Sequentially Constrained Monte Carlo

Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behavior on the model, transformation of constraints into features on the parameter space may not be possible. Incorporation of constraints into the model often leads to truncations in the parameter space and multimodality which in turn cause difficulties in posterior sampling. A variant of the Sequential Monte Carlo algorithm is proposed by defining a sequence of densities through the imposition of the constraint. Particles generated from an unconstrained or mildly constrained distribution are filtered and moved through sampling and resampling steps to obtain a sample from the fully constrained target distribution. General and model specific forms of constraints enforcing strategies are defined. The Sequentially Constrained Monte Carlo algorithm is demonstrated on constraints defined by monotonicity of a function, densities constrained to low dimensional manifolds, adherence to a mechanistic differential equation model, and Approximate Bayesian Computation.