Parameter inference for stochastic kinetic models of bacterial gene regulation: a Bayesian approach to systems biology: a discussion

While very much impressed by the scope of the chimical reaction models handled by Professor Wilkinson, we will (presumably predictably!) focus on the simulation aspects of his paper. First, the solution proposed by the author to overcome the difficulties of handling the complex likelihood π(x|θ) reminds us of the auxiliary completion of Møller et al. (2006), who created (as well) an auxiliary duplicate of the data x and a pseudoposterior on the duplicate to overcome computing the normalising constant in π(x|θ). As pointed out in Cucala et al. (2009), the choice of the completion distribution in Møller et al. (2006) may be detrimental to the convergence of the algorithm and we wonder if the same happens to the likelihood-free algorithm of the author. Second, the dismissal of ABC (Approximate Bayesian computation, see, e.g., Grelaud et al., 2009) as being difficult to calibrate and to automatise is slightly unfair in that the summary statistics used in ABC are generaly suggested by the practitioners. Sequential ABC has been studied in Beaumont et al. (2009) as well, bringing a correction to Sisson et al. (2007) and building up a population Monte Carlo scheme for the approximation of π(θ,x|D). Third, when considering the sequential solution of Professor Wilkinson, we wonder about the approximation effects due to (a) the use of a kernel at each time t and (b) the lack of correction of the paths up to time t when given the new data