduction with very little theoretical considerations. In this talk, we propose an extension of the FOBI methodology to the case of Hilbertian data, FD being the go-to example used throughout. When dealing with distributions on Hilbert spaces, two major problems arise: (i) the scatter operator is, in general, non-invertible and (ii) there may not exist two different affine equivariant scatter functionals. Projections on finite dimensional subspaces and Karhunen-Lo`eve expansions are used to overcome these issues and provide an alternative to FPCA. More importantly, we show that the proposed construction is Fisher consistent for the independent components of an appropriate Hilbertian IC model.

Affine invariance properties of the resulting FOBI components will be discussed and potential extension to a FICS procedure will be sketched. Simulated and real data are analyzed throughout the presentation to illustrate the properties and the potential benefits of the new tools.

This work is supported by the EPSRC grant EP/L010429/1.

References

• J.F. Cardoso (1989), Source Separation Using Higher Moments Proceedings of IEEE international conference on acoustics, speech and signal processing 2109-2112.

• D. Tyler, F. Critchley, L. Dumbgen and H. Oja (2009), Invariant Co-ordinate Selection J.R. Statist. Soc. B., 2009,71, 549-592.

• J. Ramsay and B.W. Silverman (2006) Functional Data Analysis 2nd edn. Springer, New York

# Autumn 2015

Date: 13 October 2015, 8W 2.13, 13:15

Evangelous Evangelou (Bath)

Writing and publishing your own R package: Some techniques and useful tools.

Abstract: Publishing an R package requires quality code but also adherence to CRAN policies. I will present some techniques for automating the process of creating and maintaining an R package the and some good practices from my experience as a package author.

Date: 20 October 2015, 8W 2.13, 13:15

Causal Models and How to Refute Them

Robin Evans (Oxford)

Abstract: Directed acyclic graph models (DAG models, also called Bayesian networks) are widely used in the context of causal inference, and they can be manipulated to represent the consequences of intervention in a causal system. However, DAGs cannot fully represent causal models with confounding; other classes of graphs, such as ancestral graphs and ADMGs, have been introduced to deal with this using additional kinds of edge, but we show that these are not sufficiently rich to capture the range of possible models. In fact, no mixed graph over the observed variables is rich enough, regardless of how many edges are used. Instead we introduce mDAGs, a class of hyper-graphs appropriate for representing causal models when some of the variables are unobserved. Results on the Markov equivalence of these models show that when interpreted causally, mDAGs are the minimal class of graphs which can be sensibly used. Understanding such equivalences is critical for the use of automatic causal structure learning methods, a topic in which there is considerable interest. We elucidate the state of the art as well as some open problems.

Date: 27 October 2015, 8W 2.13, 13:15

Jonty Rougier (Bristol)

Predicting large explosive eruptions for individual volcanoes

Abstract:Large explosive volcanic eruptions can be devastating, given that many volcanoes capable of such eruptions are close to cities. But data, on which predictions could be based, is very limited. Globally, such eruptions happen about once every two years, but the record is rapidly thinned going backwards in time, where the rate of under-recording depends not just on time, but also on location and magnitude. I describe our approach to assessing the under-recording rate, and to making predictions for sets of volcanoes with similar recorded histories, based on an exchangeable model of eruption rates. This is part of our larger project to provide a return period curve for each volcano. This is joint work with volcanologists Profs Steve Sparks and Kathy Cashman.

Date: 10 November 2015, 8W 2.13, 13:15

Haakon Bakka (NTNU)

A spatial random effect with one range for each region (the Difficult Terrain model component)

Abstract:Classical models in spatial statistics assume that the correlation between two points depends only on the distance between them (i.e. the models are stationary). In practice, however, the shortest distance may not be appropriate. Real life is not stationary! For example, when modelling fish near the shore, correlation should not take the shortest path going across land, but should travel along the shoreline. In ecology, animal movement depends on the terrain or the existence of animal corridors. We will show how this kind of information can be included in a spatial non-stationary model, by defining a different spatial range (distance) in each region.

We will answer the following questions:

• How to make a model with one range in each region?
• Is the algorithm fast enough for real data? (Hint: Yes!)
• How to avoid overfitting with flexible random effects?
• How to interpret the inference when you have flexible random effects?
• How do we model a point process with different cluster sizes in different regions, without changing the average number of points?

Date: 17 November 2015, 8W 2.13, 13:15

Daniel Williamson (Exeter)

Earth system models and probabilistic Bayesian calibration: a screw meets a hammer?

Abstract: The design and analysis of computer experiments, now called “Uncertainty Quantification” or “UQ” has been an active area of statistical research for 25 years. One of the most high profile methodologies, that of calibrating a complex computer code using the Bayesian solution to the inverse problem as described by Kennedy and O’Hagan’s seminal paper in 2001, has become something of a default approach to tackling applications in UQ and has over 1200 citations. However, is this always wise? Though the method is well tested and arguably appropriate for many types of model, particularly those for which large amounts of data are readily available and in which the limitations of the underlying mathematical expressions and solvers are well understood, many models, such as those found in climate simulation, go far beyond those successfully studied in terms of non-linearity, run time, output size and complexity of the underlying mathematics.

Have we really solved the calibration problem? To what extent is our “off the shelf approach” appropriate for the problems faced in fields such as Earth system modelling? In this talk we will discuss some of the known limitations of the Bayesian calibration framework (and some perhaps unknown) and we explore the extent to which the conditions in which calibration is known to fail are met in climate model problems. We will then present and argue for an alternative approach to the problem and apply it an ocean GCM known as NEMO.

Date: 24 November 2015, 8W 2.13, 14:15 (Note the kick-off time of 2:15)

Georg Lindgren (Lund)

Stochastic models for ocean waves - Gaussian fields made more realistic by Rice formula and some physics

Abstract: Gaussian fields were introduced in the early fifties as models for irregular ocean waves and they have been used in ocean engineering ever since. A simple modification leads to the more realistic stochastic Lagrange models, which account for horizontal and vertical movements of individual water particles, leading to realistic asymmetry of the generated waves.

Rice formula for the expected number of level crossings and its modern implementation to “level sets” makes it possible to derive exact statistical distributions for many important wave characteristics, like steepness and asymmetry. In the talk I will describe the stochastic Lagrange model and some of its statistical properties.

Date: 9 December 2015, CB 4.1, 13:15 (Note the different day (Wednesday) and venue)

John Copas (Warwick)

Title Model choice and goodness of fit

Abstract: How do we know whether a statistical model is sensible? The usual answer is to check that the model gives a reasonable fit to the data. The seminar will look at the variation between inferences based on different models, and show that this can be extremely large, even amongst models which seem to fit the data equally well. What does this tell us about most applications of statistics which completely ignore the problem of model uncertainty? What does it tell us about formal methods of model selection and model averaging which all, directly or indirectly, depend on model fit?