On A Simpler and Faster Derivation of Single Use Reliability Mean and Variance for Model-Based Statistical Testing

Markov chain usage-based statistical testing has proved sound and effective in providing audit trails of evidence in certifying software-intensive systems. The system end-toend reliability is derived analytically in closed form, following an arc-based Bayesian model. System reliability is represented by an important statistic called single use reliability, and defined as the probability of a randomly selected use being successful. This paper continues our earlier work on a simpler and faster derivation of the single use reliability mean, and proposes a new derivation of the single use reliability variance by applying a well-known theorem and eliminating the need to compute the second moments of arc failure probabilities. Our new results complete a new analysis that could be shown to be simpler, faster, and more direct while also rendering a more intuitive explanation. Our new theory is illustrated with three simple Markov chain usage models with manual derivations and experimental results

Sublinear expectation linear regression

Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management. Under the nonlinear expectation framework, however, the related statistical models and statistical inferences have not yet been well established. The goal of this paper is to construct the sublinear expectation regression and investigate its statistical inference. First, a sublinear expectation linear regression is defined and its identifiability is given. Then, based on the representation theorem of sublinear expectation and the newly defined model, several parameter estimations and model predictions are suggested, the asymptotic normality of estimations and the mini-max property of predictions are obtained. Furthermore, new methods are developed to realize variable selection for high-dimensional model. Finally, simulation studies and a real-life example are carried out to illustrate the new models and methodologies. All notions and methodologies developed are essentially different from classical ones and can be thought of as a foundation for general nonlinear expectation statistics