Monte Carlo Approximations for General State-Space Models

Improved Monte Carlo Methods for State-Space Models

The recent availability of low cost powerful computational resources has led to the development of a plethora of Monte Carlo based inference mechanisms for use in complex statistical problems, many of which involve temporally evolving systems. Sequential Monte Carlo (SMC), which is based around Sequential Importance Sampling and Resampling, is a class of Monte Carlo algorithm that can be applie...

An Overview of Sequential Monte Carlo Methods for Parameter Estimation in General State-Space Models

Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. Sequential Monte Carlo (SMC) methods, also known as Particle Filters, are numerical techniques based on Importance Sampling for solving the optimal state estimation problem. The task of calibrating the state-space model is an important problem frequently faced by practitioners and the obse...

On the Monte Carlo Marginal MAP Estimator for General State Space Models

where xk is the (unobserved) state with initial density p(x0), yk is the measurement at time step k. wk and vk are the corresponding process and measurement noises. The dynamic estimation problem is concerned with estimating the unknown state xk given the set of measurements y1:n = y1, ..., yn. The classic solution is the posterior probability density function p(xk|y1:n) which reflects all know...

On Extended State-Space Constructions for Monte Carlo Methods

Exponential Models: Approximations for Probabilities

Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property ...