skip to content
 

Timetable (SCBW03)

Stochastic Computation for the Analysis of Ecological and Epidemiological Data

Monday 20th November 2006 to Friday 24th November 2006

Monday 20th November 2006
08:30 to 10:00 Registration
10:00 to 10:05 Welcome address
Chair: ST Buckland
INI 1
10:05 to 11:00 A Frigessi ([Norwegian Computing Center])
Investigating the spread of infectious salmon anemia in Atlantic salmon farming: a stochastic space-time model
Chair: ST Buckland

Infectious salmon anemia is an infectious disease of farmed salmon. The first outbreak was in Norway in 1984. Control strategies have not yet succeeded in controlling the spread in Norway and North America. The purpose of this research was to investigate the relative importance of teh main risk factore associated with different routes of transmission. We study proximity to an infectious farm, measured by distance and contact network, and the amount of biomass at farm sites. We allow for a further un-identified transmission route, possibly representing boat traffic or infected smolt. We suggest a stochastic space-time model for the disease along the farm sites of the norwegian coast. We analyse data betweenn 2000 and 2005, containig 73 cases and about 1100 farm sites. We shall present the model and preliminary results.

This is joint work with Ida Scheel (University of Oslo), Magne Aldrin (NR Norwegian Computing Centre) and Peder A. Jansen (The Norwegian Veterinary Institute).

INI 1
11:00 to 11:30 Coffee
11:30 to 12:30 RB O'Hara ([Helsinki])
Estimation of births deaths and immigration from mark-recapture data
Chair: ST Buckland

The analysis of mark-recapture data is undergoing a period of development and expansion.Here we contribute to that by presenting a model which include both births and immigration,as well as the usual deaths.Data come from a long-term study of the willow tit (Parus montanus ), where we can assume that all births are recorded,and hence immigrants can also be identified. We model the rates of immigration,birth rare per parent,and death rates of juveniles and adults. Using a hierarchical model allows us to incorporate annual variation in these parameters.The model is fitted to the data using MCMC,as a Bayesian analysis. In addition to the model fitting,we also check several aspects of the model fit,in particular whether survival varies with age or immigrant status,and whether capture probability is affected by previous capture history.The latter check is important,as independence of capture histories is a key assumption that simplifies the model considerably.Here we find that the capture probability depends strongly on whether the individual was captured in the previous year. Our work moves MRR modelling closer to a description of the dynamics of the whole population,with the obvious potential for prediction,and use in making decisions about population management.

INI 1
12:30 to 13:30 Lunch at Churchill College INI 1
14:00 to 15:15 Recent advances in statistical ecology using computationally intensive methods
Chair: A Frigessi

Computationally intensive methods are becoming increasing popular within statistical ecology for analysing complex stochastic systems. Particular attention will focus on capture-recapture (and/or tag-recovery) data. We will concentrate on the use of Bayesian methods within this area and the (reversible jump) Markov chain Monte Carlo algorithm, for exploring the posterior distribution of interest. A number of issues will be discussed, including model discrimination and model-averaging, incorporating individual heterogeneity and dealing with missing data. Real data sets will be considered, illustrating the application and implementation of these methods and demonstrating the increased understanding of the systems obtained through the analysis. Areas of continuing and future research will also be discussed.

INI 1
15:15 to 15:45 Tea
15:45 to 17:00 ST Buckland ([CREEM])
Embedding population dynamics models in inference
Chair: A Frigessi

Increasing pressures on the environment are generating an ever-increasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical models, so that the consequences of management action can be predicted, and the uncertainty in these predictions quantified. These models must be able to predict the response of populations to anthropogenic change, while handling the major sources of uncertainty. We describe a simple ‘building block’ approach to formulating discrete-time models. These models may include demographic stochasticity, environmental variability through covariates or random effects, multi-species dynamics such as in predator-prey and competition models, movement such as in metapopulation models, non-linear effects such as density dependence, and mating models. We discuss methods for fitting such models to time series of data, and quantifying uncertainty in parameter estimates and population states, including model uncertainty, using computer-intensive Bayesian methods.

INI 1
17:00 to 18:00 Welcome Wine Reception
Tuesday 21st November 2006
09:00 to 10:00 Use of Monte Carlo particle filters to fit and compare models for the dynamics of wild animal populations
Chair: E Arjas
INI 1
10:00 to 11:00 Do wandering albatrosses really perform Levy flights when foraging?
Chair: E Arjas

We examine the hypothesis that wandering albatrosses (Diomedea exulans) undergo Levy flights when roaming the skies in search of oceanic food sources. Levy flights are random walks whose step lengths are taken from a distribution with infinte variance, such as a power-law. The Levy flight consequently has no typical scale, and this has been interpreted as being an efficient way of searching for food on the ocean surface. We first re-analyse the original data that were used to infer Levy flights. These data come from wet/dry loggers that record the time periods for which the birds were airborne or on the ocean surface. We cast doubt as to whether these data are sufficient to conclude Levy flight behaviour. This prompts us to analyse recent data from birds fitted with much higher resolution wet/dry loggers. We find that the widely-held Levy flight hyopthesis can be refuted by the newer data. We will also briefly discuss other data sets and ecological questions arising from the unique Antarctic environment.

