The Art of Causal Conjecture: (Artificial Intelligence Series)

In "The Art of Causal Conjecture", Glenn Shafer lays out a mathematical and philosophical foundation for probability and uses it to explain concepts of causality used in statistics, artificial intelligence and philosophy. The various disciplines that use causal reasoning differ in the relative weight they put on security and precision of knowledge as opposed to timeliness of action. The natural and social sciences seek high levels of certainty in the identification of causes and high levels of precision in the measurement of their effects. The practical sciences - medicine, business, engineering and artificial intelligence - must act on causal conjectures based on more limited knowledge. Shafer's understanding of causality contributes to both of these uses of causal reasoning. His language for causal explanation can guide statistical investigation in the natural and social sciences, and it can also be used to formulate assumptions of causal uniformity needed for decision making in the practical sciences. Causal ideas permeate the use of probability and statistics in all branches of industry, commerce, government and science. "The Art of Causal Conjecture" shows that causal ideas can be equally important in theory. It does not challenge the maxim that causation cannot be proven from statistics alone, but by bringing causal ideas into the foundations of probability, it allows causal conjectures to be more clearly quantified, debated and confronted by statistical evidence.

Table of Contents:
Part 1 Introduction: probability trees; many observers, many stances, many natures; causal relations as relations in nature's tree; evidence; measuring the average effect of a cause; causal diagrams; Humean events; three levels of causal language; an outline of the book. Part 2 Event trees: situations and events; the ordering of situations and Moivrean events; cuts; Humean events; Moivrean variables; Humean variables; event trees for stochastic processes; timing in event trees; intersecting event trees; notes on the literature. Part 3 Probability trees: some types of probability trees; axioms for the probabilities of Moivrean events; zero probabilities; a sample-space analysis of the event-tree axioms; probabilities and expected values for variables; Martingales; the expectation of a variable in a cut; conditional expected value and conditional expectation. Part 4 The meaning of probability: the interpretation of expected value; the interpretation of expectation; the long run; changes in belief; the empirical validation of probability; the diversity of uses of probability; notes on the literature. Part 5 Independent events: independence; weak independence; the principle of the common cause; conditional independence; notes on the literature. Part 6 Events tracking events: tracking; tracking and conditional independence; stochastic subsequence; singular diagrams for stochastic subsequence; conjunctive and interactive forks. Part 7 Events as signs of events: sign; weak sign; the ethics of causal talk; screening off. Part 8 Independent variables: unconditional independence; conditional independence; independence for partitions; independence for families of variables; individual properties of the independence relations. Part 9 Variables tracking variables: tracking and conditional independence - a summary; strong tracking; strong tracking and conditional independence; stochastic subsequence; functional dependence; tracking in mean; linear tracking; tracking by partitions; tracking by families of variables. Part 10 Variables as signs of variables: sign; linear sign; scored sign; families of variables. Part 11 An abstract theory of event trees: event trees as sets of sets; event trees as partially ordered sets; regular event trees; the resolution of Moivrean variables; Humean events and variables. Part 12 Martingale trees: examples of decision trees; the meaning of probability in a decision tree; Martingales; the structures of Martingale trees; probability and causality; lower and upper probability; the law of large numbers; notes on the literature. Part 13 Refining; examples of refinement; a constructive definition of finite refinement; axioms for refinement; lifting Moivrean events and variables; refining Martingale trees; grounding. Part 14 Principles of causal conjecture: the diversity of causal explanation; the mean effect of the happening of a Moivrean event. (Part contents).

About the Author :
Glenn Shafer is University Professor and Board of Governors Professor in the Accounting and Information Systems Department at Rutgers Business School.

Review :
"Causality plays an important role in many fields, from engineering to medicine to artificial intelligence. Glenn Shafer has written an important, scholarly study of causality. He starts with a novel foundation for probability that is mathematically and philosophically solid, uses it to distinguish carefully between notions of causality--all of which have played an important role in the literature--and shows how each can be discovered from evidence. This is a book that will be of interest to those interested in foundational questions of statistics and philosophy, as well as in practical applications of causality." Joseph Y. Halpern, Professor, Computer Science Department, Cornell University