相关论文: Guessing probability distributions from small samp…
This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
The entropy is a measure of uncertainty that plays a central role in information theory. When the distribution of the data is unknown, an estimate of the entropy needs be obtained from the data sample itself. We propose a semi-parametric…
This article presents the calculation of the entropy of a system with Zipfian distribution and shows that a communication system tends to present an exponent value close to one, but still greater than one, so that it might maximize entropy…
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
A fundamental problem in analysis of complex systems is getting a reliable estimate of entropy of their probability distributions over the state space. This is difficult because unsampled states can contribute substantially to the entropy,…
Supplement 1 to GUM (GUM-S1) recommends the use of maximum entropy principle (MaxEnt) in determining the probability distribution of a quantity having specified properties, e.g., specified central moments. When we only know the mean value…
We model the generation of words with independent unequal probabilities of occurrence of letters. We prove that the probability $p(r)$ of occurrence of words of rank $r$ has a power asymptotics. As distinct from the paper published earlier…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
In this paper, entropies, including measure-theoretic entropy and topological entropy, are considered for random $\mathbb{Z}^k$-actions which are generated by random compositions of the generators of $\mathbb{Z}^k$-actions. Applying Pesin's…
This paper deals with the problem of quantifying the approximation a probability measure by means of an empirical (in a wide sense) random probability measure, depending on the first n terms of a sequence of random elements. In Section 2,…
Sinner et al. (2016) recently introduced a five-parameter family of size distributions, coined Interpolating Family or IF distribution for short. In this complementary note, we take advantage of the tractability of the IF distribution to…
In this paper, we introduce a flexible and widely applicable nonparametric entropy-based testing procedure that can be used to assess the validity of simple hypotheses about a specific parametric population distribution. The testing…
Probability estimation by maximum entropy reconstruction of an initial relative frequency estimate from its projection onto a hypergraph model of the approximate conditional independence relations exhibited by it is investigated. The…
Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective…
Given samples from a distribution, how many new elements should we expect to find if we continue sampling this distribution? This is an important and actively studied problem, with many applications ranging from unseen species estimation to…
We consider random sub-graphs of a fixed graph $G=(V,E)$ with large minimum degree. We fix a positive integer $k$ and let $G_k$ be the random sub-graph where each $v\in V$ independently chooses $k$ random neighbors, making $kn$ edges in…
Permutation tests are widely used for statistical hypothesis testing when the sampling distribution of the test statistic under the null hypothesis is analytically intractable or unreliable due to finite sample sizes. One critical challenge…