16,145 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
Local cohomology properties of direct summands
In this article, we prove that if is a homomorphism of Noetherian
rings that splits, then for every and ideal , \Ass_R
H^i_I(R) is finite when \Ass_S H^i_{IS}(S) is finite. In addition, if is
a Cohen-Macaulay ring that is finitely generated as an -module, such that
all the Bass numbers of , as an -module, are finite, then all
the Bass numbers of , as an -module, are finite. Moreover, we
show these results for a larger class a functors introduced by Lyubeznik. As a
consequence, we exhibit a Gorenstein -regular UFD of positive characteristic
that is not a direct summand, not even a pure subring, of any regular ring.Comment: 8 pages. References updated. Minor change
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