The Logical Foundations of Statistical Inference

1. Front Matter

   Pages I-IX

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2. The Probability Framework

   • Henry E. Kyburg Jr.

   Pages 1-21

3. Classical Statistical Theory

   • Henry E. Kyburg Jr.

   Pages 22-60

4. R. A. Fisher: Likelihood and Fiducial Inference

   • Henry E. Kyburg Jr.

   Pages 61-75

5. Decision Theory

   • Henry E. Kyburg Jr.

   Pages 76-93

6. Subjective and Logical Approaches

   • Henry E. Kyburg Jr.

   Pages 94-128

7. Comparison of Approaches

   • Henry E. Kyburg Jr.

   Pages 129-155

8. The Language: Syntax

   • Henry E. Kyburg Jr.

   Pages 156-186

9. Rational Corpora

   • Henry E. Kyburg Jr.

   Pages 187-215

10. Randomness

    • Henry E. Kyburg Jr.

    Pages 216-246

11. Probability

    • Henry E. Kyburg Jr.

    Pages 247-285

12. Conditional Probability

    • Henry E. Kyburg Jr.

    Pages 286-313

13. Interpretations of Probability

    • Henry E. Kyburg Jr.

    Pages 314-327

14. Bayesian Inference

    • Henry E. Kyburg Jr.

    Pages 328-347

15. The Fiducial Argument

    • Henry E. Kyburg Jr.

    Pages 348-356

16. Confidence Methods

    • Henry E. Kyburg Jr.

    Pages 357-369

17. Epistemological Considerations

    • Henry E. Kyburg Jr.

    Pages 370-391

18. Back Matter

    Pages 392-433

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Everyone knows it is easy to lie with statistics. It is important then to be able to tell a statistical lie from a valid statistical inference. It is a relatively widely accepted commonplace that our scientific knowledge is not certain and incorrigible, but merely probable, subject to refinement, modifi­ cation, and even overthrow. The rankest beginner at a gambling table understands that his decisions must be based on mathematical ex­ pectations - that is, on utilities weighted by probabilities. It is widely held that the same principles apply almost all the time in the game of life. If we turn to philosophers, or to mathematical statisticians, or to probability theorists for criteria of validity in statistical inference, for the general principles that distinguish well grounded from ill grounded generalizations and laws, or for the interpretation of that probability we must, like the gambler, take as our guide in life, we find disagreement, confusion, and frustration. We might be prepared to find disagreements on a philosophical and theoretical level (although we do not find them in the case of deductive logic) but we do not expect, and we may be surprised to find, that these theoretical disagreements lead to differences in the conclusions that are regarded as 'acceptable' in the practice of science and public affairs, and in the conduct of business.

• conditional
• decision theory
• foundation
• interpret
• probability
• subject

• University of Rochester, USA

  Henry E. Kyburg

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