Log In Sign Up

Second Order Probabilities for Uncertain and Conflicting Evidence

by   Gerhard Paaß, et al.

In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived reflecting the uncertainty of the input probabilities. The algorithm is based on an approximate sample representation of the basic probabilities. This sample is continuously modified by a stochastic simulation procedure, the Metropolis algorithm, such that the sequence of successive samples corresponds to the desired posterior distribution. The procedure is able to combine inconsistent probabilities according to their reliability and is applicable to general inference networks with arbitrary structure. Dempster-Shafer probability mass functions may be included using specific measurement distributions. The properties of the approach are demonstrated by numerical experiments.


page 1

page 8


SOLBP: Second-Order Loopy Belief Propagation for Inference in Uncertain Bayesian Networks

In second-order uncertain Bayesian networks, the conditional probabiliti...

Uncertain Bayesian Networks: Learning from Incomplete Data

When the historical data are limited, the conditional probabilities asso...

Investigation of Variances in Belief Networks

The belief network is a well-known graphical structure for representing ...

Properties of Chromy's sampling procedure

Chromy (1979) proposed a unequal probability sampling algorithm, which e...

A Method for Random Packing of Spheres with Application to Bonding Modeling in Powder Bed 3D Printing Process

A Matlab-based computational procedure is proposed to fill a given volum...

Why Is Diagnosis Using Belief Networks Insensitive to Imprecision In Probabilities?

Recent research has found that diagnostic performance with Bayesian beli...

Blackwell dominance in large samples

We study repeated independent Blackwell experiments; standard examples i...