  Motivated by a challenging problem in financial trading we are presented with
a mixture of regressions with variable selection problem. In this regard, one
is faced with data which possess outliers, skewness and, simultaneously, due to
the nature of financial trading, one would like to be able to construct
clusters with specific predictors that are fairly sparse. We develop a Bayesian
mixture of lasso regressions with $t-$errors to reflect these specific demands.
The resulting model is necessarily complex and to fit the model to real data,
we develop a state-of-the-art Particle Markov chain Monte Carlo (PMCMC)
algorithm based upon sequential Monte Carlo (SMC) methods. The model and
algorithm are investigated on both simulated and real data.
