By John Geweke

ISBN-10: 0471679321

ISBN-13: 9780471679325

Similar mathematicsematical statistics books

Peter J. Brockwell, Richard A. Davis's Time Series: Theory and Methods, Second Edition (Springer PDF

This paperback version is a reprint of the 1991 variation. Time sequence: concept and strategies is a scientific account of linear time sequence versions and their software to the modeling and prediction of knowledge accumulated sequentially in time. the purpose is to supply particular recommendations for dealing with facts and while to supply a radical realizing of the mathematical foundation for the strategies.

Extra info for Contemporary Bayesian Econometrics and Statistics

Sample text

34 ELEMENTS OF BAYESIAN INFERENCE Then p(ω | y, A) = p(ω | y, θ A , A)p(θ A | y, A) dν(θ A ) A ∝ p(ω | y, θ A2 , A)p(θ A2 | A)p(s2 | s1 , θ A2 , A) dν(θ A2 ). A2 This means that for purposes of learning about ω from the data yo it is necessary only to use the prior density of θ A2 , p(θ A2 | A), and the conditional density of s2 , p(s2 | s1 , θ A2 , A). 34). The random vector s1 (yT ; A) can be treated as fixed, and the parameter vector θ A1 can be ignored. 2 by making X random, with pdf p(X | η, A),η ∈ H .

In an application of a linear–linear (or “lin-lin”) loss function, it would be the case that q < 12 . 63) and the Bayes risk is R(a) = q(1 − q) · [E(a − ω | ω ≤ a) + E(ω − a | ω > a)]. Proof: To verify the solution note that R(a) = E[L(a, ω)] = (1 − q) a −∞ ∞ (a − ω)p(ω) dω + q (ω − a)p(ω) dω. a This function is twice differentiable: dR(a)/da = (1 − q)P (ω ≤ a) − qP (ω > a), d R(a)/da 2 = p(a). 2 The first-order condition implies (1 − q)P (ω ≤ a) = q[1 − P (ω ≤ a)] ⇔ P (ω ≤ a) = q. 64), there is a unique Bayes action, and if not, then a is set valued.

G(θ A )]γ 1 exp A i=1 The posterior density of θ A has kernel r T [g(θ A )]γ 1 +T exp ci φ i (θ A ) γ i+1 + i=1 hi (yt ) . 60) t=1 Thus the conjugate prior may be interpreted as a set of γ 1 observations, with sufficient statistics γ i (i = 2, . . , r + 1). The multiplicative interaction between the prior and the likelihood function is of precisely the same form as the multiplicative interaction between successive observations. Consequently it is a simple matter to combine prior information of this form as well.