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...

In this paper, it is demonstrated that an extension to the exponential power family allows for robustness characteristics for the normal location parameter problem, previously thought to be restricted to the Student-t and a subclass of the positive stable families.

We show that the cumulative distribution function corresponding to a kernel density estimator with optimal bandwidth lies outside any confidence interval, around the empirical distribution function, with probability tending to 1 as the sample size increases.

Let Ω be a space of densities with respect to some "σ"-finite measure "μ" and let <b>Π</b> be a prior distribution having support Ω with respect to some suitable topology. Conditional on "f", let <b>X</b>-super-<b>n</b> = ("X"₁&hairsp;,…, &hairsp;"X"_"n") be an independent and identically distributed sample of size <b>"n"</b>...

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. Crucially, no sieve or entropy measures are required and so rates do not depend on the rate of convergence...

This paper extends recent ideas for constructing classes of stationary autoregressive processes of order 1. A Gibbs sampler representation of such processes is extended in a straightforward way to introduce new processes. These maintain a linear expectation property which provides a simple...

An approach to constructing strictly stationary AR(1)-type models with arbitrary stationary distributions and a flexible dependence structure is introduced. Bayesian nonparametric predictive density functions, based on single observations, are used to construct the one-step ahead predictive...