Sequential Monte Carlo (SMC) methods are a class of techniques to sample
approximately from any sequence of probability distributions using a
combination of importance sampling and resampling steps. This paper is
concerned with the convergence analysis of a class of SMC methods where the
times at which resampling occurs are computed online using criteria such as the
effective sample size. This is a popular approach amongst practitioners but
there are very few convergence results available for these methods.

This report is a collection of comments on the Read Paper of Fearnhead and
Prangle (2011), to appear in the Journal of the Royal Statistical Society
Series B, along with a reply from the authors.

Let $\mathscr{P}(E)$ be the space of probability measures on a measurable
space $(E,\mathcal{E})$. In this paper we introduce a class of nonlinear Markov
chain Monte Carlo (MCMC) methods for simulating from a probability measure
$\pi\in\mathscr{P}(E)$. Nonlinear Markov kernels (see [Feynman--Kac Formulae:
Genealogical and Interacting Particle Systems with Applications (2004)
Springer]) $K:\mathscr{P}(E)\times E\rightarrow\mathscr{P}(E)$ can be
constructed to, in some sense, improve over MCMC methods.

We explore the use of generalized t priors on regression coefficients to help
understand the nature of association signal within "hit regions" of genome-wide
association studies. The particular generalized t distribution we adopt is a
Student distribution on the absolute value of its argument. For low degrees of
freedom we show that the generalized t exhibits 'sparsity-prior' properties
with some attractive features over other common forms of sparse priors and
includes the well known double-exponential distribution as the degrees of
freedom tends to infinity.

Switching state-space models (SSSM) are a very popular class of time series
models that have found many applications in statistics, econometrics and
advanced signal processing. Bayesian inference for these models typically
relies on Markov chain Monte Carlo (MCMC) techniques. However, even
sophisticated MCMC methods dedicated to SSSM can prove quite inefficient as
they update potentially strongly correlated discrete-valued latent variables
one-at-a-time (Carter and Kohn, 1996; Gerlach et al., 2000; Giordani and Kohn,
2008).

We present a new class of interacting Markov chain Monte Carlo algorithms for
solving numerically discrete-time measure-valued equations. The associated
stochastic processes belong to the class of self-interacting Markov chains. In
contrast to traditional Markov chains, their time evolutions depend on the
occupation measure of their past values. This general methodology allows us to
provide a natural way to sample from a sequence of target probability measures
of increasing complexity.

This paper presents a new approach for channel tracking and parameter
estimation in cooperative wireless relay networks. We consider a system with
multiple relay nodes operating under an amplify and forward relay function. We
develop a novel algorithm to efficiently solve the challenging problem of joint
channel tracking and parameters estimation of the Jakes' system model within a
mobile wireless relay network. This is based on a novel particle Markov chain
Monte Carlo (PMCMC) method.