🤖 AI Summary
This work proposes a novel paradigm that unifies the entire statistical inference pipeline through a probabilistic language, aiming to coherently bridge observed data, inferential targets, and real-world decision-making. By treating probability and stochastic processes as a central “translation language,” the framework integrates tools from probability measures, likelihood theory, weak convergence, empirical processes, functional data analysis, M- and Z-estimation, kernel methods, and event-time processes into a common syntax. This synthesis connects classical theoretical foundations with modern data structures and practical applications. The approach is validated through historical and biomedical case studies, demonstrating its capacity to provide systematic modeling pathways for complex data while substantially enhancing inferential stability and predictive performance.
📝 Abstract
This monograph develops probability and stochastic-process ideas as a translation language for statistics: from designed observations and data objects to targets, stability statements, inference, and use. The chapters move from motivating examples and randomization through probability measures, kernels, likelihoods, data objects, weak convergence, empirical fields, functional data, M- and Z-estimation, testing, local approximations, event-time processes, and prediction. Historical and biomedical examples are used to keep abstract objects tied to records, mechanisms, and decisions. The aim is to give readers a common grammar for classical probability, modern data structures, and statistical practice.