Variability of the IFN-γ ELISpot assay in the context of proficiency testing and bridging studies.

Assays that assess cellular mediated immune responses performed under Good Clinical Laboratory Practice (GCLP) guidelines are required to provide specific and reproducible results. Defined validation procedures are required to establish the Standard Operating Procedure (SOP), include pass and fail criteria, as well as implement positivity criteria. However, little to no guidance is provided on how to perform longitudinal assessment of the key reagents utilized in the assay. Through the External Quality Assurance Program Oversight Laboratory (EQAPOL), an Interferon-gamma (IFN-γ) Enzyme-linked immunosorbent spot (ELISpot) assay proficiency testing program is administered. A limit of acceptable within site variability was estimated after six rounds of proficiency testing (PT). Previously, a PT send-out specific within site variability limit was calculated based on the dispersion (variance/mean) of the nine replicate wells of data. Now an overall 'dispersion limit' for the ELISpot PT program within site variability has been calculated as a dispersion of 3.3. The utility of this metric was assessed using a control sample to calculate the within (precision) and between (accuracy) experiment variability to determine if the dispersion limit could be applied to bridging studies (studies that assess lot-to-lot variations of key reagents) for comparing the accuracy of results with new lots to results with old lots. Finally, simulations were conducted to explore how this dispersion limit could provide guidance in the number of replicate wells needed for within and between experiment variability and the appropriate donor reactivity (number of antigen-specific cells) to be used for the evaluation of new reagents. Our bridging study simulations indicate using a minimum of six replicate wells of a control donor sample with reactivity of at least 150 spot forming cells per well is optimal. To determine significant lot-to-lot variations use the 3.3 dispersion limit for between and within experiment variability.

Bayesian Learning with Dependency Structures via Latent Factors, Mixtures, and Copulas

Bayesian methods offer a flexible and convenient probabilistic learning framework to extract interpretable knowledge from complex and structured data. Such methods can characterize dependencies among multiple levels of hidden variables and share statistical strength across heterogeneous sources. In the first part of this dissertation, we develop two dependent variational inference methods for full posterior approximation in non-conjugate Bayesian models through hierarchical mixture- and copula-based variational proposals, respectively. The proposed methods move beyond the widely used factorized approximation to the posterior and provide generic applicability to a broad class of probabilistic models with minimal model-specific derivations. In the second part of this dissertation, we design probabilistic graphical models to accommodate multimodal data, describe dynamical behaviors and account for task heterogeneity. In particular, the sparse latent factor model is able to reveal common low-dimensional structures from high-dimensional data. We demonstrate the effectiveness of the proposed statistical learning methods on both synthetic and real-world data.

Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.