A Flaming-Viot Process and Bayesian non Parametric

This paper provides a construction of a Fleming-Viot measure valued diffusion process, for which the transition function is known, by extending recent ideas of Gibbs sampler based Markov processes. In particular, we concentrate on the Chapman-Kolmogorov consistency conditions which allows a simple derivation of such a Fleming-Viot process, once a key, and apparently new combinatorial result for P´olya-urn sequences has been established.Chapman-Kolmogorov; Diffusion process; Dirichlet process; Polyaurn scheme; Population genetics.

A Fleming-Viot process and Bayesian nonparametrics

This paper provides a construction of a Fleming-Viot measure valued diffusion process, for which the transition function is known, by extending recent ideas of the Gibbs sampler based Markov processes. In particular, we concentrate on the Chapman-Kolmogorov consistency conditions which allows a simple derivation of such a Fleming-Viot process, once a key and apparently new combinatorial result for Polya-urn sequences has been establishe

Rates of convergence of estimates, Kolmogorov's entropy and the dimensionality reduction principle in regression

L1-optimal minimum distance estimators are provided for a projection pursuit regression type function with smooth functional components that are either additive or multiplicative, in the presence of or without interactions. The obtained rates of convergence of the estimate to the true parameter depend on Kolmogorov's entropy of the assumed model and confirm Stone's heuristic dimensionality reduction principle. Rates of convergence are also obtained for the error in estimating the derivatives of a regression type function

Random function prediction and Stein's identity

Let X=(X1,X2,...,Xn) be a size n sample of i.i.d. random variables, whose distribution belong to the one-parameter ([theta]) continuous exponential family. We examine prediction functions of the form [theta]mh(X),m[greater-or-equal, slanted]1, where h is a polynomial in X. A natural identity that first appeared in Stein (Stein, 1973) and has been widely exploited since, is discussed in relation to members of such a family. Mild regularity conditions are also introduced that imply the nonexistence of a uniformly minimum mean squared error predictor for these functions.Prediction Random function of a parameter Exponential family

Parameter estimation for random dynamical systems using slice sampling

We provide details on the full reconstruction of the dynamic equations from measured time series data, given the general class of the underlying physical process. Our results can be used by researchers in physical modelling and statistical mechanics interested in an efficient estimation of low dimensional models, incorporating dynamic as well as observational noise. Our approach is Bayesian, based on an auxiliary variables algorithm that is fast and accurate, and direct, in the sense that only uniform distributions need to be sampled. This method is simpler than other Bayesian approaches where one has to sample from non-standard-unknown distributions using MCMC methods. (c) 2007 Elsevier B.V. All rights reserved