Bayesian Economics Through Numerical Methods: A Guide to by Jeffrey H. Dorfman

By Jeffrey H. Dorfman

Delivering researchers in economics, finance, and facts with an updated advent to making use of Bayesian suggestions to empirical stories, this e-book covers the entire diversity of the hot numerical ideas that have been built during the last thirty years. significantly, those are: Monte Carlo sampling, antithetic replication, value sampling, and Gibbs sampling. the writer covers either advances in thought and glossy methods to numerical and utilized difficulties, and contains functions drawn from numerous varied fields inside of economics, whereas additionally delivering a brief assessment of the underlying statistical rules of Bayesian inspiration. the result's a ebook which provides a roadmap of utilized monetary questions that may now be addressed empirically with Bayesian tools. therefore, many researchers will locate this a without problems readable survey of this becoming subject.

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Flournoy and R. K. Tsutakawa. Providence: American Mathematical Society. Geyer, C. (1992). Practical Markov chain Monte Carlo. Statistical Science 7, 473– 482. Hammersley, J. , and D. C. Handscomb (1964). Monte Carlo Methods. London: Chapman and Hall. , and H. K. van Dijk (1978). Bayesian estimates of simultaneous equation system parameters: An application of integration by Monte Carlo. Econometrica 46, 1–19. , and P. E. Rossi (1994). An exact likelihood analysis of the multinomial probit model.

5 10 s=1 s=5 Figure 2. s = 10 s = 100 Restricted Parameter Spaces 33 very different from the likelihood function (or a close relative) and importance sampling can be used. If the posterior distribution of σ 2 is not of particular interest, one might use a multivariate Student-t distribution centered at the mode of the likelihood function (the maximum likelihood estimator of β) as the substitute density; this would be the marginal posterior distribution of β if we had a constant (diffuse) prior on β.

B, where B might be 500 or 1000; note that the total number of observations in the empirical distribution will be 2B. 6. Using the saved values for θ (i) and g(θ (i) ), compute means, medians, interquartile ranges, and so on as desired. Calculation of means, medians, percentiles, and measures of precision are exactly as in the case of standard Monte Carlo integration. Almost sure convergence of the numerical estimator to its analytical counterpart still holds. The benefit of antithetic replication is that in many cases an equally precise numerical approximation can be achieved on a much smaller number of observations in the empirical distribution.

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