Lecture+5+Bayesian+Statistics+II

Lecture+5+Bayesian+Statistics+II - ECON 123A, Fall 2011,...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
ECON 123A, Fall 2011, Lecture 5 Dale J. Poirier 5-1 Lecture 5 3 Point Estimation
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ECON 123A, Fall 2011, Lecture 5 Dale J. Poirier 5-2 C Frequentist point estimation is based in part on intuitive criteria (e.g., method of moments, maximum likelihood) and the statistical properties of the resulting estimators are addressed indirectly after-the-fact. C Bayesian point estimation begins by announcing a criterion for determining what constitutes a good point estimate, and then derives a method for producing an “optimal” point estimate given the data at hand.
Background image of page 2
ECON 123A, Fall 2011, Lecture 5 Dale J. Poirier 5-3 C We presuppose a loss (cost) function , i.e., a nonnegative function satisfying C( 2 , 2 ) = 0 and which measures the consequences of using when the “state of nature” is 2 . B Usually is a nondecreasing function of the sampling error B Clearly, it is desired to “minimize” in some sense, but its randomness must first be eliminated.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ECON 123A, Fall 2011, Lecture 5 Dale J. Poirier 5-4 (3.1) C From the sampling theory point of view, 2 is non-stochastic but is nonetheless stochastic because the estimator is a random variable. B An obvious way to circumscribe the randomness of is to focus attention on its expected value, assuming it exists. B Frequentist consider the risk function where the expectation (assumed to exist) is taken with respect to the sampling p.f. f(y| 2 ).
Background image of page 4
ECON 123A, Fall 2011, Lecture 5 Dale J. Poirier 5-5 C In contrast the Bayesian perspective is entirely ex post : find a function of the observed data y to serve as a point estimate of the unknown parameter 2 . B Unlike the frequentist approach, no role is provided for data that could have been observed, but were not observed. B The Bayesian perspective suggests formulation of subjective degrees of belief about 2 , given all the information at hand. B Such information is fully contained in the posterior distribution of 2 : it reflects both prior and sample information.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ECON 123A, Fall 2011, Lecture 5 Dale J. Poirier 5-6 C For the Bayesian the randomness in loss function is fundamentally different than for the frequentist approach, . B For the Bayesian is random because 2 is unknown. B From the classical perspective, although 2 is also unknown, it is treated as a fixed constant. B The ex ante perspective of the classical view implies that is random because is viewed as random variable with a sampling distribution in repeated samples.
Background image of page 6
ECON 123A, Fall 2011, Lecture 5 Dale J. Poirier 5-7 C The Bayesian solution to the randomness of the loss function is similar to the classical solution: take its expectation before minimization. B The expectation, however, is with respect to the posterior distribution 2 |y, and not the sampling distribution Y| 2 used to obtain the risk function. B The Bayesian prescription is equivalent to the principle usually advocated for economic agents acting in a world of uncertainty: using all available information, choose actions so as to maximize expected utility, or equivalently, minimize expected loss.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ECON 123A, Fall 2011, Lecture 5 Dale J. Poirier 5-8 (3.2) (3.3) Definition 3.1:
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 45

Lecture+5+Bayesian+Statistics+II - ECON 123A, Fall 2011,...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online