Likelihood ratios for diffusion processes with shifted mean values.

Sensitivity, specificity, predictive values, and likelihood ratios.

Inferences for Likelihood Ratios

Likelihood ratios are extensively used to evaluate the performances of diagnostic tests and to update prior odds of disease to posttest odds. Since few tests are truly 100% accurate, including many used as “gold standards,” it is important to be able to estimate likelihood ratios in cases where no such standard is available. In this paper, methods to calculate point and interval estimates for l...

The trouble with likelihood ratios.

ity scale for clinicians is symmetrically skewed in both directions. In primary care, elective surgery, and oncology, clinicians work at the extremes of the probability scale. The time has come to apply the Feynman-Tufte principle to clinical logic, to offer a visual representation of Bayesian logic. Earlier attempts with natural logarithmics do not allow a simple graphic. We teach a scale of l...

Monte Carlo maximum likelihood estimation for discretely observed diffusion processes

This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s. continuous estimators of the likelihood function for a family of diffusion models and its performance in numerical examples is computationally efficient. It uses a recently developed technique for the exact simulation of diffus...

Likelihood Based Statistics for Partially Observed Diffusion Processes

The purpose of this paper is to study some statistical problems : parameter estimation, binary detection , change detection (disorder problem), etc. for partially observed diiusion processes, using the likelihood approach. It is shown that the stochastic PDE related to the state estimation problem, provides also a way to compute the likelihood function/ratio. A recent result on consistency of t...