  We present the Causal Gaussian Process Convolution Model (CGPCM), a doubly
nonparametric model for causal, spectrally complex dynamical phenomena. The
CGPCM is a generative model in which white noise is passed through a causal,
nonparametric-window moving-average filter, a construction that we show to be
equivalent to a Gaussian process with a nonparametric kernel that is biased
towards causally-generated signals. We develop enhanced variational inference
and learning schemes for the CGPCM and its previous acausal variant, the GPCM
(Tobar et al., 2015b), that significantly improve statistical accuracy. These
modelling and inferential contributions are demonstrated on a range of
synthetic and real-world signals.
