The Art of Causal ConjectureIn The Art of Causal Conjecture, Glenn Shafer lays out a new 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. |
Wat mensen zeggen - Een review schrijven
Inhoudsopgave
Event Trees | 31 |
3 | 63 |
4 | 89 |
5 | 113 |
Events Tracking Events | 135 |
Events as Signs of Events | 153 |
Independent Variables | 167 |
Variables Tracking Variables | 189 |
SampleSpace Concepts of Independence | 425 |
Overview | 426 |
Independence Proper | 432 |
Unpredictability in Mean | 434 |
Simple Uncorrelatedness | 437 |
Mixed Uncorrelatedness | 438 |
Partial Uncorrelatedness | 440 |
Independence for Partitions | 442 |
Variables as Signs of Variables | 215 |
An Abstract Theory of Event Trees | 229 |
Martingale Trees | 247 |
Refining | 275 |
Principles of Causal Conjecture | 299 |
Causal Models | 331 |
Representing Probability Trees | 359 |
Some Elements of Order Theory | 393 |
The SampleSpace Framework for Probability | 399 |
Prediction in Probability Spaces | 409 |
Conditional Distribution | 411 |
Regression on a Single Variable | 412 |
Regression on a Partition or a Family of Variables | 415 |
Linear Regression on a Single Variable | 418 |
Linear Regression on a Family of Variables | 422 |
Independence for Families of Variables | 445 |
The Basic Role of Uncorrelatedness | 448 |
Dawids Axioms | 449 |
Prediction Diagrams | 453 |
Path Diagrams | 454 |
Generalized Path Diagrams | 462 |
Relevance Diagrams | 466 |
Bubbled Relevance Diagrams | 475 |
Abstract Stochastic Processes | 477 |
Abstract Stochastic Processes | 479 |
Embedding Variables and Processes in a Sample Space | 480 |
Glossary of Notation | 485 |
References | 491 |
501 | |