5,355 research outputs found
Cruising The Simplex: Hamiltonian Monte Carlo and the Dirichlet Distribution
Due to its constrained support, the Dirichlet distribution is uniquely suited
to many applications. The constraints that make it powerful, however, can also
hinder practical implementations, particularly those utilizing Markov Chain
Monte Carlo (MCMC) techniques such as Hamiltonian Monte Carlo. I demonstrate a
series of transformations that reshape the canonical Dirichlet distribution
into a form much more amenable to MCMC algorithms.Comment: 5 pages, 0 figure
Nested Sampling with Constrained Hamiltonian Monte Carlo
Nested sampling is a powerful approach to Bayesian inference ultimately
limited by the computationally demanding task of sampling from a heavily
constrained probability distribution. An effective algorithm in its own right,
Hamiltonian Monte Carlo is readily adapted to efficiently sample from any
smooth, constrained distribution. Utilizing this constrained Hamiltonian Monte
Carlo, I introduce a general implementation of the nested sampling algorithm.Comment: 15 pages, 4 figure
When Standards Collide: How the Federal Death Penalty Fails the Supreme Court\u27s Eighth Amendment Evolving Standards of Decency Test When Applied to Puerto Rican Federal Capital Defendants
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