We introduce an estimate for the likelihood of hidden Markov models (HMMs) using sequential Monte Carlo (SMC) approximations of the generalized two-filter smoothing decomposition (Briers et al., 2010). This estimate is unbiased and a central limit theorem (CLT) is established. The new estimate...

The theory of general state-space Markov chains can be strongly related to the case of discrete state-space by use of the notion of small sets and associated minorization conditions. The general theory shows that small sets exist for all Markov chains on state-spaces with countably generated...

A number of recent emerging applications call for studying data streams, potentially infinite flows of information updated in real-time. When multiple co-evolving data streams are observed, an important task is to determine how these streams depend on each other, accounting for dynamic...

In this paper we develop a Bayesian procedure for estimating multivariate stochastic volatility (MSV) using state space models. A multiplicative model based on inverted Wishart and multivariate singular beta distributions is proposed for the evolution of the volatility, and a flexible sequential...

Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been proposed as a model for such spreads under the assumption that...

In this paper we have demonstrated a complete framework for the analysis of microarray time series data. The unique characteristics of microarry data lend themselves well to a functional data analysis approach and we have shown how this naturally extends to the inclusion of covariates such as...

This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon sequential Monte Carlo methods, investigating the problems of...

This article establishes sufficient conditions for a linear-in-time bound on the non-asymptotic variance for particle approximations of time-homogeneous Feynman–Kac formulae. These formulae appear in a wide variety of applications including option pricing in finance and risk sensitive control...

We present an extension of population-based Markov chain Monte Carlo to the transdimensional case. A major challenge is that of simulating from high- and transdimensional target measures. In such cases, Markov chain Monte Carlo methods may not adequately traverse the support of the target; the...