Gaussian Process-based learning with new MCMC-based implementation of Wishart prior on correlation matrix

In probabilstic supervised learning of an input-output relationship - as a sample function of a Gaussian Process (GP) - priors are typically specified for the hyperparameters of the kernel that parametrises the covariance function of the GP, where the induced covariance matrix of the (resulting multivariate Normal) likelihood, governs the learning and prediction. When the sought function is highly multivariate, multiple lengthscale parameters must be learnt simultaneously, making inference difficult. We develop a ``self-assembled'' Wishart prior for the covariance matrix, while undertaking Bayesian inference on the kernel hyperparameters using MCMC. The construction uses a look-back windo...

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