  Hidden Markov models (HMMs) are general purpose models for time-series data
widely used across the sciences because of their flexibility and elegance.
However fitting HMMs can often be computationally demanding and time consuming,
particularly when the the number of hidden states is large or the Markov chain
itself is long. Here we introduce a new Graphical Processing Unit (GPU) based
algorithm designed to fit long chain HMMs, applying our approach to an HMM for
nonvolcanic tremor events developed by Wang et al.(2018). Even on a modest GPU,
our implementation resulted in a 1000-fold increase in speed over the standard
single processor algorithm, allowing a full Bayesian inference of uncertainty
related to model parameters. Similar improvements would be expected for HMM
models given large number of observations and moderate state spaces (<80 states
with current hardware). We discuss the model, general GPU architecture and
algorithms and report performance of the method on a tremor dataset from the
Shikoku region, Japan.
