Data conditioned simulation and inference

With the increasing power of personal computers, computational intensive statistical methods such as approximate Bayesian computation (ABC) are becoming an attractive and viable proposition to analyse complex statistical problems. There are three main aspects to ABC: • Proposing parameters. • Simulation of the process. • Some acceptance or approximation criteria for assessing the simulation. Majority of the publications on ABC explores the parameter proposition and the acceptance criteria aspects. Our work focuses on the simulation aspect of the algorithm. Our research has led us to the development of Data Conditioned Simulation. The data conditioned simulation utilises a mixture of the importance sampling algorithm and data augmentation to steer simulations towards the observed data with a corresponding weight to take account of the steering. The consequence of the steering is that even though each simulation takes more time than the unconditioned simulation, fewer simulations are required to make reasonable inference. Without the steering in the simulation, the acceptance rate can be extremely small. We demonstrate the data conditioned simulation through the data conditioned approximate Bayesian Computation (dcABC) and the grouped independence Metropolis-Hastings (GIMH) algorithm. The methodology is demonstrated through three examples, a homogeneous mixing SIR epidemic model, a time inhomogeneous Markov chain model and the stochastic Ricker model. The implementation of the methodology is problem-specific and we demonstrate the benefits of our approach in all three examples