Probability and Statistics Seminars

Spring 2012:

23/3 Li Chen (Bristol) 3E 2.4 -- 14:15 Info
30/3 Fiona Underwood (Reading) Cancelled
20/4 Stephen Sharp (Cambridge) Info
27/4 Brendan McCabe (Liverpool) Info
25/5 Sue Todd (Reading) 6E 2.1 -- 16:15

Autumn 2011:

28/10 David Steinsaltz (Oxford) 3E 4.17 -- 15:00 Info
04/11 James Martin (Oxford) 3E 4.17 -- 14:15 Info
11/11 Augustyn Markiewicz (Poznan University, Poland) 3E 4.17 -- 14:15 Info
18/11 Jan Obloj (Oxford) 3E 4.17 -- 14:15 Info
25/11 Chris Jewell (Warwick) 3E 4.17 -- 14:15 Info
09/12 Theodore Kypraios (Nottingham) 3E 4.17 -- 14:15 Info

Spring 2011:

04/03 Ajay Jarsa (Imperial) 3E 2.4 -- 14:15 Info
11/03 Martin Hairer (Warwick) 3E 2.4 -- 14:15 Info
18/03 Howell Tong 3E 2.4 -- 14:15 Info
25/03 James Marting (Oxford) 3E 2.4 -- 14:15 Info
01/04 Wei Liu (Southampton) 3E 2.4 -- 14:15 Info

Autumn 2010:

22/10 Dr Alison Nightingale (Bath Pharmacology) 4W 1.7 -- 14:15 Info
05/11 Dr Michael Monoyios (Oxford) 3E 4.17 -- 15:00 Info
12/11 Richard Gill (Leiden) Landscapes seminar
19/11 Jason Matthiopoulos (St Andrews) 4W 1.7 -- 14:15 Info
26/11 Sach Mukherjee (Warwick) 3E 4.17 -- 14:15 Info
03/12 Philip Dawid (Cambridge) 3E 4.17 -- 14:15 Info
10/12 Alan Hammond (Oxford) 3E 4.17 -- 14:15 Info

Brendan McCabe, 27/4/12, 3E 2.4, 14:15

School of Management, University of Liverpool

Identifying structural change in OLS regressions

This talk takes another look at testing for structural change in OLS regressions and derives optimal small sample tests to identify the change point. The approach is decision theory based and Bayes rules are found. Part of the idea is to try and understand "how and where" the usual CUSUM procedures perform well. The talk finishes on a much more practical note where the performance of the CUSUM tests are investigated for a broad class of stochastic processes which have conditional expectations (given the past) of a known form. It is shown that the CUSUM test weakly converges to the suprememum of a Brownian bridge.

Stephen Sharp 20/4/12, 3E 2.4, 14:15

MRC Epidemiology Unit, Cambridge

InterAct: a multi-centre case-cohort study -- statistical considerations

The InterAct study is a nested case-cohort study based on data from 26 centres in 8 European countries, set up to investigate how genetic and lifestyle factors interact on the risk of developing Type 2 diabetes. I will describe the rationale for using a case-cohort design and the main statistical approach we have used for the analysis (weighted Cox regression and random effects meta-analysis). Other statistical issues I will discuss include estimation of interactions, estimation of incidence in a case-cohort study, and assessment of the impact of measurement error. I will conclude by highlighting some of the practical issues involved in coordinating the statistical analysis of this large study across multiple European partners.

Li Chen 23/3/12, 3E 2.4, 14:15

Department of Mathematics, University of Bristol

Spatial prediction, data assimilation and ensemble adjustment Kalman filter

This talk gives a brief overview of spatial prediction, data assimilation and Kalman filter type techniques. Particularly, a new approach is presented for data assimilation using the ensemble adjustment Kalman filter for surface measurements of carbon monoxide in a single tracer version of the community air quality model. Three different sets of numerical experiments were performed to test the effectiveness of the procedure and the range of key parameters used in implementing the procedure. In each case the proposed method provided better results than the method without data assimilation.

