相关论文: On the Concentration of the Missing Mass
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ points from an arbitrary probability measure in $\mathbf{R}^d$ relates to the wet part of that measure. This extends classical results for…
When data are missing due to at most one cause from some time to next time, we can make sampling distribution inferences about the parameter of the data by modeling the missing-data mechanism correctly. Proverbially, in case its mechanism…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
For a given spatial distribution of the lenses and distribution of the transverse velocity of the lens relative to the line-of-sight, a probability distribution for the lens mass for a single observed event is derived. In addition, similar…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Our main result is a proof that for sufficiently small values of the rate parameter $\lambda$,…
Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow…
Missing data is a common issue in many biomedical studies. Under a paired design, some subjects may have missing values in either one or both of the conditions due to loss of follow-up, insufficient biological samples, etc. Such partially…
I review the data relating to the appearance of the missing mass problem at a particular acceleration scale. Rotation curves are examined in detail, with emphasis on the empirical connection between baryonic and total mass distributions.…
Due to instrumental limitations, the nature of which vary from case to case, spectroscopic galaxy redshift surveys usually do not collect redshifts for all galaxies in the population of potential targets. Especially problematic is the…
A manifestly covariant relativistic statistical mechanics of the system of $N$ indistinguishable events with motion in space-time parametrized by an invariant ``historical time'' $\tau $ is considered. The relativistic mass distribution for…
Negative probabilities arise primarily in physics, statistical quantum mechanics and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link…
In many real-world applications, it is common that a proportion of the data may be missing or only partially observed. We develop a novel two-sample testing method based on the Maximum Mean Discrepancy (MMD) which accounts for missing data…
A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of…
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the…
In the context of tomographic cosmic shear surveys, a theoretical model for the one-point statistics of the aperture mass (Map) is developed. This formalism is based on the application of the large deviation principle to the projected…
We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…
Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied…
Sensitivity analysis is popular in dealing with missing data problems particularly for non-ignorable missingness. It analyses how sensitively the conclusions may depend on assumptions about missing data e.g. missing data mechanism (MDM). We…
In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of {available data} and prior information. When the distribution of random variables is {intractable}, Monte Carlo (MC)…
In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…