  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 behaviour on the
model, transformation of constraints into features on the parameter space may
not be possible. Difficulties in sampling from the posterior distribution as a
result of incorporation of constraints into the model is a common challenge
leading to truncations in the parameter space and inefficient sampling
algorithms. We propose a variant of sequential Monte Carlo algorithm for
posterior sampling in presence of constraints 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 theoretically derived
model, and model feature matching.
