This paper presents a flexible stochastic model developed for a class of
cooperative wireless relay networks, in which the relay processing
functionality is not known at the destination. The challenge is then to perform
online system identification in this wireless relay network. To address this
challenging problem we develop a novel class of statistical models and a
computationally efficient algorithm that can be performed in real time
processing, to undertake system identification for each relay channel in the
presence of partial Channel State Information (CSI).

Approximate Bayesian computation (ABC) is a popular technique for
approximating likelihoods and is often used in parameter estimation when the
likelihood functions are analytically intractable. Although the use of ABC is
widespread in many fields, there has been little investigation of the
theoretical properties of the resulting estimators. In this paper we give a
theoretical analysis of the asymptotic properties of ABC based maximum
likelihood parameter estimation for hidden Markov models.

This technical report is the union of two contributions to the discussion of
the Read Paper "Riemann manifold Langevin and Hamiltonian Monte Carlo methods"
by B. Calderhead and M. Girolami, presented in front of the Royal Statistical
Society on October 13th 2010 and to appear in the Journal of the Royal
Statistical Society Series B. The first comment establishes a parallel and
possible interactions with Adaptive Monte Carlo methods.

We consider a statistical model for pairs of traded assets, based on a
Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR
models to incorporate estimation of model parameters in the presence of price
series level shifts which are not accurately modeled in the standard Gaussian
error correction model (ECM) framework. This involves developing a novel matrix
variate Bayesian CVAR mixture model comprised of Gaussian errors intra-day and
Alpha-stable errors inter-day in the ECM framework.

This paper deals with the challenging problem of spectrum sensing in
cognitive radio. We consider a stochastic system model where the the Primary
User (PU) transmits a periodic signal over fading channels. The effect of
frequency offsets due to oscillator mismatch, and Doppler offset is studied. We
show that for this case the Likelihood Ratio Test (LRT) cannot be evaluated
poitnwise. We present a novel approach to approximate the marginilisation of
the frequency offset using a single point estimate.

The intention of this paper is to estimate a Bayesian distribution-free chain
ladder (DFCL) model using approximate Bayesian computation (ABC) methodology.
We demonstrate how to estimate quantities of interest in claims reserving and
compare the estimates to those obtained from classical and credibility
approaches. In this context, a novel numerical procedure utilising Markov chain
Monte Carlo (MCMC), ABC and a Bayesian bootstrap procedure was developed in a
truly distribution-free setting.