  The increasing size of data sets has lead to variable selection in regression
becoming increasingly important. Bayesian approaches are attractive since they
allow uncertainty about the choice of variables to be formally included in the
analysis. The application of fully Bayesian variable selection methods to large
data sets is computationally challenging. We describe an adaptive Markov chain
Monte Carlo approach called Individual Adaptation which adjusts a general
proposal to the data. We show that the algorithm is ergodic and discuss its use
within parallel tempering and sequential Monte Carlo approaches. We illustrate
the use of the method on two data sets including a gene expression analysis
with 22 577 variables.

Computation