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Bayesian Analysis of Cognitive Social Structures
Johan
Koskinen
Summary
This report consists
of the two papers Bayesian Analysis of Perceived Social Networks and Bayesian
Analysis of Cognitive Social Structures with Covariates. Both concern
statistical modelling of reports about social interaction between actors
in social networks. More specifically, they concern the differing views
perceivers have of who is interacting with whom.
In the first paper the focus is on the likelihood function resulting from
a few basic assumptions and what inference procedures could be possible.
For a fixed set of actors it is assumed that there exists one ''true''
constellation of relationships. Observable data consists of the representation
of this ''true'' configuration as perceived and reported by each member
of a set of perceivers. These perceivers could be the set of actors but
not necessarily so. What is estimated is the ''true'' configuration and
the probability that the ''true'' structure is accurately reported allowing
for differences in detection of absent and present relationships respectively.
Applying a Bayesian approach, priors are suggested and posteriors obtained
from an easy to implement Markov chain Monte Carlo algorithm. The issue
of model selection is addressed and a method for obtaining posterior distributions
over models is presented.
In the second paper, the relationship between attributes of the perceivers
and attributes of the actors and the tendencies to underestimate or exaggerate
interaction is developed further, using a probit model. The probabilities,
of ''accurate'' reporting, are modelled as functions of observable covariates.
The covariates can be attributes of the perceivers, attributes of the
actors in the network or can be interaction terms between the two. The
posterior distributions of the coefficients in the probit model and the
posterior of the ''true'' configuration are shown to be obtainable from
a Gibbs sampling scheme involving standard statistical distributions.
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