Theodore Kypraios 09/12/11, 3E 4.17, 14:15

Department of Statistics, University of Nottingham

A class of semi-parametric time series models: Construction and Bayesian Inference

In this talk a novel class of semi-parametric time series models will be presented, for which we can specify in advance the marginal distribution of the observations and then build the dependence structure of the observations around them by introducing an underlying stochastic process termed as 'latent branching tree'. It will be demonstrated how can we draw Bayesian inference for the model parameters using Markov Chain Monte Carlo methods as well as Approximate Bayesian Computation methodology. Finally a real dataset on genome scheme data will be fitted to these models and we will also discuss how this kind of models can be used in modelling Internet traffic.

Chris Jewell 25/11/11, 3E 4.17, 14:15

Department of Statistics, University of Warwick

From livestock to likelihoods: Bayesian risk prediction for epidemics in animals.

Large scale livestock disease outbreaks, such as that witnessed by the UK in 2001, quickly outstrip the standing capabilities of government control agencies. Careful decisions must therefore be made in order to maximise the efficiency of this limited resource. However, co-ordinating the information from localised disease control centres as well as synchronising their efforts has historically proved a difficult task. In the 2001 outbreak of foot and mouth disease in the UK, simulation-based mathematical modelling was used to try to study the epidemic progress on a national scale, and thereby to more effectively inform control decisions. However, this was widely criticised due to lack of rigour in coupling the models to the observed epidemic timeseries.

This talk will present a generic approach to risk prediction for epidemics, in which data is taken from the field in real time during an outbreak and fitted to a dynamical epidemic model in a Bayesian framework. Predictive distributions are then used to inform control strategy, being presented to policy makers using primarily GIS techniques. Examples of foot and mouth disease and avian influenza will illustrate some of the difficulties in dealing with epidemic data, as well as the parallelised reversible jump MCMC algorithms we have developed to address them.

Jan Obloj 18/11/11, 3E 4.17, 14:15

Mathematical Institute, University of Oxford

An SDE perspective on Azema-Yor processes with applications to constrained portfolio optimisation problems

In the first part of the talk I will present some general results on Azema-Yor processes. These processes can be written as M_t=H(S_t,X_t), where S is the continuous running maximum of a semimartinagle X and H is such that if X is a local martingale then so is M. I will focus on an SDE perspective and characterise AY processes as the unique (strong) solution to two SDEs: the Bachelier equation and the Drawdown equation. The latter leads to investigation of the drawdown properties: M_t stays above a given function of the past maximum of M.

In the second part of the talk I will present applications to portfolio optimisation problems in mathematical finance. I will show that, in a very general context, solving portfolio optimisation under a drawdown constraint is equivalent to an unconstraint optimisation problem but with a suitably modified reward (utility) function. The relation between the value function and the maximising portfolios is explicit.

The talk is based on joint works with L. Carraro and N. El Karoui and with V. Cherny.
The references are available at:
http://arxiv.org/abs/0902.1328
http://arxiv.org/abs/1110.6289

Augustyn Markiewicz 11/11/11, 3E 4.17, 14:15

Department of Mathematical and Statistical Methods, Poznan University of Life Sciences, Poland

On optimal designs under the interference model

We consider optimality of circular block designs under the interference model. The only so far known optimal designs under this model are circular neighbor balanced designs (CNBDs). Their universal optimality under fixed model is proved in Druilhet (1999) and under mixed model in Filipiak and Markiewicz (2003, 2007). However, when the number of blocks is not proportional to the number of treatments minus one then CNBDs cannot exist. Therefore our aim is to characterize D- and E-optimal designs as well as universally optimal designs in classes of complete designs with specific numbers of blocks.

