Stochastic space-time models, non-trivial observation mechanisms, and practical inference
Many natural phenomena can be modelled hierarchically, with latent random fields taking the role of unknown quantities for which we may have some idea about smoothness properties and multiscale behaviour. The mechanisms generating observed data can have additional unknown properties, such as animal detection probabilities depending on the size of a group of dolphins, or temperature biases depending on the local terrain near a weather station. Combining these models and mechanisms often lead to non-Gaussian likelihoods or Bayesian posteriors, requiring careful thought to construct computationally efficient practical inference methods. I will discuss these issues in the context of some recent and ongoing work for spatially resolved animal abundance estimation and historical climate reconstruction.