BAYESIAN
AND OTHER APPROACHES FOR
ANALYZING NETWORK BLOCKSTRUCTURES
Akademisk
avhandling
som för avläggande av filosofie doktorsexamen
vid Stockholms universitet
offentligen försvaras i
Hörsal 8, hus D, Södra huset, Frescati
tisdagen den 27 maj 2003 kl 13.00
av
Christian Tallberg
fil lic
Statistiska
institutionen
Stockholms universitet

Abstract
This thesis is concerned
with statistical analysis within a field usually referred to as social
network analysis. The major distinguishing feature of this field is that
the basic data units are attributes of the network members as well as
attributes of specific relations between the network members. The analysis
of such data requires a set of methods and analytic concepts that are
to a large extent distinct from the methods of traditional statistics
and data analysis.
The thesis consists of four papers titled ''Testing centrality in random
graphs'', ''Estimating the size of hidden populations: A Bayesian approach'',
''A Bayesian approach to modeling stochastic blockstructures with covariates''
and ''Bayesian estimation of blockstructures from snowball samples''.
The first paper deals with the important concept of network centrality,
i.e. the presence of one or several network members with a particularly
rich contact pattern. Eight different measures of graph centrality are
used as test statistics of graph centrality and the performance of the
tests is evaluated by comparing their power functions.
The second paper concerns statistical inference in so called hidden populations,
that is populations consisting of individuals who are reluctant to disclose
themselves, e.g. populations of drug users. The main focus is the size
of the population which is estimated by Bayesian methods from a so called
snowball sample. The performance of the posterior mean estimator of the
population size under repeated sampling is compared to the maximum likelihood
estimator using simulation methods.
A Bayesian approach to blockmodels is presented in the third paper. Covariates
on actor level are included in the model, and the block affiliation probabilities
are modeled conditional on the covariates via a multinomial probit model.
Posterior distributions of the model parameters, and predictive posterior
distributions of the block affiliation probabilities are computed by Gibbs
sampling.
In the fourth and last paper, we once again consider the problem of estimating
the size of a hidden population using the snowball sampling design. This
time we assume that the contact patterns among the members follow a probabilistic
blockmodel. A Bayesian analysis to compute posterior distributions of
model parameters is derived both when the block labels are known and unknown.
Key words: Bayesian
inference, Blockmodel, Centrality, Hidden population, Social network,
Snowball sampling.
ISBN 9172656662
