Inference for dynamic systems and conformational sampling for protein folding are two problems motivated by applied data, which pose computational challenges from a statistical perspective. Dynamic systems are often described by a set of coupled differential equations, and methods of parametric estimation for these models from noisy data can require repeatedly solving the equations numerically. Many of these models also lead to rough likelihood surfaces, which makes sampling difficult. We introduce a method for Bayesian inference on these models, using a multiple chain framework that exploits the underlying mathematical structure and interpolates the posterior to improve efficiency. In protein folding, a large conformational space must be searched for low energy states, where any energy function constructed on the states is at best approximate. We propose a method for sampling fragment conformations that accounts for geometric and energetic constraints, and explore ideas for folding entire proteins that account for uncertain energy landscapes and learning from data more effectively. These ingredients are combined into a framework for tackling the problem of generating improvements to protein structure predictions. / Statistics

The growth of the Internet has opened up tremendous opportunities for cooperative computations where the results depend on the private data inputs of distributed participating parties. In most cases, such computations are performed by multiple mutually untrusting parties. This has led the research community into studying methods for performing computation across the Internet securely and efficiently. This thesis investigates security methods in the search for an optimum solution to privacy- preserving distributed statistical computation problems. For this purpose, the nonparametric sign test algorithm is chosen as a case for study to demonstrate our research methodology. Two privacy-preserving protocol suites using data perturbation techniques and cryptographic primitives are designed. The first protocol suite, i.e. the P22NSTP, is based on five novel data perturbation building blocks, i.e. the random probability density function generation protocol (RpdfGP), the data obscuring protocol (DOP), the secure two-party comparison protocol (STCP), the data extraction protocol (DEP) and the permutation reverse protocol (PRP). This protocol suite enables two parties to efficiently and securely perform the sign test computation without the use of a third party. The second protocol suite, i.e. the P22NSTC, uses an additively homomorphic encryption scheme and two novel building blocks, i.e. the data separation protocol (DSP) and data randomization protocol (DRP). With some assistance from an on-line STTP, this protocol suite provides an alternative solution for two parties to achieve a secure privacy-preserving nonparametric sign test computation. These two protocol suites have been implemented using MATLAB software. Their implementations are evaluated and compared against the sign test computation algorithm on an ideal trusted third party model (TTP-NST) in terms of security, computation and communication overheads and protocol execution times. By managing the level of noise data item addition, the P22NSTP can achieve specific levels of privacy protection to fit particular computation scenarios. Alternatively, the P22NSTC provides a more secure solution than the P22NSTP by employing an on-line STTP. The level of privacy protection relies on the use of an additively homomorphic encryption scheme, DSP and DRP. A four-phase privacy-preserving transformation methodology has also been demonstrated; it includes data privacy definition, statistical algorithm decomposition, solution design and solution implementation.