Bayesian methods for outliers in uniform and Pareto samples
Abstract
We begin by reviewing the current literature on outliers and look at what has
been done both classically and from a Bayesian viewpoint. We then extend
these Bayesian ideas to model outliers in uniform and Pareto samples.
We consider the problem of deciding if there are any outliers in a sample
from a uniform distribution. For a sample from a one parameter uniform distribution
we show that the largest observation in the sample has the smallest
conditional predictive ordinate. Hence we derive the Bayes factor for testing
whether it is an outlier when the amount of contamination is known and
unknown using two di erent outlier models. Then we investigate this problem
when we have multiple outliers, assuming that our outliers are generated
by the same probability distribution or by di erent probability distributions.
Similarly for two parameter uniform samples we show that the most extreme
observation in the sample has the smallest conditional predictive ordinate.
Hence we derive the Bayes factors for testing whether extreme observations
are outliers using the stricter outlier model that we had for the one parameter
case.
We consider the problem of deciding if there are any outliers in a sample
from a Pareto distribution. For a sample from a univariate Pareto distribution
we show that the largest observation in the sample has the smallest conditional
predictive ordinate and derive the Bayes factor for testing whether
Abstract 4
it is an outlier when the amount of contamination is known and unknown.
Then we investigate this problem when we have multiple outliers, assuming
that our outliers are generated by the same probability distribution or
by di erent probability distributions. Finally we extend these ideas to the
multivariate case both when the marginal samples are independent of one
another and when there are correlations/partial correlations.
Authors
Gaby, Benjamin CharlesCollections
- Theses [4122]