Andy Kitchen gives a short tutorial on Bayesian modelling with JAX and NumPyro (and ArviZ) using a continuous change point example Recorded from the Melbourne Machine Learning and AI Meetup, August 2020 event.
Thanks for posting the video, I have missed the talk unfortunately. I have two questions: 1) Is the notebook available? 2) Poisson is a single parameter (mean) distribution. The higher the mean, the higher the variance. Is it correct that this will lead to a bias towards higher mean for regions with a higher spread of data points (earlier years)?
Thanks for watching! 1) Just put it up here: github.com/andykitchen/numpyo-examples/blob/master/sigmoid-changepoint.ipynb 2) Yes, this is a very insightful observation. Higher variance would be evidence of a higher mean and should push the posterior higher; this is the correct inference only under the assumption of the Poisson observations. If this assumption was strongly violated, it would cause problems, e.g. if the mining disasters where overdispersed (one plausible mechanism would be if a small number of very dangerous mines were opening and then getting quickly shutdown) During posterior predictive checking one would look for residuals much larger than would be expected. If you did find overdispersion, you could use a gamma-poisson/negative-binomial observation model or add per year random effects to the model.
