In this paper, an improved nonlinear Gaussian mixture probability hypothesis density (GM-PHD) filter is proposed to address bearings-only measurements in multi-target tracking. The proposed method, called the Gaussian mixture measurements-probability hypothesis density (GMM-PHD) filter, not only approximates the posterior intensity using a Gaussian mixture, but also models the likelihood functi...

i=1 each of which is presumed to be randomly drawn independently from some probability distribution with density p(x). The goal is to test the hypothesis that p(x) = p0(x), where p0(x) is some specified reference probability density. Ideally, the test should have power against all alternatives. That is as the sample size N becomes arbitrarily large, N → ∞, the test will reject the hypothesis fo...

In economies with nonconvexities consumers can increase their expected utility by consuming lotteries. Lotteries are probability distributions over bundles in the consumption set. Standard revealed preference logic can be applied to choices in lottery space, however the implications are not readily interpretable. In this paper, we formulate the law of demand for lottery economies in terms of co...

Kernel density estimation (KDE) is a popular nonparametric density estimation method. We (1) derive finite-sample high-probability density estimation bounds for multivariate KDE under mild density assumptions which hold uniformly in x ∈ R and bandwidth matrices. We apply these results to (2) mode, (3) density level set, and (4) class probability estimation and attain optimal rates up to logarit...

In crossing his pea plants, Mendel obtained genetic ratios that were in excellent agreement with his model of factor segregation. Other workers soon obtained comparable results. The favorable agreement of data with theory reflected a basic property of Mendel’s model: if Mendelian factors are considered independent, then the probability of observing any one factor segregating among progeny must ...

In this paper, the reconcilability between the P-value and the posterior probability in testing a point null hypothesis against the one-sided hypothesis is considered. Two essential families, non regular and exponential family of distributions, are studied. It was shown in a non regular family of distributions; in some cases, it is possible to find a prior distribution function under which P-va...