Bayesian methods and computation in complex models

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The main objective of the proposed research program is to develop new Bayesian methodologies that deal with complex model structures. Two of the main areas of application are network data and ordinal survey data.For most standard types of data, there are well-developed approaches guiding sampling, modelling and inference. However, in many areas of application including, in particular, network problems and survey data, non-standard datasets have been collected that require innovative analyses. As an example, Data may be continuous or discrete, there may be complex dependencies, relationships may be directed or non-directed, data may be dynamic, multivariate, have missing values, include covariates, etc. In these problems, it is also possible that there are partitions of the data such that data within classes are similar. These types of complexities rarely allow a researcher to consider a simple model structure that explains the reality of the problem.In the case of complex models, complex posteriors are usually leading to integration problems that cannot be solved analytically. Instead, simulation procedures are often used to sample variates from the posterior. In this proposal, I consider the development of new methodologies to facilitate sampling, modelling and inference on network and survey models. The methodologies will be generalized to many applications of network analysis such as citation analysis which identifies influential papers in a research area, dynamics of the spread of disease in epidemiology, identifying most effective areas for product/service distributions in business and telecommunications and coalition formation dynamics in political science. In the context of survey data, as a by-product of the proposed methodologies in this proposal, one can identify survey questions where the corresponding performance has been poor or exceptional and also the survey questions that are redundant. This is important in the cost management of survey.