Default Bayesian Priors for Regression Models with First‐Order Autoregressive Residuals

Abstract. The objective of this paper is to develop default priors when the parameter of interest is the autocorrelation coefficient in normal regression models with first‐order autoregressive residuals. Jeffreys’ prior as well as reference priors are found. These priors are compared in the light of how accurately the coverage probabilities of Bayesian credible intervals match the corresponding frequentist coverage probabilities. It is found that the reference priors have a definite edge over Jeffreys’ prior in this respect. Also, the credible intervals based on these reference priors seem superior to similar intervals based on certain divergence measures.

[1]  Daniel Gianola,et al.  Bayesian Analysis of Linear Models , 2002 .

[2]  D. Brillinger.  Time series - data analysis and theory , 1981, Classics in applied mathematics.

[3]  M. Ghosh,et al.  Second-order probability matching priors , 1997 .

[4]  Huaiyu Zhu.  On Information and Sufficiency , 1997 .

[5]  G. Datta.  On priors providing frequentist validity of Bayesian inference for multiple parametric functions , 1996 .

[6]  Keying Ye,et al.  Frequentist validity of posterior quantiles for a two-parameter exponential family , 1996 .

[7]  Malay Ghosh,et al.  ON THE INVARIANCE OF NONINFORMATIVE PRIORS , 1996 .

[8]  Malay Ghosh,et al.  Some remarks on noninformative priors , 1995 .

[9]  Jayanta K. Ghosh,et al.  Noninformative priors for maximal invariant parameter in group models , 1995 .

[10]  Jayanta K. Ghosh,et al.  On priors providing frequentist validity for Bayesian inference , 1995 .

[11]  Jayanta K. Ghosh,et al.  Higher Order Asymptotics , 1994 .

[12]  D. Dey,et al.  Frequentist validity of posterior quantiles in the presence of a nuisance parameter : higher order asymptotics , 1993 .

[13]  James O. Berger,et al.  Ordered group reference priors with application to the multinomial problem , 1992 .

[14]  R. Tibshirani.  Noninformative priors for one parameter of many , 1989 .

[15]  James O. Berger,et al.  Estimating a Product of Means: Bayesian Analysis with Reference Priors , 1989 .

[16]  D. Cox,et al.  Parameter Orthogonality and Approximate Conditional Inference , 1987 .

[17]  Charles Stein,et al.  On the coverage probability of confidence sets based on a prior distribution , 1985 .

[18]  J. Bernardo.  Reference Posterior Distributions for Bayesian Inference , 1979 .

[19]  Chris Chatfield,et al.  Introduction to Statistical Time Series. , 1976 .

[20]  G. Chow,et al.  MULTIPERIOD PREDICTIONS FROM STOCHASTIC DIFFERENCE EQUATIONS BY BAYESIAN METHODS , 1973 .

[21]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[22]  H. Thornber.  Finite Sample Monte Carlo Studies: An Autoregressive Illustration , 1967 .

[23]  H. W. Peers.  On Confidence Points and Bayesian Probability Points in the Case of Several Parameters , 1965 .

[24]  Arnold Zellner,et al.  BAYESIAN ANALYSIS OF THE REGRESSION MODEL WITH AUTOCORRELATED ERRORS. , 1964 .

[25]  B. L. Welch,et al.  On Formulae for Confidence Points Based on Integrals of Weighted Likelihoods , 1963 .

[26]  T. Haavelmo.  Methods of Measuring the Marginal Propensity to Consume , 1947 .