Approximate Sampling for Doubly-intractable Distributions and Modeling Choice Interdependence in a Social Network.

With the advent and continuous growth of social media such as Facebook and Twitter, innovative advertising strategies have been invented to capitalize on the social networks embedding on these websites. Users’ behavior thus becomes more visible to their friends, which may facilitate social influences. The need to examine and justify the necessity for new marketing tools calls for statistical models that are capable of measuring and quantifying the effect of social network in this process. Random field models offer a class of statistical models to realize this objective. However, the applicability of many models, such as Markov random fields, is hampered by the existence of intractable normalizing constants. In this thesis, we propose an efficient Markov chain Monte Carlo (MCMC) algorithm to tackle this problem, which allows researchers to fit realistic models to interdependent choice data in a Bayesian framework. The theoretical and empirical studies show that our algorithm is asymptotically consistent with good mixing properties, and particularly efficient on large data sets. In addition, we propose a Metropolis-Hastings algorithm to efficiently simulate social networks from exponential random graph models, which are special cases of random field models. To better understand how consumers make choices in a network, we conducted a novel field experiment that mimics interactive advertising on Facebook. A Markov random field, estimated by the above MCMC algorithm, and a discrete-time Markov chain are applied to model two different types of data. We are able to build a theoretical connection between the two models. We propose model specifications that can accommodate multiple sources of dependence and asymmetric social interactions. Our findings suggest that consumers rely on choices of others both at the micro (friends) and macro (a reference group) levels in making their own decisions. Finally, we study the problem of estimating ratio of normalizing constants, which has a wide range of applications, including the calculation of Bayes factor, a key quantity in Bayesian inference. We propose a flexible implementation of the path sampling identity (Gelman and Meng 1998), which generates a consistent estimator. The preliminary simulation study indicates a good potential of the method.PhDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86260/1/jingjw_1.pd