(Ebook) Theory of probability 3rd Edition by Harold Jeffreys ISBN 9780198503682 0198503687

(Ebook) Theory of probability 3rd Edition by Harold Jeffreys ISBN 9780198503682 0198503687

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ISBN 10: 0198503687
ISBN 13: 9780198503682
Author: Harold Jeffreys

(Ebook) Theory of probability 3rd Edition Table of contents:

I. Fundamental Notions

II. Direct Probabilities

• Sampling

• The normal law of error

• The Pearson laws

• The negative binomial law

• Correlation

• Distribution functions

  • Characteristic functions

  • Theorems on limits

• The χ² distribution

• The t and z distributions

• The specification of random noise

III. Estimation Problems

• Sampling

• The Poisson distribution

• The normal law of error

• The method of least squares

• The rectangular distribution

  • Reading of a scale

• Sufficient statistics

  • The Pitman–Koopman theorem

• The posterior probabilities that the true value, or the third observation, will lie between the first two observations

• Correlation

• Invariance theory

• Maximum likelihood

  • Relation of maximum likelihood to invariance

  • An approximation to maximum likelihood

• Combination of estimates with different estimated uncertainties

• The use of expectations

  • Orthogonal parameters

• If the law of error is unknown and the observations are too few

  • Grouping

  • Effects of grouping: Sheppard's corrections

• Smoothing of observed data

• Correction of a correlation coefficient

• Rank correlation

  • Grades and contingency

• The estimation of an unknown and unrestricted integer

• Artificial randomization

IV. General Discussion

• Treatment of old parameters

• Required properties of f(a)

• Comparison of two sets of observations

• Selection of alternative hypotheses

• Test of whether a suggested value of a chance is correct

  • Simple contingency

  • Comparison of samples

• Test of whether the true value in the normal law is zero: standard error originally unknown

  • Test of whether a true value is zero: σ taken as known

• Generalization by invariance theory

  • General approximate forms

  • Test of whether two true values are equal, standard errors supposed the same

  • Test of whether two location parameters are the same, standard errors not supposed equal

  • Test of whether a standard error has a suggested value

  • Test of agreement of two estimated standard errors

  • Test of both the standard error and the location parameter

  • The discovery of argon

• Comparison of a correlation coefficient with a suggested value

  • Comparison of correlations

• The intraclass correlation coefficient

  • Suspiciously close agreement

• Test of the normal law of error

• Test for independence in rare events

• Introduction of new functions

  • Allowance for old functions

  • Two sets of observations relevant to the same parameter

  • Continuous departure from a uniform distribution of chance

V. Combination of Tests

• Several new parameters often arise for consideration simultaneously

• Two new parameters considered simultaneously

  • Grouping

• Partial and serial correlation

• Contingency affecting only diagonal elements

• Deduction as an approximation

VI. Frequency Definitions and Direct Methods

VII. General Questions

Appendix A: Mathematical Theorems

• Inversion of the order of integration

• Abel's lemma

• Watson's lemma

Appendix B: Tables of K

• Analysis for periodicities

• Autocorrelation

Index

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Tags: Harold Jeffreys, Theory, probability