ABSTRACT
This chapter describes a general framework for statistical inference and state estimation for point processes. One crucial point to remember is that inference is a tripartite subject, whose components is statistical inference, state estimation and combined statistical inference and state estimation. The goal of statistical estimation is to determine the operative probability, or functionals of it, as accurately as possible and to characterize the errors that arise. One must also collect data suited to methods available for its analysis and make effective use of limited sampling resources. The chapter outlines a conceptual framework for statistical inference for point processes and to elucidate it with "sample" problems meant to convey the breadth and scope of point process inference, but not as a complete description. The great principles of estimation, maximum likelihood, the method of moments and least squares, and the principle of likelihood ratios for hypothesis testing, rule classical statistics.
