Pete Bunch

Improved Particle Approximations to the Joint Smoothing Distribution Using Markov Chain Monte Carlo

Particle filtering and smoothing algorithms approximate posterior state distributions with a set of samples drawn from those distributions. Conventionally, samples from the joint smoothing distribution are generated by sequentially resampling from the particle filter results. If the number of filtering particles is high, this process is limited by computational complexity. In addition, the support of the smoothing distribution is restricted to the values which appear in the filtering approximation. In this paper, a Metropolis-Hastings sampling procedure is used to improve the efficiency of the particle smoother, achieving comparable error performance but with a lower execution time. In addition, an algorithm for approximating the joint smoothing distribution without limited support is presented, which achieves simultaneous improvements in both execution time and error. These algorithms also provide a greater degree of flexibility over existing methods, allowing a trade-off between execution time and error, controlled by the length of the Markov chains.

Rao-Blackwellized particle smoothers for mixed linear/nonlinear state-space models

We consider the smoothing problem for a class of conditionally linear Gaussian state-space (CLGSS) models, referred to as mixed linear/nonlinear models. In contrast to the better studied hierarchical CLGSS models, these allow for an intricate cross dependence between the linear and the nonlinear parts of the state vector. We derive a Rao-Blackwellized particle smoother (RBPS) for this model class by exploiting its tractable substructure. The smoother is of the forward filtering/backward simulation type. A key feature of the proposed method is that, unlike existing RBPS for this model class, the linear part of the state vector is marginalized out in both the forward direction and in the backward direction.

Approximations of the Optimal Importance Density Using Gaussian Particle Flow Importance Sampling

ABSTRACT Recently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution, and a number of particle filters based on this principle have been proposed. Samples are drawn from the prior and then moved according to some dynamics over an interval of pseudo-time such that their final values are distributed according to the desired posterior. In practice, implementing a particle flow sampler requires multiple layers of approximation, with the result that the final samples do not in general have the correct posterior distribution. In this article we consider using an approximate Gaussian flow for sampling with a class of nonlinear Gaussian models. We use the particle flow within an importance sampler, correcting for the discrepancy between the target and actual densities with importance weights. We present a suitable numerical integration procedure for use with this flow and an accompanying step-size control algorithm. In a filtering context, we use the particle flow to sample from the optimal importance density, rather than the filtering density itself, avoiding the need to make analytical or numerical approximations of the predictive density. Simulations using particle flow importance sampling within a particle filter demonstrate significant improvement over standard approximations of the optimal importance density, and the algorithm falls within the standard sequential Monte Carlo framework.

A Backward-Simulation Based Rao-Blackwellized Particle Smoother for Conditionally Linear Gaussian Models

Abstract In this article, we develop a new Rao-Blackwellized Monte Carlo smoothing algorithm for conditionally linear Gaussian models. The algorithm is based on the forward-filtering backward-simulation Monte Carlo smoother concept and performs the backward simulation directly in the marginal space of the non-Gaussian state component while treating the linear part analytically. Unlike the previously proposed backward-simulation based Rao-Blackwellized smoothing approaches, it does not require sampling of the Gaussian state component and is also able to overcome certain normalization problems of two-filter smoother based approaches. The performance of the algorithm is illustrated in a simulated application.

Antarctic last interglacial isotope peak in response to sea ice retreat not ice-sheet collapse

Several studies have suggested that sea-level rise during the last interglacial implies retreat of the West Antarctic Ice Sheet (WAIS). The prevalent hypothesis is that the retreat coincided with the peak Antarctic temperature and stable water isotope values from 128,000 years ago (128 ka); very early in the last interglacial. Here, by analysing climate model simulations of last interglacial WAIS loss featuring water isotopes, we show instead that the isotopic response to WAIS loss is in opposition to the isotopic evidence at 128 ka. Instead, a reduction in winter sea ice area of 65±7% fully explains the 128 ka ice core evidence. Our finding of a marked retreat of the sea ice at 128 ka demonstrates the sensitivity of Antarctic sea ice extent to climate warming.

