# Bayesian Poisson Regression and Tensor Train Decomposition Model for Learning Mortality Pattern Changes during COVID-19 Pandemic

**Authors:** Wei Zhang, Antonietta Mira, Ernst C. Wit  
**arXiv:** [2307.05649](https://arxiv.org/abs/2307.05649)  
**Date:** 2023-07-11  
**Summary page:** https://www.summarizepaper.com/en/paper/2307.05649v1/

## Key points

- Study focuses on understanding the wider impact of COVID-19 on causes of death in Italy
- Researchers develop a model called Bayesian Poisson Regression and Tensor Train Decomposition (BPRTTD)
- BPRTTD combines conventional Poisson regression with tensor train decomposition
- Model allows for analysis of cause-specific mortality rates and latent classes underlying demographic characteristics, temporal patterns, and causes of death
- Bayesian approach used with priors imposed on model parameters
- Posterior inference performed using efficient Metropolis-Hastings within Gibbs algorithm
- Approach validated through simulation studies
- BPRTTD model effectively identifies effects of interventions on cause-specific mortality rates
- Provides informative interpretations of relationship between COVID-19 and other causes of death
- Tensor decomposition component allows for deeper understanding of joint effects of age, gender, and causes of death on mortality rates
- Study offers valuable insights into impact of COVID-19 on different causes of death
- Provides framework for analyzing complex mortality data
- Findings can contribute to better understanding and managing public health interventions during pandemics.

## Summary

This study focuses on understanding the wider impact of COVID-19 on causes of death by analyzing Italian mortality data from January 2015 to December 2020. The researchers develop a model called Bayesian Poisson Regression and Tensor Train Decomposition (BPRTTD) to explore the lower dimensional structure of the high-dimensional data. The BPRTTD model combines conventional Poisson regression with tensor train decomposition, allowing for a comprehensive analysis of both cause-specific mortality rates and latent classes that underlie demographic characteristics, temporal patterns, and causes of death. The researchers use a Bayesian approach and impose priors on model parameters. They perform posterior inference using an efficient Metropolis-Hastings within Gibbs algorithm. To validate their approach, they conduct simulation studies. The results show that the BPRTTD model effectively identifies the effects of interventions on cause-specific mortality rates through the Poisson regression component. Additionally, it provides informative interpretations of the relationship between COVID-19 and other causes of death. The tensor decomposition component allows for a deeper understanding of the joint effects of age, gender, and causes of death on mortality rates. Overall, this study offers valuable insights into the impact of COVID-19 on different causes of death and provides a framework for analyzing complex mortality data. The findings can contribute to better understanding and managing public health interventions during pandemics.