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.
展开▼
机译：随着诸如Facebook和Twitter之类的社交媒体的出现和持续增长，已经发明了创新的广告策略来利用嵌入在这些网站上的社交网络。用户的行为因此对他们的朋友变得更加可见，这可以促进社会影响。需要检查和证明使用新营销工具的必要性，因此需要能够测量和量化社交网络在此过程中的影响的统计模型。随机字段模型提供了一类统计模型来实现此目标。但是，由于难于归一化常数的存在，许多模型（例如马尔可夫随机场）的适用性受到限制。在本文中，我们提出了一种有效的马尔可夫链蒙特卡洛（MCMC）算法来解决该问题，这使研究人员可以将现实模型拟合到贝叶斯框架中相互依赖的选择数据。理论和经验研究表明，我们的算法渐近一致且具有良好的混合特性，并且在大型数据集上特别有效。此外，我们提出了一种Metropolis-Hastings算法，可从指数随机图模型（这是随机字段模型的特殊情况）有效地模拟社交网络；为了更好地了解消费者如何在网络中做出选择，我们进行了模仿在Facebook上进行互动广告。通过上述MCMC算法估计的马尔可夫随机场和离散时间马尔可夫链被应用于对两种不同类型的数据进行建模。我们能够在两个模型之间建立理论联系。我们提出了模型规范，该模型规范可以容纳依赖和不对称社会互动的多种来源。我们的发现表明，消费者在做出自己的决定时依赖微观（朋友）和宏观（参考群体）两个人的选择。最后，我们研究了归一化常数比率的估计问题，该问题范围很广。应用程序，包括贝叶斯因子的计算，贝叶斯因子是贝叶斯推理中的关键量。我们提出了路径采样标识的灵活实现（Gelman and Meng 1998），它产生了一个一致的估计量。初步的仿真研究表明该方法具有良好的潜力。
展开▼
