2. Standard Normal Theory Inference Problems

  1. George E.P. Box1 and
  2. George C. Tiao2

Published Online: 25 JAN 2011

DOI: 10.1002/9781118033197.ch2

Bayesian Inference in Statistical Analysis

Bayesian Inference in Statistical Analysis

How to Cite

Box, G. E.P. and Tiao, G. C. (1992) Standard Normal Theory Inference Problems, in Bayesian Inference in Statistical Analysis, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118033197.ch2

Author Information

  1. 1

    University of Wisconsin

  2. 2

    University of Chicago

Publication History

  1. Published Online: 25 JAN 2011
  2. Published Print: 6 APR 1992

ISBN Information

Print ISBN: 9780471574286

Online ISBN: 9781118033197



  • normal distribution;
  • distributional assumptions;
  • Bayesian intervals;
  • linear model;
  • asymptotic distribution


This chapter contains sections titled:

  • Introduction

  • Inferences Concerning a Single Mean from Observations Assuming Common Known Variance

  • Inferences Concerning the Spread of a Normal Distribution from Observations Having Common Known Mean

  • Inferences When Both Mean and Standard Deviation are Unknown

  • Inferences Concerning the Difference Between Two Means

  • Inferences Concerning a Variance Ratio

  • Analysis of the Linear Model

  • A General Discussion of Highest Posterior Density Regions

  • H.P.D. Regions for the Linear Model: A Bayesian Justification of Analysis of Variance

  • Comparison of Parameters

  • Comparison of the Means of k Normal Populations

  • Comparison of the Spread of k Distributions

  • Summarized Calculations of Various Posterior Distributions