Complex data structures with intrinsic multivariate and multilevel characteristics arise frequently in various scientific disciplines. This proposal discusses two such application domains, namely, the areas of health monitoring and fingerprint based authentication. The scientific questions posed are usually associated with high-dimensional parameter spaces, such as spaces of point patterns and functions, and are addressed in a conceptually unified and meaningful way with the development of novel hierarchical models on general object spaces. These hierarchical models are flexible and adept at capturing salient data characteristics, such as clustering and spatial dependence, whose forms vary from one application to another. The proposal develops statistical methodology utilizing parametric multivariate generalized linear mixed models and non-parametric Dirichlet process priors, extended to the space of objects, for studying attributes and the effect of covariates encountered in fingerprint and socio-economic-health applications. Due to the high-dimensionality of the intrinsic spaces, several innovative procedures are developed to overcome ensuing computational challenges in the Bayesian framework, including theoretically justified approximations to the likelihood and predictive inference. An added feature of these inferential tools is to extend posterior analysis of quantities such as means, variances and credible sets, in a meaningful way to the space of objects.
The scientific goals addressed in this proposal will benefit research in public and social health, engineering and legal forensics. The impact on societal and demographic policy making, for example, will be in the discovery of socio-demographic regions with extreme health and economic conditions, the identification of their potential causes and in the decisions made to mobilize resources accordingly. The proposed research has impact on how forensic evidence should be reported as well. Many forensic scientists as well as legal scholars have become increasingly aware of the shortcomings of fingerprint evidence as is presented in a court of law, and that methodology for assessing the extent of uniqueness of fingerprints requires further scientific validity. Several of these issues are addressed by developing quantitative methods for reporting fingerprint evidence, for example, when additional fingerprint attributes such as quality are available. This research will have broader impact in health and security surveillance, and their monitoring.