Druilhet, P. (1999). Optimality of circular neighbor balanced designs. J. Statist. Plann. Infer. 81, 141-152.
Filipiak, K. and A. Markiewicz (2003). Optimality of neighbor balanced designs under mixed effects model. Statistics and Probability Letters 61, 225-234.
Filipiak, K. and A. Markiewicz (2007). Optimal designs for a mixed interference model. Metrika 65, 369-386.

James Martin 04/11/11, 3E 4.17, 14:15

Department of Statistics, University of Oxford

Lipschitz surfaces in percolation

For p in (0,1), consider a percolation model on Z^d under which each site is open with probability p and closed with probability 1-p.

Given a graph G and an integer m, one can ask: is there an injective map from G to Z^d such that (i) the image of every point in G is an open site; (ii) the images of any two neighbours in G are at distance at most m.

Such "Lipschitz embeddings into percolation" have been previously considered by Grimmett, Holroyd and others. For example, it was known that for sufficiently large p, such embeddings exist with probability 1 if G is the lattice Z^{d-1}, but do not exist if G is Z^d.

I'll describe such results, and go on to consider the case where G is a d-dimensional version of a "comb graph". We show that Lipschitz embeddings do exist in this case.

The proof involves several interesting new stochastic domination results.

Joint work with Alexander Holroyd.

David Steinsaltz 28/10/11, 3E 4.17, 15:00

Department of Statistics, University of Oxford

Asymptotics of killed one-dimensional diffusions, with applications to the biodemography of ageing

The convergence of Markov processes to stationary distributions is a basic topic of introductory courses in stochastic processes, and the theory has been thoroughly developed. What happens when we add killing to the process? The process as such will not converge in distribution, but the survivors may; that is, the distribution of the process, conditioned on survival up to time t, converges to a "quasistationary distribution" as t goes to infinity.

This talk presents recent work with Martin Kolb and earlier work with Steve Evans, proving an analogue of the transience-recurrence dichotomy for killed one-dimensional diffusions. Under fairly general conditions, a killed one-dimensional diffusion conditioned to have survived up to time t either escapes to infinity almost surely (meaning that the probability of finding it in any bounded set goes to 0) or it converges to the quasistationary distribution, whose density is given by the top eigenfunction of the adjoint generator.

These theorems arose in solving part of a longstanding problem in biological theories of ageing, and then turned out to play a key role in a very different problem in population biology, the effect of unequal damage inheritance on population growth rates.

Dr Ajay Jarsa 04/03/11, 3E 2.4, 14:15

Department of Mathematics, Imperial College

On the stability of a class of sequential Monte Carlo methods in High Dimensions

We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a single target density on R for large d. It is well known, using a single importance sampling step, one produces an approximation for the target distribution that deteriorates as the dimension d increases, unless the number of MC samples N increases at an exponential rate in d. This degeneracy can be avoided by introducing a sequence of artificial targets, starting from a `simple' target density and moving to the one of interest and using an SMC method to sample from the sequence. Using this class of SMC methods with a fixed number of samples, one can produce an approximation for which the effective sample size (ESS) converges to a random variable \varepsilon_N as d -> \infty, such that 1<\varepsilon_{N}<N. The convergence is achieved when the overall computational cost is proportional to Nd^2. If \varepsilon_{N} is reasonably close to N no additional work is needed otherwise one needs to resample; the case of resampling is not discussed, but we have proved the results in the technical report. This is a joint work with Alex Beskos (UCL) and Dan Crisan (Imperial College London).

Dr Martin Hairer 11/03/11, 3E 2.4, 14:15

Department of Mathematics, University of Warwick

Rough stochastic PDEs

We consider Burgers-type equations driven by space-time white noise that arise naturally as the Langevin equations associated to a diffusion measure. Classically, the solutions to such equations are too irregular for the nonlinearity to be well-defined, even in a weak sense. We show that, using the theory of rough paths, it is nevertheless possible to give a meaning to the notion of solution and we show that such solutions arise as limits of a natural class of smooth approximations.

