  Causal inference in cue combination is to decide whether the cues have a
single cause or multiple causes. Although the Bayesian causal inference model
explains the problem of causal inference in cue combination successfully, how
causal inference in cue combination could be implemented by neural circuits, is
unclear. The existing method based on calculating log posterior ratio with
variable elimination has the problem of being unrealistic and task-specific. In
this paper, we take advantages of the special structure of the Bayesian causal
inference model and propose a hierarchical inference algorithm based on
importance sampling. A simple neural circuit is designed to implement the
proposed inference algorithm. Theoretical analyses and experimental results
demonstrate that our algorithm converges to the accurate value as the sample
size goes to infinite. Moreover, the neural circuit we design can be easily
generalized to implement inference for other problems, such as the
multi-stimuli cause inference and the same-different judgment.
