Lecture+4+Bayesian+Statistics+I

Lecture+4+Bayesian+Statistics+I - ECON 123A Fall 2011...

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ECON 123A, Fall 2011, Lecture 4 Dale J. Poirier 4-1 Lecture 4 Bayesian Statistics I: Subjective Probability and Bayesian Inference
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ECON 123A, Fall 2011, Lecture 4 Dale J. Poirier 4-2 1 The Subjective Interpretation of Probability Reverend Thomas Bayes (born circa 1702 and died in 1761) was the oldest son of Reverend Joshua Bayes who was one of the first ordained nonconformist ministers in England. Relatively little is known about the personal life of Thomas Bayes. His only known mathematical works, although he was elected a Fellow of the Royal Society in 1742, are two articles published posthumously by his friend Richard Price in 1763. His ideas appear to have been independently developed by James Bernoulli in 1713, also, published posthumously, and later popularized independently by Pierre Laplace in 1774.
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ECON 123A, Fall 2011, Lecture 4 Dale J. Poirier 4-3 Reverend Bayes Says You are now an initiate of the Bayesian Conspiracy.
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ECON 123A, Fall 2011, Lecture 4 Dale J. Poirier 4-4
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ECON 123A, Fall 2011, Lecture 4 Dale J. Poirier 4-5
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ECON 123A, Fall 2011, Lecture 4 Dale J. Poirier 4-6 Bernardo and Smith (1994, Bayesian Theory , p. 4): “Bayesian Statistics offers a rationalist theory of personalistic beliefs in contexts of uncertainty, with the central aim of characterizing how an individual should act in order to avoid certain kinds of undesirable behavioral inconsistencies. The theory establishes that expected utility maximization provides the basis for rational decision making and that Bayes’ theorem provides the key to the ways in which beliefs should fit together in the light of changing evidence. The goal, in effect, is to establish rules and procedures for individuals concerned with disciplined uncertainty accounting. The theory is not descriptive, in the sense of claiming to model actual behavior. Rather, it is perspective, in the sense of saying ‘if you wish to avoid the possibility of these undesirable consequences you must act in the following way.’
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ECON 123A, Fall 2011, Lecture 4 Dale J. Poirier 4-7 C Bayesian econometrics consists of the tools of Bayesian statistics applicable to the models and phenomena of interest to economists. C Non-Bayesians, who we hereafter refer to as frequentists , argue that situations not admitting repetition under essentially identical conditions are not within the realm of statistical enquiry, and hence, “probability” should not be used in such situations. B Frequentists define the probability of an event as its long-run relative frequency.
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ECON 123A, Fall 2011, Lecture 4 Dale J. Poirier 4-8 B This frequentist interpretation cannot be applied: < to unique, once-and-for-all type of phenomenon, < to hypotheses, or < to uncertain past events. B The frequentist interpretation is nonoperational since only a finite number of trials can ever be conducted.
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ECON 123A, Fall 2011, Lecture 4 Dale J. Poirier 4-9 Note: Microsoft have been a strong investor in Bayesian analysis, especially in areas where fuzzy data (incoming emails) needs sorting and processing.
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This note was uploaded on 12/13/2011 for the course ECON 123a taught by Professor Staff during the Fall '08 term at UC Irvine.

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Lecture+4+Bayesian+Statistics+I - ECON 123A Fall 2011...

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