HSMR is calculated as a ratio of the actual number of deaths to the expected number of deaths among patients in acute care hospitals. An HSMR of 100 indicates there is no difference between the hospital’s mortality rate and the overall average rate. Therefore a rate greater than 100 means the hospital’s mortality rate is higher than the overall average and a rate lower than 100 means the hospit...

What are they? In human health it is generally the case that the more people studied, and the longer the surveillance of them, the greater the number of new occurrences of any specified condition there are likely to be. This is because of the increase in total time ‘at risk’ of having an event, that is, the increased persons-and-time of observation. A rate is an arithmetic way of quantifying th...

Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic subsets of the parameter space. We consider large sample asymptotics for the likelihood ratio test of such hypotheses in models that satisfy standard probabilistic regularity conditions. We show that the assumptions of Chernoff's theore...

Local ratio is a well-known paradigm for designing approximation algorithms for combinatorial optimization problems. At a very high level, a local-ratio algorithm first decomposes the input weight function w into a positive linear combination of simpler weight functions or models. Guided by this process, a solution S is constructed such that S is α-approximate with respect to each model used in...

A family of arc-transitive graphs is studied. The vertices of these graphs are ordered pairs of distinct points from a finite projective line, and adjacency is defined in terms of the cross ratio. A uniform description of the graphs is given, their automorphism groups are determined, the problem of isomorphism between graphs in the family is solved, some combinatorial properties are explored, a...

The dimension of delivered placentae mirrors the cumulative conception to parturition. Placental weight is the gross summary of fetal growth under the influence of many extrinsic and intrinsic factors. Hence, the present study evaluated the influence of gestation, sex of the newborn, and parity on feto singleton newborn from a teaching hospital of North Karnataka, India. Data was collected from...

Likelihood ratio tests are intuitively appealing. Nevertheless, a number of examples are known in which they perform very poorly. The present paper discusses a large class of situations in which this is the case, and analyzes just how intuition misleads us; it also presents an alternative approach which in these situations is optimal. 1. The popularity of likelihood ratio tests Faced with a new...

The covariate shift is a challenging problem in supervised learning that results from the discrepancy between the training and test distributions. An effective approach which recently drew a considerable attention in the research community is to reweight the training samples to minimize that discrepancy. In specific, many methods are based on developing Density-ratio (DR) estimation techniques ...

In this work, we introduce an information-theoretic based correction term to the likelihood ratio classification method for multiple classes. Under certain conditions, the term is sufficient for optimally correcting the difference between the true and estimated likelihood ratio, and we analyze this in the Gaussian case. We find that the new correction term significantly improves the classificat...