TY - CHAP
T1 - Wiley StatsRef: Statistics Reference
AU - Argiento, Raffaele
PY - 2016
Y1 - 2016
N2 - In this article, we discuss set estimation in a Bayesian framework. In particular,
we give a formal definition for a credible set in the general multivariate parameter setting
and detail the unidimensional case when the set estimator is restricted to be an interval.
Moreover, we comment upon differences and similarities between interval estimates via
Bayesian and non-Bayesian methods.
It is customary to ask that the credible set satisfies a minimum size optimality criterion,
leading to the definition of highest posterior density regions. We mention some theoretical
and computational issues of these optimal regions.
AB - In this article, we discuss set estimation in a Bayesian framework. In particular,
we give a formal definition for a credible set in the general multivariate parameter setting
and detail the unidimensional case when the set estimator is restricted to be an interval.
Moreover, we comment upon differences and similarities between interval estimates via
Bayesian and non-Bayesian methods.
It is customary to ask that the credible set satisfies a minimum size optimality criterion,
leading to the definition of highest posterior density regions. We mention some theoretical
and computational issues of these optimal regions.
KW - Keywords: credible region, Bayesian confidence interval, highest posterior density region, Bayesian coverage, confidence interval, frequentist coverage
KW - Keywords: credible region, Bayesian confidence interval, highest posterior density region, Bayesian coverage, confidence interval, frequentist coverage
UR - http://hdl.handle.net/10807/148072
UR - https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118445112.stat07830
U2 - 10.1002/9781118445112.stat07830
DO - 10.1002/9781118445112.stat07830
M3 - Chapter
SN - 9781118445112
SP - 1
EP - 7
BT - Wiley StatsRef: Statistics Reference
ER -