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An Efficient and Portable Pseudo-Random Number Generator. .. .. .. .. .. .. .. 89--89 S. An alternative to this approach is offered by Bayesian inference, although it requires establishing a prior probability. [24] Rejecting the null hypothesis does not automatically prove the alternative hypothesis. Though not required, it is strongly encouraged that one of the faculty be from outside the Statistics Department. Divergence functions can induce other important structures/quantities, such as bi-orthogonal coordinates (namely expectation and natural parameters), parallel volume form (in modeling Bayesian priors), symplectic structure (for Hamiltonian dynamics as in HMC algorithm), and Kahler/para-Kahler structure that synthesizes the metric, the symplectic, and the complex structures on the manifold.

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