Hidden Markov models (HMMs) and related models have become standard in statistics during the last 15--20 years, with applications in diverse areas like speech and other statistical signal processing, hydrology, financial statistics and econometrics, bioinformatics etc. Inference in HMMs is traditionally often carried out using the EM algorithm, but examples of Bayesian estimation, in general implemented through Markov chain Monte Carlo (MCMC) sampling are also frequent in the HMM literature. The purpose of this paper is to compare the EM and MCMC approaches in three cases of different complexity; the examples include model order selection, continuous-time HMMs and variants of HMMs in which the observed data depends on many hidden variables in an overlapping fashion. All these examples in some way or another originate from real-data applications. Neither EM nor MCMC analysis of HMMs is a black-box methodology without need for user-interaction, and we will illustrate some of the problems, like poor mixing and long computation times, one may expect to encounter.

Adaptive cluster sampling is useful for exploring populations of rare plant and animal species which cluster together because it allows sampling effort to be concentrated in areas where observed values are high. This allows more useful data to be collected with less effort than simpler sampling methods which ignore the population structure. In this paper, we take a model based approach in a Bayesian framework to make inference about the number of individuals in a sparse, clustered population. This approach allows us to use knowledge of the population to inform both the sampling design and inference, thereby making coherent use of the data in the analysis and resulting in improved population estimates. The methodology is compared to the design-based modified Horvitz-Thompson estimator through analysis of the examples presented in the defining paper of Thompson (1990)

In recent years there has been considerable activity in the development and application of Bayesian inferential methods for infectious disease data using stochastic epidemic models. Most of this activity has employed computationally intensive approaches such as Markov chain Monte Carlo methods. In contrast, here we address fundamental questions for Bayesian inference in the setting of the standard SIR (Susceptible-Infective-Removed) epidemic model via simple methods. Our main focus is on the basic reproduction number, a quantity of central importance in mathematical epidemic theory, whose value essentially dictates whether or not a large epidemic outbreak can occur. We specifically consider two SIR models routinely employed in the literature, namely the model with exponentially distributed infectious periods, and the model with fixed length infectious periods. It is assumed that an epidemic outbreak is observed through time. Given complete observation of the epidemic, we derive explicit expressions for the posterior densities of the model parameters and the basic reproduction number. For partial observation of the epidemic, when the entire infection process is unobserved, we derive conservative bounds for quantities such as the mean of the basic reproduction number and the probability that a major epidemic outbreak will occur. If the time at which the epidemic started is observed, then linear programming methods can be used to derive suitable bounds for the mean of the basic reproduction number and similar quantities. Numerical examples are used to illustrate the practical consequences of our findings. In addition, we also examine the implications of commonly-used prior distributions on the basic model parameters as regards inference for the basic reproduction number.

A new class of space-time models derived from standard dynamic factor models is proposed. The temporal dependence is modeled by latent factors while the spatial dependence is modeled by the factor loadings. Factor analytic arguments are used to help identify temporal components that summarize most of the spatial variation of a given region. The temporal evolution of the factors is described in a number of forms to account for different aspects of time variation such as trend and seasonality. The spatial dependence is incorporated into the factor loadings by a combination of deterministic and stochastic elements thus giving them more flexibility and generalizing previous approaches. The new structure implies nonseparable space-time variation to observables, despite its conditionally independent nature, while reducing the overall dimensionality, and hence complexity, of the problem. The number of factors is treated as another unknown parameter and fully Bayesian inference is performed via a reversible jump Markov Chain Monte Carlo algorithm. The new class of models is tested against one synthetic dataset and applied to pollution data obtained from the Clean Air Status and Trends Network (CASTNet). Our factor model exhibited better predictive performance when compared to benchmark models, while capturing important aspects of spatial and temporal behavior of the data.

Bayesian classification and regression with high-order interactions is largely infeasible because Markov chain Monte Carlo (MCMC) would need to be applied with a great many parameters, whose number increases rapidly with the order. In this paper we show how to make it feasible by effectively reducing the number of parameters, exploiting the fact that many interactions have the same values for all training cases. Our method uses a single "compressed" parameter to represent the sum of all parameters associated with a set of patterns that have the same value for all training cases. Using symmetric stable distributions as the priors of the original parameters, we can easily find the priors of these compressed parameters. We therefore need to deal only with a much smaller number of compressed parameters when training the model with MCMC. After training the model, we can split these compressed parameters into the original ones as needed to make predictions for test cases. We show in detail how to compress parameters for logistic sequence prediction models. Experiments on both simulated and real data demonstrate that a huge number of parameters can indeed be reduced by our compression method.

Intensive computational methods have been used by Earth scientists in a wide range of problems in data inversion and uncertainty quantification such as earthquake epicenter location and climate projections. To quantify the uncertainties resulting from a range of plausible model configurations it is necessary to estimate a multidimensional probability distribution. The computational cost of estimating these distributions for geoscience applications is impractical using traditional methods such as Metropolis/Gibbs algorithms as simulation costs limit the number of experiments that can be obtained reasonably. Several alternate sampling strategies have been proposed that could improve on the sampling efficiency including Multiple Very Fast Simulated Annealing (MVFSA) and Adaptive Metropolis algorithms. The performance of these proposed sampling strategies are evaluated with a surrogate climate model that is able to approximate the noise and response behavior of a realistic atmospheric general circulation model (AGCM). The surrogate model is fast enough that its evaluation can be embedded in these Monte Carlo algorithms. We show that adaptive methods can be superior to MVFSA to approximate the known posterior distribution with fewer forward evaluations. However the adaptive methods can also be limited by inadequate sample mixing. The Single Component and Delayed Rejection Adaptive Metropolis algorithms were found to resolve these limitations, although challenges remain to approximating multi-modal distributions. The results show that these advanced methods of statistical inference can provide practical solutions to the climate model calibration problem and challenges in quantifying climate projection uncertainties. The computational methods would also be useful to problems outside climate prediction, particularly those where sampling is limited by availability of computational resources.

The MAPK/ERK pathway is one of the major signal transduction systems which regulates the cellular growth control of all eukaryotes like the cell proliferation and the apoptosis. Because of its importance in cellular lifecycle, it has been studied intensively, resulting in a number of qualitative descriptions of this regulatory mechanism. In this study we describe the MAPK/ERK pathway as an explicit set of reactions by combining different sources. Our reaction set takes into account the localization and different binding sites of the molecules in the cell by implementing the multiple parametrization. Then we estimate the model parameters of the network in a Bayesian setting via MCMC and data augmentation schemes. In the estimation we apply the Euler approximation, which is the discretized version of the diffusion technique. Additionally in inference of such a realistic and complex system we consider all possible kinds of dependencies coming from distinct stages of updates. To test the inference method we use the simulated data generated by the Gillespie algorithm. From the analysis it is clear that the sampler mixes well and partially is able to identify the dynamics of the MAPK/ERK pathway.