Annual Report 2008.pdf - SAMSI

Many problems and existing simulation methods can be formulated for analysis via SMC:
sequential and batch Bayesian inference, computation of p-values, inference in contingency
tables, rare event probabilities, optimization, counting the number of objects with a certain
property for combinatorial structures, computation of eigenvalues and eigenmeasures of positive
operators, PDE's admitting a Feynman-Kac representation and so on. This research area is poised
to explode, as witnessed by this major growth in adoption of the methods.
The SAMSI SMC program will:
• Address methodological and theoretical problems of SMC methods, including
synthesis of concepts underlying variants of SMC that have proven apparently successful
across multiple fields, and the development of methodological and theoretical advances.
• Develop the methodological research -- with broad opportunities for test-bed
examples, methods evaluation and refinement of generic approaches -- in the contexts of
a number of important applied problems (e.g. data assimilation, inference for large state
spaces, finance, tracking, continuous time models).
The program will be an opportunity for exchange between communities; it will help to shape the
future of stochastic computation and sequential methods, will involve statisticians, computer
scientists and engineers as core participants as well as others working collaboratively in a range
of applied fields.
2.4 Research Foci
2.4.1 Continuous time modeling and parameter estimation
Modeling and parameter estimation for continuous time stochastic processes might
include exact simulation methods for inference in partially observed diffusions, jump diffusions
and Levy processes. Both batch-based and on-line strategies will be studied, as will both
parameter estimation and state estimation. This group will have strong links to the Decision
Theory and Finance Group, the Tracking Group and the Theory group, as continuous time
models underly many of these applications, as well as applications in other areas including
emerging studies in systems biology.
2.4.2 Tracking and large-scale dynamical systems
There is much interest in tracking and inference for large groups of objects, with
applications in medical imaging, dynamic object tracking in robotic control in industrial,
commercial and military areas, and tracking in media applications. Particular focus areas might
be drawn from representations of many interacting objects using random fields, graphical
models, and automated inference about group structures, types of interaction, intentionalities,
etc.. Methodology of interest utilises combinations of techniques such as particle filtering,
MCMC, SMC samplers. It also includes dynamic point process methods such as the Probability
Hypothesis Density Filtering which is an example of the interest in cross-over research between
core statistical methodology and applied probability.
2.4.3 Decision making, econometrics and finance
SMC methods are under-explored and appear to have a gret deal of potential in problems
of numerical solution of decision problems under uncertainty. Some areas might include: (i)
applications in policy-oriented macro-economic modelling; and (ii) state and parameter