The hierarchical Dirichlet process hidden Markov model (HDP-HMM) is a flexible, nonparametric model which allows state spaces of unknown size to be learned from data. We demonstrate some limitations of the original HDP-HMM formulation (Teh et al., 2006), and propose a sticky extension which allows more robust learning of smoothly varying dynamics. Using DP mixtures, this formulation also allows learning of more complex, multimodal emission distributions. We further develop a sampling algorithm that employs a truncated approximation of the DP to jointly resample the full state sequence, greatly improving mixing rates. Via extensive experiments with synthetic data and the NIST speaker diarization database, we demonstrate the advantages of our sticky extension, and the utility of the HDP-HMM in real-world applications. 1.

We show how to apply the efficient Bayesian changepoint detection techniques of Fearnhead in the multivariate setting. We model the joint density of vector-valued observations using undirected Gaussian graphical models, whose structure we estimate. We show how we can exactly compute the MAP segmentation, as well as how to draw perfect samples from the posterior over segmentations, simultaneously accounting for uncertainty about the number and location of changepoints, as well as uncertainty about the covariance structure. We illustrate the technique by applying it to financial data and to bee tracking data. 1.

Abstract. In this paper we present an initial analysis of job arrivals in a production data-intensive Grid and investigate several traffic models to characterize the interarrival time processes. Our analysis focuses on the heavy-tail behavior and autocorrelation structures, and the modeling is carried out at three different levels: Grid, Virtual Organization (VO), and region. A set of m-state Markov modulated Poisson processes (MMPP) is investigated, while Poisson processes and hyperexponential renewal processes are evaluated for comparison studies. We apply the transportation distance metric from dynamical systems theory to further characterize the differences between the data trace and the simulated time series, and estimate errors by bootstrapping. The experimental results show that MMPPs with a certain number of states are successful to a certain extent in simulating the job traffic at different levels, fitting both the interarrival time distribution and the autocorrelation function. However, MMPPs are not able to match the autocorrelations for certain VOs, in which strong deterministic semi-periodic patterns are observed. These patterns are further characterized using different representations. Future work is needed to model both deterministic and stochastic components in order to better capture the correlation structure in the series. 1

In this paper we develop a general simulation-based approach to filtering and sequential parameter learning. We begin with an algorithm for filtering in a general dynamic state space model and then extend this to incorporate sequential parameter learning. The key idea is to express the filtering distribution as a mixture of lag-smoothing distributions and to implement this sequentially. Our approach has a number of advantages over current methodologies. First, it allows for sequential parmeter learning where sequential importance sampling approaches have difficulties. Second

The infinite hidden Markov model is a nonparametric extension of the widely used hidden Markov model. Our paper introduces a new inference algorithm for the infinite Hidden Markov model called beam sampling. Beam sampling combines slice sampling, which limits the number of states considered at each time step to a finite number, with dynamic programming, which samples whole state trajectories efficiently. Our algorithm typically outperforms the Gibbs sampler and is more robust. We present applications of iHMM inference using the beam sampler on changepoint detection and text prediction problems. 1.

This chapter develops Markov Chain Monte Carlo (MCMC) methods for Bayesian inference in continuous-time asset pricing models. The Bayesian solution to the inference problem is the distribution of parameters and latent variables conditional on observed data, and MCMC methods provide a tool for exploring these high-dimensional, complex distributions. We first provide a description of the foundations and mechanics of MCMC algorithms. This includes a discussion of the Clifford-Hammersley theorem, the Gibbs sampler, the Metropolis-Hastings algorithm, and theoretical convergence properties of MCMC algorithms. We next provide a tutorial on building MCMC algorithms for a range of continuous-time asset pricing models. We include detailed examples for equity price models, option pricing models, term structure models, and regime-switching models. Finally, we discuss the issue of sequential Bayesian inference, both for parameters and state variables.

Network intrusion occurs when a criminal gains access to a customer's telephone, computer, bank, or other type of account. Detecting network intrusion is an important problem that has received little attention in the statistics literature. This article proposes a Markov modulated nonhomogeneous Poisson process (MMNHPP) to monitor transactions on a customer's account for deviations from the customer's established behavior patterns. An important benefit of the MMNHPP is its ability to model the posterior probability of a criminal presence as a function of time. The MMNHPP combines aspects of the Markov modulated Poisson process and the nonhomogeneous Poisson process to model point processes exhibiting both regular patterns and irregular bursts of activity. The need to accommodate both types of behavior is demonstrated using data from two telephone accounts. MMNHPP parameters are sampled from their posterior distribution given a set of observed event times using an MCMC algorithm. The alg...

We introduce a new probability distribution over a potentially infinite number of binary Markov chains which we call the Markov Indian buffet process. This process extends the IBP to allow temporal dependencies in the hidden variables. We use this stochastic process to build a nonparametric extension of the factorial hidden Markov model. After constructing an inference scheme which combines slice sampling and dynamic programming we demonstrate how the infinite factorial hidden Markov model can be used for blind source separation. 1

We consider analysis of complex stochastic models based upon partial information. MCMC and reversible jump MCMC are often the methods of choice for such problems, but in some situations they can be difficult to implement; and suffer from problems such as poor mixing, and the difficulty of diagnosing convergence. Here we review three alternatives to MCMC methods: importance sampling, the forward-backward algorithm, and sequential Monte Carlo (SMC). We discuss how to design good proposal densities for importance sampling, show some of the range of models for which the forward-backward algorithm can be applied, and show how resampling ideas from SMC can be used to improve the efficiency of the other two methods. We demonstrate these methods on a range of examples, including estimating the transition density of a diffusion and of a discrete-state continuous-time Markov chain; inferring structure in population genetics; and segmenting genetic divergence data.

This chapter considers the assessment and refinement of a dynamic stochastic process model of the cellular response to DNA damage. The proposed model is a complex nonlinear continuous time latent stochastic process. It is compared to time course data on the levels of two key proteins involved in this response, captured at the level of individual cells in a human cancer cell line. The primary goal of this study is to “calibrate ” the model by finding parameters of the model (kinetic rate constants) that are most consistent with the experimental data. Significant amounts of prior information are available for the model parameters. It is therefore most natural to consider a Bayesian analysis of the problem, using sophisticated MCMC methods to overcome the formidable computational challenges.