## Using Approximate Bayesian Computation to understand the distribution of genetic diversity in eastern massasauga rattlesnakes (Sistrurus catenatus catenatus)

## Interpreting scratch assays using pair density dynamics and approximate Bayesian computation

## Kernel Approximate Bayesian Computation for Population Genetic Inferences

## Accelerating inference for diffusions observed with measurement error and large sample sizes using Approximate Bayesian Computation

## Fast Approximate Bayesian Computation for discretely observed Markov models using a factorised posterior distribution

## Diagnostic tools of approximate Bayesian computation using the coverage property

## Adaptive approximate Bayesian computation for complex models

## Approximate Bayesian Computation: a nonparametric perspective

## On Consistency of Approximate Bayesian Computation

## Extending approximate Bayesian computation methods to high dimensions via Gaussian copula

## Approximate Bayesian Computation via Regression Density Estimation

## Approximate Bayesian computation and Bayes linear analysis: Towards high-dimensional ABC

## Sequential Monte Carlo with Adaptive Weights for Approximate Bayesian Computation

## Adaptive approximate Bayesian computation

## A comparison of emulation methods for Approximate Bayesian Computation

## Deviance Information Criteria for Model Selection in Approximate Bayesian Computation

## AABC: approximate approximate Bayesian computation when simulating a large number of data sets is computationally infeasible

## Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

## Approximate Bayesian Computation for Complex Dynamic Systems

This thesis focuses on the development of ABC methods for statistical modeling in complex dynamic systems. Motivated by real applications in biology, I propose computational strategies for Bayesian inference in contexts where standard Monte Carlo methods cannot be directly applied due to the high complexity of the dynamic model and/or data limitations.

Chapter 2 focuses on stochastic bionetwork models applied to data generated from the marginal distribution of a few network nodes at snapshots in time. I present a Bayesian computational strategy, coupled with an approach to summarizing and numerically characterizing biological phenotypes that are represented in terms of the resulting sample distributions of cellular markers. ABC and mixture modeling are used to define the approach to linking mechanistic mathematical models of network dynamics to snapshot data, using a toggle switch example integrating simulated and real data as context.

Chapter 3 focuses on the application of the methodology presented in Chapter 2 to the Myc/Rb/E2F network. This network involves a relatively high number of parameters and stochastic equations in the model specification and, thus, is substantially more complex than the toggle switch example. The analysis of the Myc/Rb/E2F network is performed with simulated and real data. I demonstrate that the proposed method can indicate which parameters can be learned about using the marginal data.

In Chapter 4...

## Topics in Modern Bayesian Computation

Collections of large volumes of rich and complex data has become ubiquitous in recent years, posing new challenges in methodological and theoretical statistics alike. Today, statisticians are tasked with developing flexible methods capable of adapting to the degree of complexity and noise in increasingly rich data gathered across a variety of disciplines and settings. This has spurred the need for novel multivariate regression techniques that can efficiently capture a wide range of naturally occurring predictor-response relations, identify important predictors and their interactions and do so even when the number of predictors is large but the sample size remains limited.

Meanwhile, efficient model fitting tools must evolve quickly to keep pace with the rapidly growing dimension and complexity of data they are applied to. Aided by the tremendous success of modern computing, Bayesian methods have gained tremendous popularity in recent years. These methods provide a natural probabilistic characterization of uncertainty in the parameters and in predictions. In addition, they provide a practical way of encoding model structure that can lead to large gains in statistical estimation and more interpretable results. However, this flexibility is often hindered in applications to modern data which are increasingly high dimensional...