Related papers: New Proofs of the Basel Problem using Stochastic P…
The decimal digits of $\pi$ are widely believed to behave like as statistically independent random variables taking the values $0, 1, 2, 3, 4, 5$, $6, 7, 8, 9$ with equal probabilities $1/10$. In this article, first, another similar…
In a given problem, the Bayesian statistical paradigm requires the specification of a prior distribution that quantifies relevant information about the unknowns of main interest external to the data. In cases where little such information…
Based on the generalized Boltzmann equation and the reverse function of the distribution function, we investigate the two-parameter generalized statistics and get an expression between the two parameters (k,r) and the physical quantities…
Throughout more than two millennia many formulas have been obtained, some of them beautiful, to calculate the number pi. Among them, we can find series, infinite products, expansions as continued fractions and expansions using radicals.…
Quantifying how distinguishable two stochastic processes are lies at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and…
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
When the data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require to find what measurand value is the most…
This paper deals with the problem of measurable lifting modification for stochastic processes in its most general form and with the 'product lifting problem'. Solutions to the positive are reduced to the existence of marginals with respect…
Causality and causal inference have emerged as core research areas at the interface of modern statistics and domains including biomedical sciences, social sciences, computer science, and beyond. The field's inherently interdisciplinary…
A fundamental problem of statistical data analysis, distribution density estimation by experimental data, is considered. A new method with optimal asymptotic behavior, the root density estimator, is developed. The method proposed may be…
This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior…
This paper considers the problem of making statistical inferences about a parameter when a narrow interval centred at a given value of the parameter is considered special, which is interpreted as meaning that there is a substantial degree…
Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence whose covariance function obeys a power law. In this paper, we further develop generalized Bernoulli processes, reveal their asymptotic behaviors,…
Statistical solutions have recently been introduced as a an alternative solution framework for hyperbolic systems of conservation laws. In this work we derive a novel a posteriori error estimate in the Wasserstein distance between…
Determining if two histograms are consistent, whether they have been drawn from the same underlying distribution or not, is a common problem in physics. Existing approaches are not only limited in power but also inapplicable to histograms…
It is known that Bernoulli scheme of independent trials with two outcomes is connected with the binomial coefficients. The aim of this paper is to indicate stochastic processes which are connected with the $q$-polynomial coefficients (in…
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…
We study the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show…
Given a sequence of $N$ positive real numbers $\{a_1,a_2,..., a_N \}$, the number partitioning problem consists of partitioning them into two sets such that the absolute value of the difference of the sums of $a_j$ over the two sets is…