Related papers: Quantization for infinite affine transformations
A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
We consider the probability by which quantum phase measurements of a given precision can be done successfully. The least upper bound of this probability is derived and the associated optimal state vectors are determined. The probability…
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
In this paper, we present a formal quantification of epistemic uncertainty induced by numerical solutions of ordinary and partial differential equation models. Numerical solutions of differential equations contain inherent uncertainties due…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
Quantization is studied from a viewpoint of field extension. If the dynamical fields and their action have a periodicity, the space of wave functions should be algebraically extended `a la Galois, so that it may be consistent with the…
Quantile matching is a strictly monotone transformation that sends the observed response values $\{y_1, . . . , y_n\}$ to the quantiles of a given target distribution. A likelihood based criterion is developed for comparing one target…
We study the probability distribution of the number of zeros of multivariable polynomials with bounded degree over a finite field. We find the probability generating function for each set of bounded degree polynomials. In particular, in the…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
Often it is assumed that a quantum state or a phase-space distribution must be normalizable. Here it is shown that even if it is not normalizable, one may be able to extract normalized observational probabilities from it.
The probability distributions for charged particle numbers and their densities are derived in statistical ensembles with conservation laws. It is shown that if this limit is properly taken then the canonical and grand canonical ensembles…
For any discrete probability distributions with bounded entropy, we can generate exactly a random variate using only a finite expected number of perfect coin flips. A perfect coin flip is the outcome of an unbiased Bernoulli random…
The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Precisely, suppose that the partial sums of a sequence of free identically distributed, infinitesimal random variables converge in distribution…
The probability integral transform (PIT) of a continuous random variable $X$ with distribution function $F_X$ is a uniformly distributed random variable $U=F_X(X)$. We define the angular probability integral transform (APIT) as $\theta_U =…
In quantum theory, it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values, and that there is no joint measurement of them. They are called preparation uncertainty and…
We study, in various special cases, total distributions on the product of a finite collection of finite probability spaces and, in particular, the question of when the probability distribution of each factor space is determined by the total…
This paper deals with (finite or infinite) sequences of arbitrary independent events in some probability space. We find sharp lower bounds for the probability of a union of such events when the sum of their probabilities is given. The…
A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite…
Given a probability distribution P, what is the minimum amount of bits needed to store a value x sampled according to P, such that x can later be recovered (except with some small probability)? Or, what is the maximum amount of uniform…