bayesestdft

Estimating the Degrees of Freedom of the Student's t-Distribution under a Bayesian Framework

A Bayesian framework to estimate the Student's t-distribution's degrees of freedom is developed. Markov Chain Monte Carlo sampling routines are developed as in <doi:10.3390/axioms11090462> to sample from the posterior distribution of the degrees of freedom. A random walk Metropolis algorithm is used for sampling when Jeffrey's and Gamma priors are endowed upon the degrees of freedom. In addition, the Metropolis-adjusted Langevin algorithm for sampling is used under the Jeffrey's prior specification. The Log-normal prior over the degrees of freedom is posed as a viable choice with comparable performance in simulations and real-data application, against other prior choices, where an Elliptical Slice Sampler is used to sample from the concerned posterior.

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