Inference in spatial and spatio-temporal models can be challenging for a variety of reasons. For example, non-Gaussianity often leads to analytically intractable integrals; we may be in a ‘big’ data setting, whereby the number of observations renders traditional methods too computationally expensive; we may wish to make inferences over spatial supports that are different to those of our measurements; or, we may wish to use a statistical model whose likelihood function is either unavailable or computationally intractable. In this thesis, I develop several techniques that help to alleviate these challenges.