Dr Howell Tong 18/03/11, 3E 2.4, 14:15

Feature Matching in Time Series Modelling

Using a time series model to mimic an observed time series has a long history. Because all models are wrong, (George Box's famous dictum), conventional estimation methods based on 1-step-ahead prediction errors are, like foot-binding, often too constrictive in at least two respects: (i) assuming that there is a true model; (ii) evaluating the efficiency of the estimation as if the postulated model is true.

In this talk, we propose a new approach to empirical time series modelling, based on some foot-unbinding ideas. By liberating ourselves from the dictatorship of one-step-ahead prediction errors, I shall illustrate, with simulations and real data, the many benefits of the liberation.

Dr James Martin 25/03/11, 3E 2.4, 14:15

Department of Statistics, University of Oxford

Last-passage percolation in one or more dimensions

Consider a vertex set {1,2,...,n}. Associate i.i.d. random weights v_{i,j} to every "edge" (i,j), i<j. Now look for the maximum weight path 1<i_1<i_2<...<i_r<n, where the weight of a path is the sum of the weights on the edges connecting successive points of the path.

This is an example of "last passage percolation": even in this simple one-dimensional setting, the model has surprisingly rich behaviour. If the common weight distribution has finite variance, the behaviour is in some sense "local": most edges used on the optimal path are short, and one can find a renewal structure within the model that yields a law of large numbers and a central limit theorem for the maximal weight of a path from 1 to n, as n grows.

On the other hand, if the weight distribution has a sufficiently heavy tail, then the dominant contributions to the weight of the optimal path come from edges whose length is on the order of n. One can obtain scaling limits both for the weight and for the "shape" of the path which are reminiscent of those for nearest-neighbour models in 2 dimensions. I'll discuss these scaling limits and related models such as "random interval graphs".

Joint work with Sergey Foss and Philipp Schmidt.

Dr Wei Liu 01/04/11, 3E 2.4, 14:15

School of Mathematics, University of Southampton

Simultaneous confidence bands for regression analysis

This talk will provide an overview of the methodology of simultaneous confidence bands for parametric regression analysis. We will look at how simultaneous confidence bands can be used in regression analysis to make sensible and informative inference, the key in the construction of simultaneous confidence bands, the two optimality criteria for comparison of simultaneous confidence bands, and some unsolved problems. The talk should be accessible to anyone who has done linear regression models.

Dr Alison Nightingale 22/10/10 4W1.7 14:15

Pharmacy and Pharmacology, University of Bath

Pharmacoepidemiology and the General Practice Research Database

The seminar will cover aspects of the role of pharmacoepidemiology in postmarketing drug surveillence and current research projects in pharmacoepidemiology at the University of Bath. The data source we use for our projects, the General Practice Research Database (GPRD), will be described as well as its strengths and weaknesses with regards to conducting pharmacoepidemiological (and epidemiological) studies. This will hopefully lead to a discussion about potential areas of collaboration between Pharmacoepidemiology, Statistics and Mathematical Biology.

Dr Michael Monoyios 5/11/10 3E4.17 15:00

Mathematical Institute, University of Oxford

Optimal exercise of an executive stock option by an insider

We consider an optimal stopping problem arising in connection with the exercise of an executive stock option by an agent with inside information. The agent is assumed to have noisy information on the terminal value of the stock, does not trade the stock or outside securities, and maximises the expected discounted payoff over all stopping times with regard to an enlarged filtration which includes the inside information. This leads to a stopping problem governed by a time-inhomogeneous diffusion and a call-type reward. We establish conditions under which the option value exhibits time decay, derive the smooth fit condition for the solution to the free boundary problem governing the maximum expected reward, and derive the early exercise decomposition of the value function. The resulting integral equation for the unknown exercise boundary is solved numerically and this shows that the insider may exercise the option before maturity, in situations when an agent without the privileged information may not. Hence we show that early exercise may arise due to the agent having inside information on the future stock price.

