We propose a new statistical method for constructing a genetic network from microarray gene expression data by using a Bayesian network. An essential point of Bayesian network construction is in the estimation of the conditional distribution of each random variable. We consider fitting nonparametric regression models with heterogeneous error variances to the microarray gene expression data to capture the nonlinear structures between genes. A problem still remains to be solved in selecting an optimal graph, which gives the best representation of the system among genes. We theoretically derive a new graph selection criterion from Bayes approach in general situations. The proposed method includes previous methods based on Bayesian networks. We demonstrate the effectiveness of the proposed method through the analysis of Saccharomyces cerevisiae gene expression data newly obtained by disrupting 100 genes. 1.

In this paper we adapt recently developed simulation-based sequential algorithms to two important stochastic volatility models. Firstly, we present a simulation-based algorithm for inference in stochastic volatility models with possible regime switching in which the regime state is governed by a first-order Markov process, the Markov switching stochastic volatility (MSSV) model. Particle filters are implemented to sequentially learn about states and parameters of the model. Two real financial time series are analized, the BOVESPA and the S&P500 indexes.

We study a Markov switching stochastic volatility model with heavy tail innovations in the observable process. Due to the economic interpretation of the hidden volatility regimes, these models have many financial applications like asset allocation, option pricing and risk management. The Markov switching process is able to capture clustering effects and jumps in volatility. Heavy tail innovations account for extreme variations in the observed process. Accurate modelling of the tails is important when estimating quantiles is the major interest like in risk management applications. Moreover we follow a Bayesian approach to filtering and estimation, focusing on recently developed simulation based filtering techniques, called Particle Filters. Simulation based filters are recursive techniques, which are useful when assuming non-linear and non-Gaussian latent variable models and when processing data sequentially. They allow to update parameter estimates and state filtering as new observations become available.

We study a Markov switching stochastic volatility model with heavy tail innovations in the observable process. Due to the economic interpretation of the hidden volatility regimes, these models have many financial applications like asset allocation, option pricing and risk management. The Markov switching process is able to capture clustering effects and jumps in volatility. Heavy tail innovations account for extreme variations in the observed process. Accurate modelling of the tails is important when estimating quantiles is the major interest like in risk management applications. Moreover we follow a Bayesian approach to filtering and estimation, focusing on recently developed simulation based filtering techniques, called Particle Filters. Simulation based filters are recursive techniques, which are useful when assuming non-linear and non-Gaussian latent variable models and when processing data sequentially. They allow to update parameter estimates and state filtering as new observations become available.

1.1 Generalized state space model The generalized state space model (GSSM) that we deal with in this study is de ned by a set of two equations system model xt = f(xt;1 � vt) � and (1.1)

The recent observed decline of business cycle variability suggests that broad macroeconomic risk may have fallen as well. This may in turn have some impact on equity risk premia. We investigate the latent structures in the volatilities of the business cycle and stock market valuations by estimating a Markov switching stochastic volatility model. We propose a sequential Monte Carlo technique for the Bayesian inference on both the unknown parameters and the latent variables of the hidden Markov model. Sequential importance sampling is used for filtering the latent variables and kernel estimator with a multiple-bandwidth is employed to reconstruct the parameter posterior distribution. We find that the switch to lower variability has occurred in both business cycle and stock market variables along similar patterns.

We consider the class of stationary nonlinear non Gaussian state space models with unknown static parameters. We propose original online stochastic gradient type algorithms to estimate these parameters. These algorithms rely on the simulation of arti cial observations. Contrary to all the methods we are aware of in this framework, optimal state estimation is not required by our methods and the proposed algorithms are computationally ecient. Their eciency is assessed through simulation.

Abstract — A novel probabilistic tracking system is presented, which includes a sequential particle sampler and a fragmentbased measurement model. Rather than generating particles independently in a generic particle filter, the correlation between particles is used to improve sampling efficiency, especially when the target moves in an unexpected and abrupt fashion. We propose to update the proposal distribution by dynamically incorporating the most recent measurements and generating particles sequentially, where the contextual confidence of the user on the measurement model is also involved. Besides, the matching template is divided into non-overlapping fragments, and by learning the background information only a subset of the most discriminative target regions are dynamically selected to measure each particle, where the model update is easily embedded to handle fast appearance changes. The two parts are dynamically fused together such that the system is able to capture abrupt motions and produce a better localization of the moving target in an efficient way. With the improved discriminative power, the new algorithm also succeeds in handling partial occlusions and clutter background. Experiments on both synthetic and real-world data verify the effectiveness of the new algorithm and demonstrate its superiority over existing methods. Index Terms — Haar, low-frame-rate videos, measurement confidence, occlusion, particle filter, proposal distribution, tracking.

Abstract not found