Sure. It's hard to make this justice on a single comment, as there are lots of applications. Basically, any scenario with small or medium size datasets where you would use generative models. PPLs are just a way to encode generative models and get an inference engine compiled for you, instead of needing to write one. For example:

* Landing the Apollo on the Moon or tracking systems used by e.g. Sidewinder employ Kalman filters. See Example 24.4 (p. 510) [1].

* Predicting ride demand on heavy-tailed time series. Uber does this all the time [2].

* Estimating the effect of some policy on data with hierarchical structures (State > County > Individual observations) [3].

[1] http://web4.cs.ucl.ac.uk/staff/D.Barber/textbook/200620.pdf

[2] https://pyro.ai/examples/forecasting_i.html

[3] https://mc-stan.org/users/documentation/case-studies/radon_c...