Charitable Hospitals’ Liability for Negligence: Abrogation of the Medical-Administrative Distinction

A characterization of the distribution of the multivariate quadratic form given by XAX′, where X is a p×n normally distributed matrix and A is an n×n symmetric real matrix, is presented. We show that the distribution of the quadratic form is the same as the distribution of a weighted sum of noncentralWishart distributed matrices. This is applied to derive the distribution of the sample covariance between the rows of X when the expectation is the same for every column and is estimated with the regular mean

Labeled Directed Acyclic Graphs: a generalization of context-specific independence in directed graphical models

We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such that unrestricted label sets determine which edges can be deleted from the underlying directed acyclic graph (DAG) for a given context. Several properties of these models are derived, including a generalization of the concept of Markov equivalence classes. Efficient Bayesian learning of LDAGs is enabled by introducing an LDAG-based factorization of the Dirichlet prior for the model parameters, such that the marginal likelihood can be calculated analytically. In addition, we develop a novel prior distribution for the model structures that can appropriately penalize a model for its labeling complexity. A non-reversible Markov chain Monte Carlo algorithm combined with a greedy hill climbing approach is used for illustrating the useful properties of LDAG models for both real and synthetic data sets.Comment: 26 pages, 17 figure

Learning Genetic Population Structures Using Minimization of Stochastic Complexity

Peer reviewe

ON THE JENSEN-SHANNON DIVERGENCE AND THE VARIATION DISTANCE FOR CATEGORICAL PROBABILITY DISTRIBUTIONS

We establish a decomposition of the Jensen-Shannon divergence into a linear combination of a scaled Jeffreys' divergence and a reversed Jensen-Shannon divergence. Upper and lower bounds for the Jensen-Shannon divergence are then found in terms of the squared (total) variation distance. The derivations rely upon the Pinsker inequality and the reverse Pinsker inequality. We use these bounds to prove the asymptotic equivalence of the maximum likelihood estimate and minimum Jensen-Shannon divergence estimate as well as the asymptotic consistency of the minimum Jensen-Shannon divergence estimate. These are key properties for likelihood-free simulator-based inference.Peer reviewe

ON THE JENSEN-SHANNON DIVERGENCE AND THE VARIATION DISTANCE FOR CATEGORICAL PROBABILITY DISTRIBUTIONS

We establish a decomposition of the Jensen-Shannon divergence into a linear combination of a scaled Jeffreys' divergence and a reversed Jensen-Shannon divergence. Upper and lower bounds for the Jensen-Shannon divergence are then found in terms of the squared (total) variation distance. The derivations rely upon the Pinsker inequality and the reverse Pinsker inequality. We use these bounds to prove the asymptotic equivalence of the maximum likelihood estimate and minimum Jensen-Shannon divergence estimate as well as the asymptotic consistency of the minimum Jensen-Shannon divergence estimate. These are key properties for likelihood-free simulator-based inference.Peer reviewe