  We propose the Gaussian-Linear Hidden Markov model (GLHMM), a generalisation
of different types of HMMs commonly used in neuroscience. In short, the GLHMM
is a general framework where linear regression is used to flexibly parameterise
the Gaussian state distribution, thereby accommodating a wide range of uses
-including unsupervised, encoding and decoding models. GLHMM is implemented as
a Python toolbox with an emphasis on statistical testing and out-of-sample
prediction -i.e. aimed at finding and characterising brain-behaviour
associations. The toolbox uses a stochastic variational inference approach,
enabling it to handle large data sets at reasonable computational time.
Overall, the approach can be applied to several data modalities, including
animal recordings or non-brain data, and applied over a broad range of
experimental paradigms. For demonstration, we show examples with fMRI,
electrocorticography, magnetoencephalo-graphy and pupillometry.