Related Links

INI 1
11:00 to 11:30 Coffee
11:30 to 12:30 Covariate information in complex event history data - some thoughts arising from a case study
Chair: E Arjas

The motivation behind this talk comes from considering epidemiological follow-up data for the purpose of studying the role of various risk factors of cardiovascular diseases. Commonly in such studies the statistical analysis is based on a hazard regression model where the covariates (e.g. blood pressure, cholesterol level, or body mass index) are measured only at the baseline. In addition to considering such more traditional risk factors, it is becoming increasingly common to try and assess also the role of some genetic factors contributing to the aetiology of such diseases, and then usually restricting the analysis to certain candidate loci that are potentially causative on the basis of the available information about their function. In principle, the corresponding causal mechanisms can involve pathways that are direct in the sense that they influence, in the postulated model structure, directly the outcome variable, or indirect in that their effect on the outcome is mediated via the levels of the measured risk factors.

INI 1
12:30 to 13:30 Lunch at Churchill College
14:00 to 15:15 A general space-time growth-interaction process for inferring and developing structure from partial observations
Chair: L Thomas

Not only have marked point processes received relatively little attention in the literature, but most analyses ignore the fact that in real life spatial structure often develops dynamically through time. We therefore develop a computationally fast and robust spatial-temporal process, based on stochastic immigration-death and deterministic growth-interaction. For this enables both single and multiple snap-shot marked point process data to be studied in considerable depth. Combining logistic and linear growth with (symmetric) disc-interaction and (asymmetric) area-interaction generates a wide variety of mark-point spatial structures. A maximum psuedo-likelihood approach is developed for parameter estimation at fixed times, and a least squares procedure for parameter estimation based on multiple time points.

A related problem in spatial statistics and stochastic geometry concerns the modelling and statistical analysis of hard particle systems involving discs or spheres. For successively filling remaining empty structure leads to a limiting maximum packing pattern whose structure depends on the given characteristics of the particles. Using our process to develop such patterns extends current methods, since a newly arrived particle is not immediately rejected if it does not fit into a specific gap, but can change size to adapt to the interaction pressure placed on it.

INI 1
15:15 to 15:45 Tea
15:45 to 17:00 Poster session
Chair: L Thomas
Wednesday 22nd November 2006
09:00 to 10:00 C Gilligan ([Cambridge])
Parameter estimation for spatio-temporal models of botanical epidemics
Chair: G Gibson
INI 1
10:00 to 11:00 T Kypraios ([Nottingham])
Roubst MCMC algorithms for Bayesian inference in stochastic eipdemic models
Chair: G Gibson

In general, inference problems for disease outbreak data are complicated by the facts that (i) the data are inherently dependent and (ii) the data are usually incomplete in the sense that the actual process of infection is not observed. We adopt a Bayesian approach and apply Markov Chain Monte Carlo (MCMC) methods in order to make inference for the parameters of interest (such as infection and removal rates). We show that once the size of the data set ncreases, the standard methods perform poorly. Therefore, apart from centered reparameterisation we extend the Non-Centered and partially Non-Centered algorithms presented in Neal and Roberts (2005). Finally, we adopt a fully Bayesian approach to analyze the Foot-and-Mouth disease occurred in 2001 in the UK and also discus modelling approaches for a potential Avian Influenza outbreak in the poultry industry of the UK.

INI 1
11:00 to 11:30 Coffee
11:30 to 12:30 The persistence of measles: from the schoolyard to sub-saharan Africa
Chair: G Gibson
INI 1
12:30 to 13:30 Lunch at Churchill College
14:00 to 15:15 Bayesian experimental design with Stochastic epidemic models
Chair: PD O'Neill

Inference and parameter estimation for stochastic epidemic models has been greatly facilitated by Bayesian methods and associated computational techniques such as Markov chain Monte Carlo. The question of how experiments should be designed ­ e.g. how populations should be sampled in space and time - to maximise the insights gained from these analyses is now being considered. This talk will describe how the Bayesian approach to experimental design, originally due to Muller, can be applied in the context of nonlinear stochastic epidemic models. In this approach, the design itself is treated as a random quantity. A distribution, which depends fundamentally on the utility of the design, is assigned to model parameters, experimental outcome and experimental design jointly. The design which is optimal, in terms of having the highest expected utility, corresponds to the mode of the design marginal distribution. We will demonstrate how, by using approximations to parameter likelihoods based on moment closure methods, it is computationally feasible to implement this approach to design experiments in practically relevant situations. In particular, we use the methods to explore possible designs for microcosm experiments on epidemics of fungal pathogens in plant communities.

