Bayesian approach to system identification by V. Peterka

In this chapter the identification problems are approached via Bayesian statistics. In Bayesian view the concept of probability is not interpreted in terms of limits of relative frequencies but more generally as a subjective measure of belief of a rationally and consistently reasoning person (here called the statistician) which is used to describe quantitatively the uncertain relationship between the statistician and the external world.

- Underlying Philosophy and Basic Relations

- System Model, Reexamined from Bayesian Viewpoint

- Parameter Estimation and Output Prediction

- Time-Varying Parameters and Adaptivity

- System Classification

Optimized Bayesian Dynamic Advising: Theory and Algorithms by M. Karny et al. (Springer, London, 2005).

The book provides the theoretical and algorithmic basis of optimized probabilistic advising. Starting from abstract ideas and formulations, and culminating in detailed algorithms, the book comprises a unified treatment of an important problem of the design of advisory systems supporting supervisors of complex processes. It introduces the theoretical and algorithmic basis of developed advising, relying on novel and powerful combination black-box modeling by dynamic mixture models and fully probabilistic dynamic optimization.

Decision Making with Imperfect Decision Makers by T.V. Guy, M. Kárný, D.H. Wolpert, Springer, 2012

Prescriptive Bayesian decision making has reached a high level of maturity and is well-supported algorithmically. However, experimental data shows that real decision makers choose such Bayes-optimal decisions surprisingly infrequently, often making decisions that are badly sub-optimal. So prevalent is such imperfect decision-making that it should be accepted as an inherent feature of real decision makers living within interacting societies.

To date such societies have been investigated from an economic and gametheoretic perspective, and even to a degree from a physics perspective. However, little research has been done from the perspective of computer science and associated disciplines like machine learning, information theory and neuroscience. This book is a major contribution to such research.

Some of the particular topics addressed include:

• How should we formalise rational decision making of a single imperfect decision maker?

• Does the answer change for a system of imperfect decision makers?

• Can we extend existing prescriptive theories for perfect decision makers to make them useful for imperfect ones?

• How can we exploit the relation of these problems to the control under varying and uncertain resources constraints as well as to the problem of the computational decision making?

• What can we learn from natural, engineered, and social systems to help us address these issues?