We consider the case of a bivariate Dirichlet process model in which the parameter is
known only through its marginal distributions. A Fréchet class on the
parameter is therefore entertained and, consequently, a class of Dirichlet processes
is obtained. We analyze the notion of robustness in such environment and introduce
some measures of robustness. The ideas are finally illustrated in an example about
earthquakes occurrences.
Andrysek J
,
Bodini A
,
Karny M
,
Kracik J
and
Ruggeri F
(2008) On combining partial and
incompatible information in e-negotiation and e-arbitration, to appear
in Group Decision and Negotiation.
2.
Betrò B
,
Garavaglia E
,
Guagenti E
,
Rotondi R
and
Tagliani A
(1989) Sulla distribuzione dei tempi di
intercorrenza fra eventi sismici in alcune zone italiane (On the
distribution of the interoccurence times between seismic events in some Italian
areas). Atti IV Convegno Nazionale di Ingegneria
Sismica,
Milano, Italy
.
3.
Campbell KW
(1982)
Bayesian analysis of extreme earthquake occurrences. Part I. Probabilistic
hazard model
. Bulletin of the Seismological Society of America,
12,
1689–705
.
4.
Çinlar E
(1975) Introduction to stochastic
processes.
Englewood Cliffs, USA: Prentice-Hall
.
5.
Dalal S R
and
Phadia EG
(1983)
Nonparametric Bayes inference for concordance in bivariate
distributions
. Communications in Statistics-Theory and Methods,
12,
947–63
.
6.
Dall’ Aglio G
,
Kotz S
and
Salinetti G
(eds) (1991) Advances in
probability distributions with given marginals.
Dordrecht, The Netherlands: Kluwer Academic
Publishers
.
7.
Ferguson TS
(1973)
A Bayesian analysis of some nonparametric problems
. Annals of Statistics, 1,
209–30
.
8.
Fréchet M
(1951)
Sur les tables de corrélation dont les marges sont
données (On the contingency tables with given
marginals)
. Annales de l'Universite de Lyon, Sciences,
4,
13–84
.
9.
Karnik V
(1971) The seismicity of the European
area.
London: Hingham
.
10.
Ladelli L
,
Mitrione M
,
Ruffoni S
and
Ruggeri F
(1992) Inferences for point processes
modelling earthquake occurrences in Sannio Matese. Technical
Report 92.7,
CNR-IAMI, Milano, Italy
.
11.
Lavine M
(1992)
Some aspects of Polya tree distributions for statistical modelling
. Annals of Statistics, 20,
1222–235
.
12.
Rios Insua D
and
Ruggeri F
(eds) (2000) Robust
Bayesian analysis, Vol. 152, Lecture Notes in Statistics.
New York: Springer
.
13.
Ruggeri F
(1993) Bayesian comparison of Italian
earthquakes. Technical Report 93-A32,
ISDS, Duke University, Durham, USA
.
14.
Ruggeri F
(1994) Bayesian nonparametrics,
robustness and Fréchet classes. PhD Dissertation,
ISDS, Duke University, Durham, USA
.
