We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.

/pdf/monte-carlo-statistical-methods-33su1g800x.pdf

Monte Carlo Statistical Methods

The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT.

/pdf/unscented-filtering-and-nonlinear-estimation-44xbx5prtw.pdf

Unscented filtering and nonlinear estimation

Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference in econometric models are developed. Conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of Monte Carlo replications increases, and the numerical accuracy of this approximation may be assessed reliably, are set forth. Methods for the analytical verification of these conditions are discussed

Bayesian Inference in Econometric Models Using Monte Carlo Integration

This paper surveys the most important developments in multivariate ARCH-type modelling. It reviews the model specifications, the inference methods, and the main areas of application of these models in financial econometrics.

Multivariate GARCH Models: A Survey

We present a stable control strategy for groups of vehicles to move and reconfigure cooperatively in response to a sensed, distributed environment. Each vehicle in the group serves as a mobile sensor and the vehicle network as a mobile and reconfigurable sensor array. Our control strategy decouples, in part, the cooperative management of the network formation from the network maneuvers. The underlying coordination framework uses virtual bodies and artificial potentials. We focus on gradient climbing missions in which the mobile sensor network seeks out local maxima or minima in the environmental field. The network can adapt its configuration in response to the sensed environment in order to optimize its gradient climb.

Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment

Adaptive Polar Sampling is proposed as an algorithm where random drawings are directly generated from the target function (posterior) in
all-but-one directions of the parameter space. The method is based on the mixed integration technique of Van Dijk, Kloek & Boender (1985) but
extends this one by replacing the one-dimensional quadrature step by Monte Carlo simulation from this one-dimensional distribution function.
The method is particularly suited for the analysis of ill-behaved surfaces. An illustrative example shows the feasibility of the
algorithm.

Adaptive polar sampling: a new MC technique for the analysis of ill behaved surfaces

Some 20 years ago, J. Dreze (1962) opened a new prospect for the statistical treatment of the « simultaneous equation model » in econometrics (SEM). Indeed, he advocated the use of Bayesian methods for the analysis of such models. In particular, he pointed out the flexibility of this approach as it allows to take account not only of the a priori information provided by economic theory or observation, but more fundamentally, of the imprecise nature of this kind of information. Ever since, it has been clear that the Bayesian approach of the SEM would be rather difficult to implement. The main problems one can identify are 1. the representation of a priori information by a prior density function which should be easily interpretable and at the same time flexible enough; 2. the numerical treatment (i.e. integration) of the posterior density so as to obtain moments and marginal densities of parameters, whether they be parameters of the structural form, of the reduced form, or functions thereof.

Posterior moments of elasticities between real wages and unemployment in Belgium : an application of Bayesian inference by Monte Carlo integration

textIn this short paper we summarize the computational steps of Adaptive Radial-Based Direction Sampling (ARDS), which can be used for Bayesian analysis of ill behaved target densities. We consider one simulation experiment in order to illustrate the good performance of ARDS relative to the independence chain MH algorithm and importance sampling.

Luc Bauwens

Papers

Adaptive polar sampling: a new MC technique for the analysis of ill behaved surfaces

Posterior moments of elasticities between real wages and unemployment in Belgium : an application of Bayesian inference by Monte Carlo integration

Explaining Adaptive Radial-Based Direction Sampling