Humans and other animals are frequently near-optimal in their ability to integrate noisy and ambiguous sensory data to form robust percepts---which are informed both by sensory evidence and by prior expectations about the structure of the environment. It is suggested that the brain does so using the statistical structure provided by an internal model of how latent, causal factors produce the observed patterns. In dynamic environments, such integration often takes the form of \emph{postdiction}, wherein later sensory evidence affects inferences about earlier percepts. As the brain must operate in current time, without the luxury of acausal propagation of information, how does such postdictive inference come about? Here, we propose a general framework for neural probabilistic inference in dynamic models based on the distributed distributional code (DDC) representation of uncertainty, naturally extending the underlying encoding to incorporate implicit probabilistic beliefs about both present and past. We show that, as in other uses of the DDC, an inferential model can be learnt efficiently using samples from an internal model of the world. Applied to stimuli used in the context of psychophysics experiments, the framework provides an online and plausible mechanism for inference, including postdictive effects.

This paper addresses the problem of biologically-plausible perceptual inference in dynamical environments. In particular, it considers situations in which informative sensory information arrives delayed with respect to the underlying state and thus require'postdiction' to update the inference of past states given new sensory observations. The authors extend a previously published method for inference in graphical models (DDC-HM) to temporally extended encoding functions and test their model in three situation cases where postdiction is relevant. Overall, I find this work valuable and interesting. It could, however, be more clearly presented and provide some relevant comparisons with alternative models.

Humans and other animals are frequently near-optimal in their ability to integrate noisy and ambiguous sensory data to form robust percepts---which are informed both by sensory evidence and by prior expectations about the structure of the environment. It is suggested that the brain does so using the statistical structure provided by an internal model of how latent, causal factors produce the observed patterns. In dynamic environments, such integration often takes the form of \emph{postdiction}, wherein later sensory evidence affects inferences about earlier percepts. As the brain must operate in current time, without the luxury of acausal propagation of information, how does such postdictive inference come about? Here, we propose a general framework for neural probabilistic inference in dynamic models based on the distributed distributional code (DDC) representation of uncertainty, naturally extending the underlying encoding to incorporate implicit probabilistic beliefs about both present and past.

Humans and other animals are frequently near-optimal in their ability to integrate noisy and ambiguous sensory data to form robust percepts---which are informed both by sensory evidence and by prior expectations about the structure of the environment. It is suggested that the brain does so using the statistical structure provided by an internal model of how latent, causal factors produce the observed patterns. In dynamic environments, such integration often takes the form of \emph{postdiction}, wherein later sensory evidence affects inferences about earlier percepts. As the brain must operate in current time, without the luxury of acausal propagation of information, how does such postdictive inference come about? Here, we propose a general framework for neural probabilistic inference in dynamic models based on the distributed distributional code (DDC) representation of uncertainty, naturally extending the underlying encoding to incorporate implicit probabilistic beliefs about both present and past.