INI 1
15:15 to 15:45 Tea
15:45 to 17:00 Small worlds and giant epidemics
Chair: PD O'Neill

Key problems for models of disease spread relate to threshold, velocity of spread, final size and control. All these aspects depend crucially on the network structure of individual interactions.

Networks of interest range from the highly localised case, where interactions are only between near neighbours, to the opposite global extreme where all interact equally with all, so that a disease can spread much more quickly through the population. Understandably, there has been much recent interest in `small-world' and meta-population models, in which a relatively small number of long-distance connections can change a network from local to effectively global. Such models seem particularly relevant to the changed patterns of human and animal diseases in a world whose connectivity, in terms of both travel and trade, has increased hugely in recent decades.

In consequence, a number of different mathematical and statistical approaches have been developed recently that focus on networks. I shall discuss the strengths and weaknesses of some of these approaches, with examples drawn from both human and animal diseases, susch as SARS, Foot and Mouth disease and avian flu. I shall also discuss the wider implications, as illustrating what mathematics can and cannot do in helping us predict and control disease outbreaks.

Related Links

INI 1
20:00 to 18:00 Conference at Trinity College (Old Kitchens)
Thursday 23rd November 2006
09:00 to 10:00 A probabilistic test of the neutral model
Chair: FG Ball

A neutral model of community dynamics has been built using the hierarchical Bayesian framework and fitted with Markov Chain Monte Carlo methods to three community datasets. To fit the data well, the model would need parameter values that are impossible. This suggests that variation in species abundances cannot be explained solely by random drift between species as suggested by the neutral model.

INI 1
10:00 to 11:00 Estimating mixing between subpopulations using respondent driven sampling
Chair: FG Ball

It is widely acknowledged that the level of mixing within a population plays an important role in the transmission dynamics of infectious diseases. However, obtaining information on mixing is notoriously difficult. Respondent-driven sampling (RDS), a kind of chain-referral sampling, is becoming an increasingly popular approach of sampling 'hidden' populations, such as injection drug users and men who have sex with men. RDS involves giving study participants a small number of coupons to give to other potential participants who are their friends or acquaintances. As a side-effect of the recruitment process, RDS provides information on mixing between different populations and, by asking individuals about their relationship to the person that recruited them, the extent of overlap between social and sexual networks. Current analytical techniques treat the recruitment process as a Markov chain, which is inappropriate as individuals may recruit more than one individual. We show how stochastic context-free grammars (SCFGs) can be used to model the tree-like recruitment process, which allows us to test for non-random mixing between subpopulations (e.g. infected/uninfected), for independence of characteristics between recruitees of a given recruiter, and for differences in patterns of mixing between different populations. We discuss the similarity of the recruitment process to a multitype branching process and a stochastic susceptible-infected epidemiological model.

INI 1
11:00 to 11:30 Coffee
11:30 to 12:30 Modeling tuberculosis in areas of high HIV prevalence
Chair: FG Ball

We describe a discrete event simulation model of tuberculosis (TB) and HIV disease, parameterized to describe the dual epidemics in Harare, Zimbabwe. TB and HIV are the leading causes of death from infectious disease among adults worldwide and the number of TB cases has risen significantly since the start of the HIV epidemic, particu-larly in Sub-Saharan Africa, where the HIV epidemic is most severe. There is a need to devise new strategies for TB control in countries with a high prevalence of HIV. This model has been designed to investigate strategies for reducing TB transmission by more efficient TB case detection. The model structure and its validation are discussed.

INI 1
12:30 to 13:30 Lunch at Churchill College
14:00 to 15:15 A Ganesh ([Cambridge])
Epidemics on graphs: thresholds and curing strategies
Chair: D Mollison

We consider the contact process (SIS epidemic) on finite undirected graphs and study the relationship between the expected epidemic lifetime, the infection and cure rates, and properties of the graph. In particular, we show the following: 1) if the ratio of cure rate to infection rate exceeds the spectral radius of the graph, then the epidemic dies our quickly. 2) If the ratio of cure rate to infection rate is smaller than a generalisation of the isoperimetric constant, then the epidemic is long-lived. These results suffice to establish thresholds on certain classes of graphs with homogeneous node degrees. In addition, we obtain thresholds for epidemics on power-law graphs. Finally, we use these techniques to study the efficacy of different schemes for distributing curing resources among the nodes.

