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

Interdependent Choices in a Social Network;Markov Chain Monte Carlo;Doubly-intractable Distribution;Path Sampling;Bayesian Inference;Statistics and Numeric Data;Science;Statistics

Wang, JingShedden, Kerby A. ;

University of Michigan

关键词: Interdependent Choices in a Social Network;    Markov Chain Monte Carlo;    Doubly-intractable Distribution;    Path Sampling;    Bayesian Inference;    Statistics and Numeric Data;    Science;    Statistics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/86260/jingjw_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

With the advent and continuous growth of social media such as Facebook and Twitter,innovative advertising strategies have been invented to capitalize on the socialnetworks embedding on these websites. Users’ behavior thus becomes more visible totheir friends, which may facilitate social influences. The need to examine and justifythe necessity for new marketing tools calls for statistical models that are capable ofmeasuring 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 hamperedby the existence of intractable normalizing constants. In this thesis, we proposean efficient Markov chain Monte Carlo (MCMC) algorithm to tackle this problem,which allows researchers to fit realistic models to interdependent choice data in aBayesian framework. The theoretical and empirical studies show that our algorithmis asymptotically consistent with good mixing properties, and particularly efficienton large data sets. In addition, we propose a Metropolis-Hastings algorithm to efficientlysimulate social networks from exponential random graph models, which arespecial cases of random field models.To better understand how consumers make choices in a network, we conducted anovel field experiment that mimics interactive advertising on Facebook. A Markovrandom field, estimated by the above MCMC algorithm, and a discrete-time Markovchain are applied to model two different types of data. We are able to build atheoretical connection between the two models. We propose model specifications thatcan 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, whichhas a wide range of applications, including the calculation of Bayes factor, a keyquantity in Bayesian inference. We propose a flexible implementation of the pathsampling identity (Gelman and Meng 1998), which generates a consistent estimator.The preliminary simulation study indicates a good potential of the method.