# Ignorable and non-ignorable missing data in hidden Markov models

arXiv: https://arxiv.org/abs/2109.02770 · HTML: https://mlsanity.com/paper/2109.02770/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2021.

## Built on by (most cited first, 2 of 2)

- [Learning Hidden Markov Models When the Locations of Missing Observations are Unknown](https://mlsanity.com/paper/2203.06527/) (2022)
- [Fast Gibbs Sampling on Bayesian Hidden Markov Model with Missing Observations](https://mlsanity.com/paper/2601.01442/) (2026)

## Abstract (arXiv)

We consider missing data in the context of hidden Markov models with a focus on situations where data is missing not at random (MNAR) and missingness depends on the identity of the hidden states. In simulations, we show that including a submodel for state-dependent missingness reduces bias when data is MNAR and state-dependent, whilst not reducing accuracy when data is missing at random (MAR). When missingness depends on time but not the hidden states, a model which only allows for state-dependent missingness is biased, whilst a model that allows for both state- and time-dependent missingness is not. Overall, these results show that modelling missingness as state-dependent, and including other relevant covariates, is a useful strategy in applications of hidden Markov models to time-series with missing data. We conclude with an application of the state- and time-dependent MNAR hidden Markov model to a real dataset, involving severity of schizophrenic symptoms in a clinical trial.