Particle filtering with progressive Gaussian approximations to the optimal importance density

A new algorithm, the progressive proposal particle filter, is introduced. The performance of a standard particle filter is highly dependent on the choice of importance density used to propagate the particles through time. The conditional posterior state density is the optimal choice, but this can rarely be calculated analytically or sampled from exactly. Practical particle filters rely on forming approximations to the optimal importance density, frequently using Gaussian distributions, but these are not always effective in highly nonlinear models. The progressive proposal method introduces the effect of each observation gradually and incrementally modifies the particle states so as to achieve an improved approximation to the optimal importance distribution.

Particle Smoothing Algorithms for Variable Rate Models

Standard state-space methods assume that the latent state evolves uniformly over time, and can be modeled with a discrete-time process synchronous with the observations. This may be a poor representation of some systems in which the state evolution displays discontinuities in its behavior. For such cases, a variable rate model may be more appropriate; the system dynamics are conditioned on a set of random changepoints which constitute a marked point process. In this paper, new particle smoothing algorithms are presented for use with conditionally linear-Gaussian and conditionally deterministic dynamics. These are demonstrated on problems in financial modelling and target tracking. Results indicate that the smoothing approximations provide more accurate and more diverse representations of the state posterior distributions.

Rao-Blackwellized Particle Smoothers for Conditionally Linear Gaussian Models

Sequential Monte Carlo (SMC) methods, such as the particle filter, are by now one of the standard computational techniques for addressing the filtering problem in general state-space models. However, many applications require post-processing of data offline. In such scenarios the smoothing problem-in which all the available data is used to compute state estimates-is of central interest. We consider the smoothing problem for a class of conditionally linear Gaussian models. We present a forward-backward-type Rao-Blackwellized particle smoother (RBPS) that is able to exploit the tractable substructure present in these models. Akin to the well known Rao-Blackwellized particle filter, the proposed RBPS marginalizes out a conditionally tractable subset of state variables, effectively making use of SMC only for the “intractable part” of the model. Compared to existing RBPS, two key features of the proposed method are: 1) it does not require structural approximations of the model, and 2) the aforementioned marginalization is done both in the forward direction and in the backward direction.

Probabilistic Intentionality Prediction for Target Selection Based on Partial Cursor Tracks

Pointing tasks, for example to select an object in an interface, constitute a significant part of human-computer interactions. This motivated several studies into techniques that facilitate the pointing task and improve its accuracy. In this paper, we introduce a number of intentionality prediction algorithms to determine the intended target a priori from partial cursor tracks. They yield notable reductions in the pointing time, aid effective selection assistance routines and enhance the overall pointing accuracy. A number of benchmark prediction models are also restated within a statistical framework and their probabilistic interpretation is utilised to calculate their corresponding outcomes. The relative performance of all considered predictors is assessed for point-click task data sets pertaining to both able-bodied and impaired users. Bayesian adaptive filtering is deployed to smooth highly perturbed mouse cursor tracks that are typically produced by motor impaired users undertaking a pointing task.

Transcription of musical audio using Poisson point processes and sequential MCMC

In this paper models and algorithms are presented for transcription of pitch and timings in polyphonic music extracts. The data are decomposed framewise into the frequency domain, where a Poisson point process model is used to write a polyphonic pitch likelihood function. From here Bayesian priors are incorporated both over time (to link successive frames) and also within frames (to model the number of notes present, their pitches, the number of harmonics for each note, and inharmonicity parameters for each note). Inference in the model is carried out via Bayesian filtering using a powerful Sequential Markov chain Monte Carlo (MCMC) algorithm that is an MCMC extension of particle filtering. Initial results with guitar music, both laboratory test data and commercial extracts, show promising levels of performance.