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Remarks on Inference in Economics
Principles of Bayesian Analysis with Selected
The Univariate Normal Linear Regression
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analyzed approximate assumed Bayesian analysis Bayesian approach Chapter coefficients common variance complete the square computed conditional pdf conditional posterior pdf conjugate prior covariance matrix denotes derive diffuse prior pdf disturbance terms Econometric elements employed equation error terms example expected loss given hypothesis independent variables independently distributed inferences integrating with respect inverted gamma investment Jacobian Jeffreys joint pdf joint posterior pdf large-sample likelihood function linear loss function marginal pdf marginal posterior pdf maximum likelihood estimate minimize ML estimate modal value multivariate Student nonsingular matrix normal pdf normalizing constant normally and independently normally distributed Note numerical integration observations obtain the marginal pdf for ft pdf's posterior probability predictive pdf prior assumptions prior information problem properties regression model sample information sampling theory sampling-theory Simpson's rule Statist Student t form univariate Student unknown parameters yields Zellner zero mean