Inference without observation-kernel densities

Develop methods for performing inference in causal state space models or non-causal state space models whose observation kernels do not possess densities, beyond the linear-Gaussian case.

Background

The paper formulates filtering and smoothing for non-causal state space models under the assumption that the observation kernels admit densities. The causal non-causal convolution autoregressive model, however, has an observation kernel without a density because its observation is the deterministic sum of the causal and non-causal latent components.

The authors state that, to their knowledge, inference is unavailable for state space models with observation kernels lacking densities except in the linear-Gaussian setting. This leaves unresolved the development of exact or generally applicable inference procedures for the broader class of non-Gaussian models, including the causal non-causal convolution autoregressive model.