By Edward Greenberg
This concise textbook is an creation to econometrics on the graduate or complex undergraduate point. It differs from different books in econometrics in its use of the Bayesian method of information. This process, unlike the frequentist method of facts, makes particular use of previous details and relies at the subjective view of chance, which takes chance conception as employing to all events within which uncertainty exists, together with uncertainty over the values of parameters.
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Extra resources for Introduction to Bayesian Econometrics
Choose G(α, β) as the prior distribution, and consider observing a total of s1 events in the first of two independent experiments and s2 in the second. Show that the median of the posterior distribution minimizes loss under the absolute value loss function. The zero–one loss function is defined as ˆ θ) = 1(|θˆ − θ | > b), L3 (θ, P1: KAE 0521858717pre CUNY1077-Greenberg 40 0 521 87282 0 August 8, 2007 20:46 Chapter 3. Posterior Distributions and Inference where 1(A) is the indicator function that equals 1 if A is true and 0 otherwise.
Sample mean. This idea can be taken one step further. If we denote the true value of θ by θ0 , it can be shown that ¯ |y) → l(θ ¯ 0 |y). 1 Properties of Posterior Distributions 27 Accordingly, for large n, the posterior distribution collapses to a distribution with all its probability at θ0 . This property is similar to the criterion of consistency in the frequentist literature and extends to the multiparameter case. Finally, we can use these ideas to say something about the form of the posterior distribution for large n.
The frequentist approach to model comparison makes use of hypothesis tests. In this approach, the null hypothesis H0 is rejected in favor of the alternative hypothesis HA if the value of a statistic computed from the data falls in the critical region. The critical region is usually specified to set the probability that H0 is rejected when it is true at a small value, where the probability is computed over the distribution of the statistic. As mentioned before, this calculation depends on values of the statistic that were not observed.