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Outline AShortHistoryofProbabilityandInductiveReasoning BayesianStatistics:AFrameworkforReasoning BayesianRadiocarbonCalibration Bayesian Statistics for Archaeologists Thomas S. Dye T.S.Dye&Colleagues,Archaeologists,Inc. 735BishopSt.,Suite315 Honolulu,Hawai‘i96813 IGERT Program University of Arizona November 15–16, 2004 ThomasS.Dye BayesianStatisticsforArchaeologists Outline AShortHistoryofProbabilityandInductiveReasoning BayesianStatistics:AFrameworkforReasoning BayesianRadiocarbonCalibration Deduction and Induction I Deduction (top) is Effects Cause or simpler than Outcomes inductive reasoning (bottom). I Diagram after Sivia (1996:Fig. 1.1). Effects Possible or Causes Observations ThomasS.Dye BayesianStatisticsforArchaeologists Outline AShortHistoryofProbabilityandInductiveReasoning BayesianStatistics:AFrameworkforReasoning BayesianRadiocarbonCalibration A Short History of Probability and Inductive Reasoning Bayesian Statistics: A Framework for Logical and Consistent Reasoning Bayesian Radiocarbon Calibration ThomasS.Dye BayesianStatisticsforArchaeologists Outline AShortHistoryofProbabilityandInductiveReasoning AnAbsentFamilyofIdeasBeforeA.D.1660 BayesianStatistics:AFrameworkforReasoning TheDualNatureofProbability BayesianRadiocarbonCalibration Outline A Short History of Probability and Inductive Reasoning An Absent Family of Ideas Before a.d. 1660 The Dual Nature of Probability Bayesian Statistics: A Framework for Logical and Consistent Reasoning Derivation of Bayes’ Theorem Conceptualizing Bayes’ Theorem Bayesian Radiocarbon Calibration How is Bayesian Calibration Diﬀerent? BCal: An On-line Bayesian Radiocarbon Tool ThomasS.Dye BayesianStatisticsforArchaeologists Outline AShortHistoryofProbabilityandInductiveReasoning AnAbsentFamilyofIdeasBeforeA.D.1660 BayesianStatistics:AFrameworkforReasoning TheDualNatureofProbability BayesianRadiocarbonCalibration Knowledge, Opinion, and Degrees of Belief I “God has chosen the most perfect of all possible worlds, that is to say that which is at once the simplest in hypotheses and the richest in phenomena” Leibniz, 1686. I “Such a fact is probable but undoubtedly false” Gibbon, 1776. I “It is not reason which is the guide of life, but custom” Hume, 1748. ThomasS.Dye BayesianStatisticsforArchaeologists Outline AShortHistoryofProbabilityandInductiveReasoning AnAbsentFamilyofIdeasBeforeA.D.1660 BayesianStatistics:AFrameworkforReasoning TheDualNatureofProbability BayesianRadiocarbonCalibration Knowledge, Opinion, and Degrees of Belief I “God has chosen the most perfect of all possible worlds, that is to say that which is at once the simplest in hypotheses and the richest in phenomena” Leibniz, 1686. I “Such a fact is probable but undoubtedly false” Gibbon, 1776. I “It is not reason which is the guide of life, but custom” Hume, 1748. ThomasS.Dye BayesianStatisticsforArchaeologists Outline AShortHistoryofProbabilityandInductiveReasoning AnAbsentFamilyofIdeasBeforeA.D.1660 BayesianStatistics:AFrameworkforReasoning TheDualNatureofProbability BayesianRadiocarbonCalibration Knowledge, Opinion, and Degrees of Belief I “God has chosen the most perfect of all possible worlds, that is to say that which is at once the simplest in hypotheses and the richest in phenomena” Leibniz, 1686. I “Such a fact is probable but undoubtedly false” Gibbon, 1776. I “It is not reason which is the guide of life, but custom” Hume, 1748. ThomasS.Dye BayesianStatisticsforArchaeologists Outline AShortHistoryofProbabilityandInductiveReasoning AnAbsentFamilyofIdeasBeforeA.D.1660 BayesianStatistics:AFrameworkforReasoning TheDualNatureofProbability BayesianRadiocarbonCalibration Outline A Short History of Probability and Inductive Reasoning An Absent Family of Ideas Before a.d. 1660 The Dual Nature of Probability Bayesian Statistics: A Framework for Logical and Consistent Reasoning Derivation of Bayes’ Theorem Conceptualizing Bayes’ Theorem Bayesian Radiocarbon Calibration How is Bayesian Calibration Diﬀerent? BCal: An On-line Bayesian Radiocarbon Tool ThomasS.Dye BayesianStatisticsforArchaeologists Outline AShortHistoryofProbabilityandInductiveReasoning AnAbsentFamilyofIdeasBeforeA.D.1660 BayesianStatistics:AFrameworkforReasoning TheDualNatureofProbability BayesianRadiocarbonCalibration Frequency and Belief Compare and contrast two probability questions: I What is the probability that a roll of the dice will yield snake eyes? I What is the probability that Hawai‘i was discovered by Polynesians in a.d. 750–800? ThomasS.Dye BayesianStatisticsforArchaeologists Outline AShortHistoryofProbabilityandInductiveReasoning AnAbsentFamilyofIdeasBeforeA.D.1660 BayesianStatistics:AFrameworkforReasoning TheDualNatureofProbability BayesianRadiocarbonCalibration Frequency and Belief Compare and contrast two probability questions: I What is the probability that a roll of the dice will yield snake eyes? I What is the probability that Hawai‘i was discovered by Polynesians in a.d. 750–800? ThomasS.Dye BayesianStatisticsforArchaeologists

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Bayesian Statistics: A Framework for Reasoning. Bayesian Radiocarbon Calibration. Bayesian Statistics for Archaeologists. Thomas S. Dye. T. S. Dye

Bayesian Statistics for Archaeologists PDF

81 Pages·2004·3.63 MB·English

by Thomas S. Dye

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Bayesian Statistics: A Framework for Reasoning. Bayesian Radiocarbon Calibration. Bayesian Statistics for Archaeologists. Thomas S. Dye. T. S. Dye

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