Related papers: On Probabilistic Proofs of Certain Binomial Identi…
Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
The likelihood function represents statistical evidence in the context of data and a probability model. Considerable theory has demonstrated that evidence strength for different parameter values can be interpreted from the ratio of…
Statistical distribution of the primes in an arithmetic progression is considered. The estimation of prime numbers is given and combinatorial methods are used to calculate the twin primes on the available interval. The distribution and…
We consider an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. two histograms are drawn from the same distribution). The…
In this work, we derive some novel properties of the bimodal normal distribution. Some of its mathematical properties are examined. We provide a formal proof for the bimodality and assess identifiability. We then discuss the maximum…
Eight combinatorial identities are listed and proved by counting paths in the one-dimensional random walk. Four of these identities are assumed to be new.
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
In this note, using the derangement polynomials and their umbral representation, we give another simple proof of an identity conjectured by Lacasse in the study of the PAC-Bayesian machine learning theory.
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
This paper considers a family of distributions constructed by a stochastic mixture of the order statistics of a sample of size two. Various properties of the proposed model are studied. We apply the model to extend the exponential and…
This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
In modern scientific research, small-scale studies with limited participants are increasingly common. However, interpreting individual outcomes can be challenging, making it standard practice to combine data across studies using random…
Switching identities have a long history in potential theory and stochastic analysis. In recent work of Cox and Wang, a switching identity was used to connect an optimal stopping problem and the Skorokhod embedding problem (SEP). Typically…
In this article, we discuss a probabilistic interpretation of McShane's identity as describing a finite measure on the space of embedded paths though a point.
In this paper we provide a probabilistic representation of Lagrange's identity which we use to obtain Papathanasiou-type variance expansions of arbitrary order. Our expansions lead to generalized sequences of weights which depend on an…
We investigate the problem of truth discovery based on opinions from multiple agents who may be unreliable or biased. We consider the case where agents' reliabilities or biases are correlated if they belong to the same community, which…
The sum of $n$ {non-independent} Bernoulli random variables could be modeled in several different ways. One of these is the Multiplicative Binomial Distribution (MBD), introduced by Altham (1978) and revised by Lovison (1998). In this work,…
This article presents new methodology for sample-based Bayesian inference when data are partitioned and communication between the parts is expensive, as arises by necessity in the context of "big data" or by choice in order to take…