We consider estimation of scalar functions that determine the dynamics of diffusion processes. It has been recently shown that nonparametric maximum likelihood estimation is ill-posed in this context. We adopt a probabilistic approach to regularize the problem by the adoption of a prior...

We consider Markov chains {[Gamma]n} with transitions of the form [Gamma]n=f(Xn,Yn)[Gamma]n-1+g(Xn,Yn), where {Xn} and {Yn} are two independent i.i.d. sequences. For two copies {[Gamma]n} and {[Gamma]n'} of such a chain, it is well known that provided E[log(f(Xn,Yn))]<0, where => is weak convergence. In...</0,>

A Bayesian perspective is taken to quantify the amount of information learned from observing a stochastic process, Xt, on the interval [0, T] which satisfies the stochastic differential equation, dXt = S([theta], t, Xt)dt+[sigma](t, Xt)dBt. Information is defined as a change in expected utility...

It is possible to implement importance sampling, and particle filter algorithms, where the importance sampling weight is random. Such random-weight algorithms have been shown to be efficient for inference for a class of diffusion models, as they enable inference without any (time discretization)...

We discuss a formal mathematical framework for certain coupling constructions via minorisation conditions, which are often used to prove bounds on convergence to stationarity of stochastic processes and Markov chain Monte Carlo algorithms.

Inference for Dirichlet process hierarchical models is typically performed using Markov chain Monte Carlo methods, which can be roughly categorized into marginal and conditional methods. The former integrate out analytically the infinite-dimensional component of the hierarchical model and sample...

A major gap exists between the conceptual suggestion of how much a nation should invest in science, innovation, and technology, and the practical implementation of what is done. We identify 4 critical challenges that must be address in order to develop an environment conducive to collaboration...