Asymptotic Theory of Hypothesis Testing

Lie group collision variational integrator - bouncing cube/dice simulation - Example 5

PIMS Marsden Memorial Lecture by Melvin Leok at UNBC in March 2023

EM algorithm applied to Gaussian mixtures

Minimizing divergence between a model manifold and a data manifold

Boltzmann machine with hidden units

Gaussian mixture model as a system with hidden variables

Statistical models with hidden variables

Asymptotic Theory of Hypothesis Testing

Higher-order Asymptotic Theory of Estimation

First-order Asymptotic Theory of Estimation

Estimation in a Curved Exponential Family

Estimation in the Exponential Family

Estimation in the context of statistical inference

Canonical divergence in dually flat manifolds

Dually Flat Manifolds

Metric and Cubic Tensor Derived from Divergence or Convex Functions

Dual affine connections

Levi-Civita (Riemannian) connection

Holonomy (Round-the-world transport)

Flat manifolds

Parallel transport of a vector

Geodesics

Covariant derivatives using affine connections

Tensors