Dr Jason Matthiopoulos 19/11/10 4W1.7 14:15

School of Biology & Centre for Research into Ecological and Environmental Modelling, University of St Andrews

Catastrophic nepotism, collective memory and wildlife population cycles

Boom and bust phenomena are often associated with advanced human societies relying on complicated communication networks and financial interdependencies. However, periodic population collapses are widespread in nature; so much so that some authors have tried to elevate cyclicity to the status of "ecological law". Much of the work on population cycles has focused on trophic interactions between species (such as predation, parasitism). In this talk, I review the social hypothesis for population cycles, the idea that the existence of ownership and aggression can explain the long-documented cycles in some wildlife populations. I illustrate throughout with facts and data from the game bird, red grouse (Lagopus lagopus scotticus), the emblematic study-species for the social hypothesis.

In the first part of the talk I explore a collection of deterministic models, ultimately aiming to extract the necessary and sufficient conditions for cycles under this hypothesis.

In the second part, I present inferential results based on state-space modeling of red grouse populations and the wider ecological community to which the species belongs.

Dr Sach Mukherjee 26/11/10 3E4.17 14:15

Department of statistics, University of Warwick

Sparse graphical models for cancer biology

Networks of proteins called "signalling networks" play a key role in the control of diverse cellular processes; their aberrant functioning is heavily implicated in many diseases, including cancer. Aberrations in cancer cells are thought to perturb the normal connectivity of these networks, with important biological and therapeutic implications. Yet cancer-specific signalling remains poorly understood, especially at the level of relevant (post-translational) protein modifications. Modern high-throughput biochemical technologies are now able to make measurements on components of these systems, and can, in principle, shed light on a number of critical, open questions in cancer biology. I will discuss statistical approaches for interpreting these data, in particular how graphical models can be used to integrate biochemical data and prior knowledge of signalling biology to facilitate the discovery process.

Dr Philip Dawid 03/12/10 3E4.17 14:15

Department of statistics, University of Cambridge

Proper Local Scoring Rules

A scoring rule S(x, Q) measures the quality of a quoted distribution Q for an uncertain quantity X in the light of the realised value x of X. It is proper when it encourages honesty, i.e, when, if your uncertainty about X is represented by a distribution P, the choice Q = P minimises your expected loss. Traditionally, a scoring rule has been called local if it depends on Q only through q(x), the density of Q at x. The only proper local scoring rule is then the log-score, -log q(x). For the continuous case, we can weaken the definition of locality to allow dependence on a finite number m of derivatives of q at x. A full characterisation is given of such order-m local proper scoring rules. In particular, any m-local scoring rule with m > 0 can be computed without knowledge of the normalising constant of the density. This last property is particularly useful in statistical applications. This is a joint work with Matthew Parry and Steffen Lauritzen.

Dr Alan Hammond 10/12/10 3E4.17 14:15

Department of statistics, University of Oxford

Biased motion in disorder: persistent discreteness, rational resonance, and stable limits

A biased random walker in open space will move at positive velocity. If the medium is disordered, however, the motion may be slowed to vanishing velocity by the walker encountering large connected structures in the disorder that acts as traps. A natural model for these effects is a walker on an infinite Galton-Watson tree with leaves, with a constant bias away from the root. Here, the finite trees hanging off the backbone act as traps. The progress of the walker is determined on all time-scales by a discrete inhomogeneity, in which trap sojourn times tend to cluster around powers of the bias parameter. This prevents the existence of a scaling limit. I will introduce an alternative model, in which biases on edges of the tree are randomised with a non-lattice distribution, so that a stable limiting law results. These two effects, of persistent discrete inhomogeneity in a constant bias model, and stable limiting laws in the randomly biased case, may have counterparts in more physical models in Euclidean space, where the persistent discreteness may arise as a rational resonance in the bias slope.

Coauthors: Alex Fribergh (Z^d and tree models), Gerard Ben Arous and Nina Gantert (tree models).

