# Efficient Bayesian estimation and use of cut posterior in semiparametric hidden Markov models

arXiv: https://arxiv.org/abs/2203.06081 · HTML: https://mlsanity.com/paper/2203.06081/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2022.

## Built on by (most cited first, 1 of 1)

- [Scalable Semi-Modular Inference with Variational Meta-Posteriors](https://mlsanity.com/paper/2204.00296/) (2022)

## Abstract (arXiv)

We consider the problem of estimation in Hidden Markov models with finite state space and nonparametric emission distributions. Efficient estimators for the transition matrix are exhibited, and a semiparametric Bernstein-von Mises result is deduced. Following from this, we propose a modular approach using the cut posterior to jointly estimate the transition matrix and the emission densities. We derive a general theorem on contraction rates for this approach. We then show how this result may be applied to obtain a contraction rate result for the emission densities in our setting; a key intermediate step is an inversion inequality relating L1 distance between the marginal densities to L1 distance between the emissions. Finally, a contraction result for the smoothing probabilities is shown, which avoids the common approach of sample splitting. Simulations are provided which demonstrate both the theory and the ease of its implementation.