Related papers: A Fuzzy Approach for Randomized Confidence Interva…
Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important…
A simple Bayesian approach to nonparametric regression is described using fuzzy sets and membership functions. Membership functions are interpreted as likelihood functions for the unknown regression function, so that with the help of a…
Given a reference lattice, we define fuzzy intervals to be the fuzzy sets such that their p-cuts are crisp closed intervals. We show that: given a complete reference lattice, the collection of its fuzzy intervals is a complete lattice.…
We consider inference post-model-selection in linear regression. In this setting, Berk et al.(2013) recently introduced a class of confidence sets, the so-called PoSI intervals, that cover a certain non-standard quantity of interest with a…
The Clopper-Pearson confidence interval has ever been documented as an exact approach in some statistics literature. More recently, such approach of interval estimation has been introduced to probabilistic control theory and has been…
Fiducial Inference, introduced by Fisher in the 1930s, has a long history, which at times aroused passionate disagreements. However, its application has been largely confined to relatively simple parametric problems. In this paper, we…
We propose modified frequentist definitions for the determination of confidence intervals for the case of Poisson statistics. We require that 1-\beta^{'} \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha^{'}. We show that this definition…
The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data…
The first part of this work considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of…
Aiming at the group decision - making problem with multi - objective attributes, this study proposes a group decision - making system that integrates fuzzy inference and Bayesian network. A fuzzy rule base is constructed by combining…
Classical frequentist approaches to inference for the lasso emphasize exact coverage for each feature, which requires debiasing and severs the connection between confidence intervals and the original lasso estimates. To address this, in…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
It is well-known that assumptions of monotonicity in size-bias couplings may be used to prove simple, yet powerful, Poisson approximation results. Here we show how these assumptions may be relaxed, establishing explicit Poisson…
We explore asymptotically optimal bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of the Shannon relative entropy and the Pearson $\chi^2$-distance. The results are based on proper non-uniform estimates for…
In practical situations, interval-valued fuzzy sets are frequently encountered. In this paper, firstly, we present shadowed sets for interpreting and understanding interval fuzzy sets. We also provide an analytic solution to computing the…
We consider interval estimation of the difference between two binomial proportions. Several methods of constructing such an interval are known. Unfortunately those confidence intervals have poor coverage probability: it is significantly…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…
Comparisons are carried out of the confidence intervals constructed with Neyman's frequentist method and with the \Delta L=1/2 likelihood method, using the example of low-statistics life time estimates.