A commentary on Kuznetsov's book
Remarkably, in 1991 two books were published on the same subject. One was 'Statistical Reasoning with Imprecise Probabilities' by P.Walley, the other was 'Interval Statistical Models' by V. Kuznetsov (in Russian). A few years later it was established that the two books describe the same reasoning and are complementary to each other. The axioms laid down to the foundation and the main constructive tool of the theory, natural extension, are identical in both Walley's and Kuznetsov's exposition. The authors had never collaborated but came to the same theory independently and at about the same time.
Eighteen years have passed from the time when the text by Kuznetsov was published and until now the rich arsenal of fundamental ideas and models have not been accessible to the wide audience.
The text, on the one hand, is very mathematical and sets out the basics of the theory and a numerous number of interval statistical models. On the other hand, the author brings soul to the models and complex concepts, hence the text appears animated. The reader comes to comprehend that the author adores the subject; he cherishes it and wants the reader to like it as well. Abstract mathematical derivations are often preceded by exquisite observations from life to support the need for a theorem or another formal statement.
I have the privilege of being able to understand the language in which the book is written (not necessarily all the models and formal derivations) and wish that one day the book is translated and its content becomes accessible to anyone interested from the community of imprecise probabilities.
There are quite a number of books that describe different approaches to reasoning about uncertainty. But there are very few that serve as a fundamental and inspiring source for many branches of statistical reasoning and their applications. And there are very few that can compete with the present work when it comes to finding a unifying approach to reasoning about uncertainty.