  Spatio-temporal data are ubiquitous in the agricultural, ecological, and
environmental sciences, and their study is important for understanding and
predicting a wide variety of processes. One of the difficulties with modeling
spatial processes that change in time is the complexity of the dependence
structures that must describe how such a process varies, and the presence of
high-dimensional complex data sets and large prediction domains. It is
particularly challenging to specify parameterizations for nonlinear dynamic
spatio-temporal models (DSTMs) that are simultaneously useful scientifically
and efficient computationally. Statisticians have developed deep hierarchical
models that can accommodate process complexity as well as the uncertainties in
the predictions and inference. However, these models can be expensive and are
typically application specific. On the other hand, the machine learning
community has developed alternative "deep learning" approaches for nonlinear
spatio-temporal modeling. These models are flexible yet are typically not
implemented in a probabilistic framework. The two paradigms have many things in
common and suggest hybrid approaches that can benefit from elements of each
framework. This overview paper presents a brief introduction to the deep
hierarchical DSTM (DH-DSTM) framework, and deep models in machine learning,
culminating with the deep neural DSTM (DN-DSTM). Recent approaches that combine
elements from DH-DSTMs and echo state network DN-DSTMs are presented as
illustrations.
