Related papers: On Missing Mass Variance
The Good-Turing (GT) estimator for the missing mass (i.e., total probability of missing symbols) in $n$ samples is the number of symbols that appeared exactly once divided by $n$. For i.i.d. samples, the bias and squared-error risk of the…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
The variance of the concentration in a sample can be estimated using knowledge of the particle masses, concentrations and the parameter for the dependent selection of particles. A number of variance estimators are constructed including a…
Randomness is a crucial resource for a broad range of important applications, such as Monte Carlo simulation and computation, generative artificial intelligence and cryptography. But what is randomness? A widely accepted definition has…
The estimation of missing input vector elements in real time processing applications requires a system that possesses the knowledge of certain characteristics such as correlations between variables, which are inherent in the input space.…
Missing data can lead to inefficiencies and biases in analyses, in particular when data are missing not at random (MNAR). It is thus vital to understand and correctly identify the missing data mechanism. Recovering missing values through a…
We explore in detail the physics potential of a measurement of the ttbar invariant mass distribution. First, we assess the accuracy of the best available predictions for this observable and find that in the low invariant mass region, the…
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…
Feature models are popular in machine learning and they have been recently used to solve many unsupervised learning problems. In these models every observation is endowed with a finite set of features, usually selected from an infinite…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
This paper provides further insight into the key concept of missing at random (MAR) in incomplete data analysis. Following the usual selection modelling approach we envisage two models with separable parameters: a model for the response of…
The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…
The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…
When are inferences (whether Direct-Likelihood, Bayesian, or Frequentist) obtained from partial data valid? This paper answers this question by offering a new asymptotic theory about inference with missing data that is more general than…
Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that…
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…
We consider an original problem that arises from the issue of security analysis of a power system and that we name optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and the…
Various strategies for active learning have been proposed in the machine learning literature. In uncertainty sampling, which is among the most popular approaches, the active learner sequentially queries the label of those instances for…
The traditional measurement theory interprets the variance as the dispersion of a measured value, which is actually contrary to a general mathematical concept that the variance of a constant is 0. This paper will fully demonstrate that the…