Performance of Test Supermartingale Confidence Intervals for the Success Probability of Bernoulli Trials.

Given a composite null hypothesis ℋ0, test supermartingales are non-negative supermartingales with respect to ℋ0 with an initial value of 1. Large values of test supermartingales provide evidence against ℋ0. As a result, test supermartingales are an effective tool for rejecting ℋ0, particularly when the p-values obtained are very small and serve as certificates against the null hypothesis. Examples include the rejection of local realism as an explanation of Bell test experiments in the foundations of physics and the certification of entanglement in quantum information science. Test supermartingales have the advantage of being adaptable during an experiment and allowing for arbitrary stopping rules. By inversion of acceptance regions, they can also be used to determine confidence sets. We used an example to compare the performance of test supermartingales for computing p-values and confidence intervals to Chernoff-Hoeffding bounds and the "exact" p-value. The example is the problem of inferring the probability of success in a sequence of Bernoulli trials. There is a cost in using a technique that has no restriction on stopping rules, and, for a particular test supermartingale, our study quantifies this cost.

The Use of Correlated Binomial Distribution in Estimating Error Rates for Firearm Evidence Identification.

In the branch of forensic science known as firearm evidence identification, estimating error rates is a fundamental challenge. Recently, a new quantitative approach known as the congruent matching cells (CMC) method was developed to improve the accuracy of ballistic identifications and provide a basis for estimating error rates. To estimate error rates, the key is to find an appropriate probability distribution for the relative frequency distribution of observed CMCs overlaid on a relevant measured firearm surface such as the breech face of a cartridge case. Several probability models based on the assumption of independence between cell pair comparisons have been proposed, but the assumption of independence among the cell pair comparisons from the CMC method may not be valid. This article proposes statistical models based on dependent Bernoulli trials, along with corresponding methodology for parameter estimation. To demonstrate the potential improvement from the use of the dependent Bernoulli trial model, the methodology is applied to an actual data set of fired cartridge cases.

Agency and social constraint among victims of domestic minor sex trafficking: A method for measuring free will.

Human agency has been a focus of philosophical and sociological concern from early debates about "free will" to recent themes in poststructuralism. Debates over the proper understanding of structure, agency, and constraint are hindered by the fact that few if any empirical measures of these concepts have been proposed. As sociologists have long recognized, the total results of the decisions of a group's members can be viewed as a distribution, and parameters can be fit to obtain a description of observed distributions. Here we propose the use of negative binomial curve to model population survival outcomes, and suggest that the parameters of such a curve represent reasonable surrogates for measures of agency, opportunity, and constraint when the decision process can be thought of as akin to a Bernoulli process. To provide an illustration of this approach, we discuss participation of legal minors in commercial sex (commonly referred to as victims of domestic minor sex trafficking (VDMST) or commercially sexually exploited children (CSEC)). In popular and advocacy-based accounts, considerable focus has been placed on the relative powerlessness of female VDMST. Using the proposed modeling technique, we test the extent to which male versus female VDMST appear to possess greater agency (or function under more limiting constraint) when deciding whether to remain in sex work or "leave the life". Contrary to existing literature, our results indicate that male and female underage sex workers are experiencing similar levels of agency, and differ mainly in opportunity, and constraint. Other individual circumstances are shown to contribute to varying levels of agency and constraint among sex workers, including street work status, community trouble, drug use, and the availability of an alternative income.

Markov counting models for correlated binary responses.

We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many previous models for correlated outcomes, admits easily interpretable parameterizations, allows different cluster sizes, and incorporates ascertainment bias in a natural way. We demonstrate several new models for dependent outcomes and provide algorithms for computing maximum likelihood estimates. We show how to incorporate cluster-specific covariates in a regression setting and demonstrate improved fits to well-known datasets from familial disease epidemiology and developmental toxicology.