Fouskakis Dimitrios 2/6/10 4W 1.7 10:00

Department of Mathematics, Technical University of Athens

Power Intrinsic Variable Selection for Normal Models based on Zellner's g-Prior: Model Formulation and Preliminary Results

In order to express prior ignorance in Bayesian variable selection problems, proper prior distributions with large variances or non-informative improper distributions can be used. Bayes factors are well known for their sensitivity on prior variances, while, when using improper priors, Bayes factors cannot be determined because of the involvement of the unknown normalizing constants. This has urged the Bayesian community to develop various methodologies to overcome the problem of prior specification in model comparison and variable selection problems. An important part of this research is focused on the so-called objective model selection methods having their source on the intrinsic priors in order to provide an approximate proper Bayesian interpretation for intrinsic Bayes factors. These intrinsic priors use improper priors as a starting point and overcome the problem of indeterminacy of the Bayes factor since the same constant is involved in all marginal likelihoods. In this paper we develop the methodology of intrinsic priors when using proper priors as a starting problem. Specifically we focus on normal linear models and we use initially the Normal-inverse gamma Zellner's g-prior. We introduce two different intrinsic priors. The power conditional intrinsic Zellner's g-prior, where we use the intrinsic prior methodology to define the prior distribution for the model parameters only, while for the error variance parameter we adopt the usual inverse gamma prior, and the power intrinsic Zellner's g-prior where we use the intrinsic prior methodology in order to define the joint prior distribution of the model parameters and the error variance. Moreover, by borrowing ideas from the power prior approach we avoid the use of a minimal training sample and the sensitivity of posterior results on the selection (and size) of this training sample in our intrinsic prior methodology. The methodology is illustrated on both simulated and real examples and sensitivity analysis reveals broad stability of our conclusions.

The slides are available at
http://www.math.ntua.gr/~fouskakis/Presentations/Bath/Presentation_Bath.pdf

Ioannis Ntzoufras 2/6/10 4W 1.7 10:00

Department of Statistics, Athens University of Economics and Business

Incorporating cost in Bayesian Variable Selection, with application to cost-effective measurement of quality of health care

In the field of quality of health care measurement, one approach to assessing patient sickness at admission involves a logistic regression of mortality within 30 days of admission on a fairly large number of sickness indicators (on the order of 100) to construct a sickness scale, employing classi- cal variable selection methods to find an "optimal" subset of 10-20 indicators. Such "benefit-only" methods ignore the considerable differences among the sickness indicators in cost of data collec- tion, an issue that is crucial when admission sickness is used to drive programs (now implemented or under consideration in several countries, including the U.S. and U.K.) that attempt to iden- tify substandard hospitals by comparing observed and expected mortality rates (given admission sickness). When both data-collection cost and accuracy of prediction of 30-day mortality are con- sidered, a large variable-selection problem arises in which costly variables that do not predict well enough should be omitted from the final scale. In this work we develop a method for solving this problem based on posterior model odds, arising from a prior distribution that accounts for the cost of each variable and results in a set of posterior model probabilities which corresponds to a generalized cost-adjusted version of the Bayesian information criterion (BIC). We use reversible-jump Markov chain Monte Carlo (RJMCMC) methods to search the model space. The proposed method provides a principled approach to performing a cost-benefit trade-off that avoids ambiguities in identification of an appropriate utility structure. Our cost-benefit approach results in a set of models with a noticeable reduction in cost and dimensionality, and only a minor decrease in predictive performance, when compared with models arising from benefit-only analyses. Additionally to the above, we present a population based reversible jump MCMC algorithm which efficiently searches the model space when an overall limit on the total data collection cost of each subset is enforced. The method is presented and compared with simpler MCMC schemes. All results are phrased in the language of health policy but apply with equal force to other quality assessment settings with dichotomous outcomes, such as the the study of retention rates in the workplace and the creation of cost-effective credit scores in business.

The slides are available at
http://stat-athens.aueb.gr/~jbn/papers/presentations/2009_cost_lse.pdf

Probability and Statistics Seminars at University of Bath