Related papers: Estimating Bernoulli trial probability from a smal…
Suppose an experimentalist wishes to verify that his apparatus produces entangled quantum states. A finite amount of data cannot conclusively demonstrate entanglement, so drawing conclusions from real-world data requires statistical…
We introduce a new model for sums of exchangeable binary random variables. The proposed distribution is an approximation to the exact distributional form, and relies on the theory of completely monotone functions and the Laplace transform…
Statistical hypothesis tests typically use prespecified sample sizes, yet data often arrive sequentially. Interim analyses invalidate classical error guarantees, while existing sequential methods require rigid testing preschedules or incur…
Estimating win probability is one of the classic modeling tasks of sports analytics. Many widely used win probability estimators use machine learning to fit the relationship between a binary win/loss outcome variable and certain game-state…
We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…
In an observational study, it is common to leverage known null effect to detect bias. One such strategy is to set aside a placebo sample -- a subset of data immune from the hypothesized cause-and-effect relationship. Existence of an effect…
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…
We propose the use of a simple intuitive principle for measuring algorithmic classification bias: the significance of the differences in a classifier's error rates across the various demographics is inversely commensurate with the sample…
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…
A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…
We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…
An iterative randomness extraction algorithm which generalized the Von Neumann's extraction algorithm is detailed, analyzed and implemented in standard C++. Given a sequence of independently and identically distributed biased Bernoulli…
We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability…
Estimating prevalence, the fraction of a population with a certain medical condition, is fundamental to epidemiology. Traditional methods rely on classification of test samples taken at random from a population. Such approaches to…
We consider the problem of estimating the probability of an observed string drawn i.i.d. from an unknown distribution. The key feature of our study is that the length of the observed string is assumed to be of the same order as the size of…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
We examine the extent to which random samplings from the values of a random set, determine the distribution of the random set itself. We also comment on how, given the statistics of the sampling, to detect the distribution. Several methods…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial random variables.