Simulated maximum likelihood for general stochastic volatility models: a change of variable approach

Maximum likelihood has proved to be a valuable tool for fitting the log-normal stochastic volatility model to financial returns time series. Using a sequential change of variable framework, we are able to cast more general stochastic volatility models into a form appropriate for importance samplers based on the Laplace approximation. We apply the methodology to two example models, showing that efficient importance samplers can be constructed even for highly non-Gaussian latent processes such as square-root diffusions.Change of Variable; Heston Model; Laplace Importance Sampler; Simulated Maximum Likelihood; Stochastic Volatility

Estimating the granularity coefficient of a Potts-Markov random field within an MCMC algorithm

This paper addresses the problem of estimating the Potts parameter B jointly with the unknown parameters of a Bayesian model within a Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because performing inference on B requires computing the intractable normalizing constant of the Potts model. In the proposed MCMC method the estimation of B is conducted using a likelihood-free Metropolis-Hastings algorithm. Experimental results obtained for synthetic data show that estimating B jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of B. On the other hand, assuming that the value of B is known can degrade estimation performance significantly if this value is incorrect. To illustrate the interest of this method, the proposed algorithm is successfully applied to real bidimensional SAR and tridimensional ultrasound images

An invitation to sequential Monte Carlo samplers

Sequential Monte Carlo samplers provide consistent approximations of sequences of probability distributions and of their normalizing constants, via particles obtained with a combination of importance weights and Markov transitions. This article presents this class of methods and a number of recent advances, with the goal of helping statisticians assess the applicability and usefulness of these methods for their purposes. Our presentation emphasizes the role of bridging distributions for computational and statistical purposes. Numerical experiments are provided on simple settings such as multivariate Normals, logistic regression and a basic susceptible-infected-recovered model, illustrating the impact of the dimension, the ability to perform inference sequentially and the estimation of normalizing constants.Comment: review article, 34 pages, 10 figure