Bayesian Nets and Causality
This book has two central claims, namely the exploration of the basic scientific and philosophical concepts probability and causality and the relationship between Bayesian nets and the maximum entropy principle as applied in computational methods. The text is based on a number of the author’s studies and papers published between 1999 and 2004 and must be considered as an important, well thought out contribution to both of the topics above. The range of philosophical and mathematical views connected with causality and probability, interpretations of experience and human mental characteristics, like the obsessive urge to think out cause-effect relationships for any event, is extreme and covers a long period of time.
The reader is confronted with views from personalities such as Francis Bacon, David Hume, Immanuel Kant and Jakob Bernoulli as well as Frank P. Ramsey, John M. Keynes, Bruno de Finneti, Richard von Mises, Karl Popper, Rudolf Carnap and many others. The book opens with a short overview of various interpretations of probability. Bayesian nets are then introduced and their use in causal reasoning is proposed in chapters 2–4. An objective Bayesian interpretation of probability and its application to net construction is examined in the two following chapters. Epistemic and recursive causalities and their close relations to causal graphs and Bayesian nets are discussed in chapters 9 and 10 and logical reasoning is covered in chapter 11. The analogies between causal and logical influence are identified and it is shown that the Bayesian net formalism is applicable to logical implications. In the closing twelfth chapter, the author shows that the changes in belief can be handled as the language changes. The book will certainly be appreciated by researchers and graduate students in computer science, mathematics and philosophy and, in particular, by all interested in the complicated relations between subjective and objective interpretations of probabilistic phenomena.