A note on nonexistence of posterior moments

2005 ◽  
Vol 33 (4) ◽  
pp. 591-601 ◽  
Author(s):  
Dongchu Sun ◽  
Paul L. Speckman
Keyword(s):  
Posterior Moments

scholarly journals Priors for Macroeconomic Time Series and Their Application

1994 ◽  
Vol 10 (3-4) ◽  
pp. 609-632 ◽  
Author(s):  
John Geweke
Keyword(s):  
Time Series ◽  
Prior Distribution ◽  
Odds Ratio ◽  
General Trend ◽  
Stationary Model ◽  
Posterior Odds ◽  
Posterior Odds Ratio ◽  
The Family ◽  
Macroeconomic Time Series ◽  
Posterior Moments

This paper takes up Bayesian inference in a general trend stationary model for macroeconomic time series with independent Student-t disturbances. The model is linear in the data, but nonlinear in parameters. An informative but nonconjugate family of prior distributions for the parameters is introduced, indexed by a single parameter that can be readily elicited. The main technical contribution is the construction of posterior moments, densities, and odd ratios by using a six-step Gibbs sampler. Mappings from the index parameter of the family of prior distribution to posterior moments, densities, and odds ratios are developed for several of the Nelson–Plosser time series. These mappings show that the posterior distribution is not even approximately Gaussian, and they indicate the sensitivity of the posterior odds ratio in favor of difference stationarity to the choice of the prior distribution.

Metropolis-Hastings Algorithms for DSGE Models

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Random Walk ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Large Scale ◽  
Likelihood Function ◽  
Dsge Models ◽  
Posterior Distributions ◽  
Dsge Model ◽  
Alternative Proposal ◽  
Posterior Moments

This chapter talks about the most widely used method to generate draws from posterior distributions of a DSGE model: the random walk MH (RWMH) algorithm. The DSGE model likelihood function in combination with the prior distribution leads to a posterior distribution that has a fairly regular elliptical shape. In turn, the draws from a simple RWMH algorithm can be used to obtain an accurate numerical approximation of posterior moments. However, in many other applications, particularly those involving medium- and large-scale DSGE models, the posterior distributions could be very non-elliptical. Irregularly shaped posterior distributions are often caused by identification problems or misspecification. In lieu of the difficulties caused by irregularly shaped posterior surfaces, the chapter reviews various alternative MH samplers, which use alternative proposal distributions.

scholarly journals Posterior moments computed by mixed integration

1985 ◽  
Vol 29 (1-2) ◽  
pp. 3-18 ◽  
Author(s):  
Herman K. Van Dijk ◽  
Teun Kloek ◽  
C.Guus E. Boender
Keyword(s):  
Posterior Moments

scholarly journals BAYESIAN REGRESSION ANALYSIS WITH SCALE MIXTURES OF NORMALS

2000 ◽  
Vol 16 (1) ◽  
pp. 80-101 ◽  
Author(s):  
Carmen Fernández ◽  
Mark F.J. Steel
Keyword(s):  
Bayesian Regression ◽  
Design Matrix ◽  
Mixing Distribution ◽  
Scale Parameters ◽  
Common Reference ◽  
Scale Mixtures ◽  
Wide Range ◽  
Under Sampling ◽  
Scale Mixtures Of Normals ◽  
Posterior Moments

This paper considers a Bayesian analysis of the linear regression model under independent sampling from general scale mixtures of normals. Using a common reference prior, we investigate the validity of Bayesian inference and the existence of posterior moments of the regression and scale parameters. We find that whereas existence of the posterior distribution does not depend on the choice of the design matrix or the mixing distribution, both of them can crucially intervene in the existence of posterior moments. We identify some useful characteristics that allow for an easy verification of the existence of a wide range of moments. In addition, we provide full characterizations under sampling from finite mixtures of normals, Pearson VII, or certain modulated normal distributions. For empirical applications, a numerical implementation based on the Gibbs sampler is recommended.

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