Related papers: Estimating Bernoulli trial probability from a smal…

This paper presents a theoretical analysis of sample selection bias correction. The sample bias correction technique commonly used in machine learning consists of reweighting the cost of an error on each training point of a biased sample to…

The Birnbaum-Saunders regression model is commonly used in reliability studies. We address the issue of performing inference in this class of models when the number of observations is small. We show that the likelihood ratio test tends to…

Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…

The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the…

Contemporary statistical publications rely on simulation to evaluate performance of new methods and compare them with established methods. In the context of meta-analysis of log-odds-ratios, we investigate how the ways in which simulations…

We consider the problem of determining feasible systems from a finite set of simulated alternatives with respect to probability constraints, where the observations from stochastic simulations are Bernoulli distributed. Most statistically…

The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…

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…

Non-probability sampling, for example in the form of online panels, has become a fast and cheap method to collect data. While reliable inference tools are available for classical probability samples, non-probability samples can yield…

Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…

While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set $X$ may be coded as a…

Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…

The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…

We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.

We investigate approximation of a Bernoulli partial sum process to the accompanying Poisson process in the non-i.i.d. case. The rate of closeness is studied in terms of the minimal distance in probability.

We consider Bayesian sample size determination using a criterion that utilizes the first two moments of the expected posterior variance. We study the resulting sample size in dependence on the chosen prior and explore the success rate for…

Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…

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…

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalising constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and…

We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can…