Stability properties of some particle filters

Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded uniformly in time, and the nonasymptotic, relative variance associated with a particle approximation of the normalizing constant is bounded linearly in time. The conditions are demonstrated to hold for some hidden Markov models on noncompact state spaces. The particle stability results are obtained by proving $v$-norm multiplicative stability and exponential moment results for the underlying Feynman-Kac formulas.Comment: Published in at http://dx.doi.org/10.1214/12-AAP909 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Dimension-free Wasserstein contraction of nonlinear filters

For a class of partially observed diffusions, sufficient conditions are given for the map from initial condition of the signal to filtering distribution to be contractive with respect to Wasserstein distances, with rate which has no dependence on the dimension of the state-space and is stable under tensor products of the model. The main assumptions are that the signal has affine drift and constant diffusion coefficient, and that the likelihood functions are log-concave. Contraction estimates are obtained from an $h$-process representation of the transition probabilities of the signal reweighted so as to condition on the observations

Dr. Jekyll and Mr. Hyde: The Complicated Identity of the Brussels International Festival of Fantastic Films

The Brussels International Festival of Fantastic Films (BIFFF) is a genre festival specializing in thriller, horror, science fiction and fantasy films. Started in 1983, with an initial audience of 32,650 for a festival of 60 films, by its most recent run in April 2015, 64,400 tickets were sold for a showing of 108 films (BIFFF Presentation 4-5; “Festival 2015” 2015). The almost doubling in audience attendance over the course of the BIFFF’s 33 year run emphasizes the manner in which the festival’s identity has become oriented towards a specific and passionate audience. Interestingly, as the festival’s audience engagement has increased, so too has its international identity, creating a unique place for the Brussels International Festival of Fantastic Film in the global festival sphere. On a local level Brussels International Festival of Fantastic Film can be seen as a cult event, differentiated from major festivals through its film selection and fandom focus; however, the festival’s proliferation of prizes and international networking demonstrates that even a genre festival is subject to the logic of proliferation described in James English’s landmark work The Economy of Prestige

The relative electoral impact of central party co-ordination and size of party membership at constituency level

Over the past decade, clear evidence has been produced showing that effective constituency campaigning in British general elections can lead to better electoral performance. This evidence has challenged the received wisdom that only national campaigning is significant and that efforts at local level are meaningless rituals. Denver et al. have focused on the role of the national parties in strengthening local campaigns in target seats; Seyd and Whiteley, by contrast, have stressed the importance of local party membership. This article attempts to assess the relative electoral impact of national party co-ordination and constituency party membership and suggests that the impact of these two factors varies by party

The Use of Precision Farming Technologies in Crop Decision Making

Precision Farming Technologies are being used by an increasing number of farmers in eastern Australia. The adoption of these technologies has resulted in a change in some agronomic practices. This project examines how the technologies are being used. Global Positioning Systems are being employed most readily with significant economic benefit particularly in setting up controlled traffic systems and the banding application of chemicals and fertilisers. Awareness of the benefits of controlled traffic has increased the use of GPS. A secondary reason for high accuracy GPS is to give the farmers greater labour options due to the shortage of experienced machine operators. Yield monitors and maps are mainly used for zoning fields with farmers being cautious about their value until better tools for analysing variance become available. Variable rate technology is not being used in a systematic manner at the present time.Farm Management,

Exploiting locality in high-dimensional factorial hidden Markov models

We propose algorithms for approximate filtering and smoothing in high-dimensional factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is `dimension-free' in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.Comment: 30 pages, 50 pages of appendix, 16 figure

Twisted particle filters

We investigate sampling laws for particle algorithms and the influence of these laws on the efficiency of particle approximations of marginal likelihoods in hidden Markov models. Among a broad class of candidates we characterize the essentially unique family of particle system transition kernels which is optimal with respect to an asymptotic-in-time variance growth rate criterion. The sampling structure of the algorithm defined by these optimal transitions turns out to be only subtly different from standard algorithms and yet the fluctuation properties of the estimates it provides can be dramatically different. The structure of the optimal transition suggests a new class of algorithms, which we term "twisted" particle filters and which we validate with asymptotic analysis of a more traditional nature, in the regime where the number of particles tends to infinity.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1167 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Calculating principal eigen-functions of non-negative integral kernels: particle approximations and applications

Often in applications such as rare events estimation or optimal control it is required that one calculates the principal eigen-function and eigen-value of a non-negative integral kernel. Except in the finite-dimensional case, usually neither the principal eigen-function nor the eigen-value can be computed exactly. In this paper, we develop numerical approximations for these quantities. We show how a generic interacting particle algorithm can be used to deliver numerical approximations of the eigen-quantities and the associated so-called "twisted" Markov kernel as well as how these approximations are relevant to the aforementioned applications. In addition, we study a collection of random integral operators underlying the algorithm, address some of their mean and path-wise properties, and obtain $L_{r}$ error estimates. Finally, numerical examples are provided in the context of importance sampling for computing tail probabilities of Markov chains and computing value functions for a class of stochastic optimal control problems.Comment: 38 pages, 4 figures, 1 table; to appear in Mathematics of Operations Researc