The material accumulated and presented in this volume can be ex­ plained easily. At the start of my graduate studies in the early 1950s, I Grenander's (1950) thesis, and was much attracted to the came across entire subject considered there. I then began preparing for the neces­ sary mathematics to appreciate and possibly make some contributions to the area. Thus after a decade of learning and some publications on the way, I wanted to write a modest monograph complementing Grenander's fundamental memoir. So I took a sabbatical leave from my teaching position at the Carnegie-Mellon University, encouraged by an Air Force Grant for the purpose, and followed by a couple of years more learning opportunity at the Institute for Advanced Study to complete the project. As I progressed, the plan grew larger needing a substantial background material which was made into an independent initial volume in (1979). In its preface I said: "My intension was to present the following material as the first part of a book treating the In­ ference Theory of stochastic processes, but the latter account has now receded to a distant future," namely for two more decades! Meanwhile, a much enlarged second edition of that early work has appeared (1995), and now I am able to present the main part of the original plan.

Preface. I. Introduction and Preliminaries. II. Some Principles of Hypothesis Testing. III. Parameter Estimation and Asymptotics. IV. Inferences for Classes of Processes. V. Likelihood Ratios for Processes. VI. Sampling Methods for Processes. VII. More on Stochastic Inference. VIII. Prediction and Filtering of Processes. IX. Nonparametric Estimation for Processes. Bibliography. Notation index. Author index. Subject index.