# Hierarchical Continuous Time Hidden Markov Model, with Application in Zero-Inflated Accelerometer Data

## TL;DR

This paper introduces a hierarchical continuous-time hidden Markov model tailored for high-dimensional, zero-inflated accelerometer data, enabling extraction of meaningful activity patterns to inform health-related decisions.

## Contribution

It presents a novel flexible model with an efficient estimation algorithm and bootstrap-based interval estimation for analyzing complex accelerometer data.

## Key findings

- Successfully applied to NHANES data sets
- Effectively captures activity patterns with zero-inflation
- Provides reliable interval estimates

## Abstract

Wearable devices including accelerometers are increasingly being used to collect high-frequency human activity data in situ. There is tremendous potential to use such data to inform medical decision making and public health policies. However, modeling such data is challenging as they are high-dimensional, heterogeneous, and subject to informative missingness, e.g., zero readings when the device is removed by the participant. We propose a flexible and extensible continuous-time hidden Markov model to extract meaningful activity patterns from human accelerometer data. To facilitate estimation with massive data we derive an efficient learning algorithm that exploits the hierarchical structure of the parameters indexing the proposed model. We also propose a bootstrap procedure for interval estimation. The proposed methods are illustrated using data from the 2003 - 2004 and 2005 - 2006 National Health and Nutrition Examination Survey.