Many statistical applications use models that incorporate latent variables. For example, random effect panel data models, use latent variables to account for dependence between observations. State space models whose latent variables follow a Markov process, are used in economics, finance, and engineering.
Gunawan, D., Carter C., Fiebig D. G., & Kohn R.
(2017). Efficient Bayesian Estimation for Flexible Panel Models for Multivariate Outcomes: Impact of Life events on mental health and excessive alcohol consumption.