INI 1
15:15 to 15:45 Tea
15:45 to 17:00 Building and fitting models of host-virus interaction
Chair: D Mollison

We treat a panmictic host population interacting with a virus. The virus is transmitted both horizontally and vertically. We modify the Moran model to describe the stochastic dynamics of individual host and viral lineages. For a sample of individuals from the population, the model gives rise to a branching and coalescing graph that contains the combined host and viral genealogies as a subgraph. The associated diffusion process, obtained in the limit of large host population, is related to the Neuhauser-Krone selection graph process.

We consider two study populations: cougars infected with FIV and a UK cohort of HIV patients. We fit the joint host-virus process to viral sequence data and known host pedigrees (which are trivial in the human case). We use MCMC to average over the variable dimension parameter space of labeled graphs.

INI 1
Friday 24th November 2006
09:00 to 10:00 Uses and abuses of stochastic models in veterinary epidemiology
Chair: D Clancy

Equine influenza causes disease that, while similar to human infection caused by Influenza A H1N1 and H3N2, at least in terms of the pathogenesis, transmission and population level phylogeny, is markedly different in terms of seasonality in that there are no obvious consistent winter peaks of transmission.

The talk will focus around a programme of work directed at better understanding of the epidemiology and control of equine influenza infection. The programme has used stochastic versions of SEIR models, parameterised from experimental and epidemiological data of the disease in the natural host. Optimising the use of vaccination is of particular interest. Empirical data have allowed the extension of the basic models into those assessing the impact of virus selection (“antigenic drift”) and explain how rather small differences observed experimentally scale up to substantial population level effects. More recent developments of explore the extension of a basic model into a one involved variably connected patches. Practical issues which face all those working in similar fields relating to parameterisation of more complex stochastic epidemiological models will be discussed and comparison will be made with other epidemiological work.

INI 1
10:00 to 11:00 Bayesian inference for structured population models given final outcome data
Chair: D Clancy

We consider the problem of Bayesian inference for infection rates in a multi-type stochastic epidemic model in which the population has a given structure, given data on final outcome. For such data, a likelihood is both analytically and numerically intractable. This problem can be overcome by imputation of suitable latent variables. We describe two such approaches based on different representations of the epidemic model. We also consider extentions to the methodology for the situation where the observed data are a fraction of the entire population. The methods are illustrated with data on influenza outbreaks.

INI 1
11:00 to 11:30 Coffee
11:30 to 12:30 Climate-driven spatial dynamics of plague among prairie dog colonies
Chair: D Clancy

I will present a Bayesian hierarchical model for the joint spatial dynamics of a host-parasite system. The model was fitted to long-term data on the regional plague dynamics and metapopulation dynamics of the black-tailed prairie dog, a declining keystone of North American prairies. The rate of plague transmission between colonies increases with increasing precipitation while the rate of infection from unknown sources decreases in response to hot weather. The annual dispersal distance of plague is about 10 km and topographic relief reduces the transmission rate. Larger colonies are more likely to become infected, but colony area does not affect the infectiousness of colonies. The results suggests that prairie dog movements do not drive the spread of plague through the landscape. Instead, prairie dogs are useful sentinels of plague epizootics. Simulations suggest that the model can be used for predicting long-term colony and plague dynamics as well as for identifying which colonies are most likely to become infected in a specific year.

INI 1
12:30 to 13:30 Lunch at Churchill College
14:00 to 15:15 Statistical inference for epidemics among a population of households
Chair: E Renshaw

This talk is concerned with a stochastic model for the spread of an SIR (susceptible $\to$ infective $\to$ removed) epidemic among a closed, finite population that contains several types of individual and is partitioned into households. A pseudolikelihood framework is presented for making statistical inference about the parameters governing such epidemics from final outcome data, when possibly only some of the households in the population are observed. The framework includes parameter estimation, hypothesis tests and goodness-of-fit. Asymptotic properties of the procedures are derived when the number of households in both the sample and the population are large, which correctly account for dependencies between households. The methodology is illustrated by applications to data on a \emph{variola minor} outbreak in Sao Paulo and to data on influenza outbreaks in Tecumseh, Michigan.

INI 1
15:15 to 15:45 Tea
15:45 to 17:00 Exact Bayesian inference and model selection for some infection models
Chair: E Renshaw

While much progress in the analysis of infectious disease data depends upon MCMC methodology, the simpler and more exact method of rejection sampling can sometimes be very useful. Using examples of influenza data from a population divided into households, this talk will illustrate the use of rejection sampling in model fitting; use of an initial sample to improve the efficiency of the algorithm; selection between competing models of differing dimensionality.

INI 1
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons