Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Methods for Imputing Missing Values and Synthesizing Confidential Values for Continuous and Magnitude Data

Abstract

Continuous variable is one of the major data types collected by the survey organizations. It can be incomplete such that the data collectors need to fill in the missingness. Or, it can contain sensitive information which needs protection from re-identification. One of the approaches to protect continuous microdata is to sum them up according to different cells of features. In this thesis, I represents novel methods of multiple imputation (MI) that can be applied to impute missing values and synthesize confidential values for continuous and magnitude data.

The first method is for limiting the disclosure risk of the continuous microdata whose marginal sums are fixed. The motivation for developing such a method comes from the magnitude tables of non-negative integer values in economic surveys. I present approaches based on a mixture of Poisson distributions to describe the multivariate distribution so that the marginals of the synthetic data are guaranteed to sum to the original totals. At the same time, I present methods for assessing disclosure risks in releasing such synthetic magnitude microdata. The illustration on a survey of manufacturing establishments shows that the disclosure risks are low while the information loss is acceptable.

The second method is for releasing synthetic continuous micro data by a nonstandard MI method. Traditionally, MI fits a model on the confidential values and then generates multiple synthetic datasets from this model. Its disclosure risk tends to be high, especially when the original data contain extreme values. I present a nonstandard MI approach conditioned on the protective intervals. Its basic idea is to estimate the model parameters from these intervals rather than the confidential values. The encouraging results of simple simulation studies suggest the potential of this new approach in limiting the posterior disclosure risk.

The third method is for imputing missing values in continuous and categorical variables. It is extended from a hierarchically coupled mixture model with local dependence. However, the new method separates the variables into non-focused (e.g., almost-fully-observed) and focused (e.g., missing-a-lot) ones. The sub-model structure of focused variables is more complex than that of non-focused ones. At the same time, their cluster indicators are linked together by tensor factorization and the focused continuous variables depend locally on non-focused values. The model properties suggest that moving the strongly associated non-focused variables to the side of focused ones can help to improve estimation accuracy, which is examined by several simulation studies. And this method is applied to data from the American Community Survey.

ADVANCED ISLANDING DETECTION METHODS FOR SINGLE PHASE GRID CONNECTED PV INVERTERS

Due to the growing concerns associated with fossil fuels, emphasis has been placed on clean and sustainable energy generation. This has resulted in the increase in Photovoltaics (PV) units being integrated into the utility system. The integration of PV units has raised some concerns for utility power systems, including the consequences of failing to detect islanding. Numerous methods for islanding detection have been introduced in literature. They can be categorized into local methods and remote methods. The local methods are categorically divided into passive and active methods. Active methods generally have smaller Non-Detection Zone (NDZ) but the injecting disturbances will slightly degrade the power quality and reliability of the power system. Slip Mode Frequency Shift Islanding Detection Method (SMS IDM) is an active method that uses positive feedback for islanding detection. In this method, the phase angle of the converter is controlled to have a sinusoidal function of the deviation of the Point of Common Coupling (PCC) voltage frequency from the nominal grid frequency. This method has a non-detection zone which means it fails to detect islanding for specific local load conditions. If the SMS IDM employs a different function other than the sinusoidal function for drifting the phase angle of the inverter, its non-detection zone could be smaller. In addition, Advanced Slip Mode Frequency Shift Islanding Detection Method (Advanced SMS IDM), which has been introduced in this thesis, eliminates the non-detection zone of the SMS IDM. In this method the parameters of SMS IDM change based on the local load impedance value. Moreover, the stability of the system is investigated by developing the dynamical equations of the system for two operation modes; grid connected and islanded mode. It is mathematically proven that for some loading conditions the nominal frequency is an unstable point and the operation frequency slides to another stable point, while for other loading conditions the nominal frequency is the only stable point of the system upon islanding occurring. Simulation and experimental results show the accuracy of the proposed methods in detection of islanding and verify the validity of the mathematical analysis.

Ethical reasoning through simulation: a phenomenological analysis of student experience

Background
Medical students transitioning into professional practice feel underprepared to deal with the emotional complexities of real-life ethical situations. Simulation-based learning (SBL) may provide a safe environment for students to probe the boundaries of ethical encounters. Published studies of ethics simulation have not generated sufficiently deep accounts of student experience to inform pedagogy. The aim of this study was to understand students’ lived experiences as they engaged with the emotional challenges of managing clinical ethical dilemmas within a SBL environment.

Methods
This qualitative study was underpinned by an interpretivist epistemology. Eight senior medical students participated in an interprofessional ward-based SBL activity incorporating a series of ethically challenging encounters. Each student wore digital video glasses to capture point-of-view (PoV) film footage. Students were interviewed immediately after the simulation and the PoV footage played back to them. Interviews were transcribed verbatim. An interpretative phenomenological approach, using an established template analysis approach, was used to iteratively analyse the data.

Results
Four main themes emerged from the analysis: (1) ‘Authentic on all levels?’, (2)‘Letting the emotions flow’, (3) ‘Ethical alarm bells’ and (4) ‘Voices of children and ghosts’. Students recognised many explicit ethical dilemmas during the SBL activity but had difficulty navigating more subtle ethical and professional boundaries. In emotionally complex situations, instances of moral compromise were observed (such as telling an untruth). Some participants felt unable to raise concerns or challenge unethical behaviour within the scenarios due to prior negative undergraduate experiences.

Conclusions
This study provided deep insights into medical students’ immersive and embodied experiences of ethical reasoning during an authentic SBL activity. By layering on the human dimensions of ethical decision-making, students can understand their personal responses to emotion, complexity and interprofessional working. This could assist them in framing and observing appropriate ethical and professional boundaries and help smooth the transition into clinical practice.

Simulation of Distributed Contact in String Instruments: a Modal Expansion Approach

Impactive contact between a vibrating string and a barrier is a strongly nonlinear phenomenon that presents several challenges in the design of numerical models for simulation and sound synthesis of musical string instruments. These are addressed here by applying Hamiltonian methods to incorporate distributed contact forces into a modal framework for discrete-time simulation of the dynamics of a stiff, damped string. The resulting algorithms have spectral accuracy, are unconditionally stable, and require solving a multivariate nonlinear equation that is guaranteed to have a unique solution. Exemplifying results are presented and discussed in terms of accuracy, convergence, and spurious high-frequency oscillations.

Large Numerical Models in Continuous Hybrid Simulation

Hybrid simulation is a technique that combines experimental and numerical testing and has been used for the last decades in the fields of aerospace, civil and mechanical engineering. During this time, most of the research has focused on developing algorithms and the necessary technology, including but not limited to, error minimisation techniques, phase lag compensation and faster hydraulic cylinders. However, one of the main shortcomings in hybrid simulation that has pre- vented its widespread use is the size of the numerical models and the effect that higher frequencies may have on the stability and accuracy of the simulation. The first chapter in this document provides an overview of the hybrid simulation method and the different hybrid simulation schemes, and the corresponding time integration algorithms, that are more commonly used in this field. The scope of this thesis is presented in more detail in chapter 2: a substructure algorithm, the Substep Force Feedback (Subfeed), is adapted in order to fulfil the necessary requirements in terms of speed. The effects of more complex models on the Subfeed are also studied in detail, and the improvements made are validated experimentally. Chapters 3 and 4 detail the methodologies that have been used in order to accomplish the objectives mentioned in the previous lines, listing the different cases of study and detailing the hardware and software used to experimentally validate them. The third chapter contains a brief introduction to a project, the DFG Subshake, whose data have been used as a starting point for the developments that are shown later in this thesis. The results obtained are presented in chapters 5 and 6, with the first of them focusing on purely numerical simulations while the second of them is more oriented towards a more practical application including experimental real-time hybrid simulation tests with large numerical models. Following the discussion of the developments in this thesis is a list of hardware and software requirements that have to be met in order to apply the methods described in this document, and they can be found in chapter 7. The last chapter, chapter 8, of this thesis focuses on conclusions and achievements extracted from the results, namely: the adaptation of the hybrid simulation algorithm Subfeed to be used in conjunction with large numerical models, the study of the effect of high frequencies on the substructure algorithm and experimental real-time hybrid simulation tests with vibrating subsystems using large numerical models and shake tables. A brief discussion of possible future research activities can be found in the concluding chapter.

Methods, Models & Systems for Dealing with Some Business, Management & Engineering Problems

This keynote presentation will report some of our research work and experience on the development and applications of relevant methods, models, systems and simulation techniques in support of different types and various levels of decision making for business, management and engineering. In particular, the following topics will be covered. Modelling, multi-agent-based simulation and analysis of the allocation management of carbon dioxide emission permits in China (Nanfeng Liu & Shuliang Li Agent-based simulation of the dynamic evolution of enterprise carbon assets (Yin Zeng & Shuliang Li) A framework & system for extracting and representing project knowledge contexts using topic models and dynamic knowledge maps: a big data perspective (Jin Xu, Zheng Li, Shuliang Li & Yanyan Zhang) Open innovation: intelligent model, social media & complex adaptive system simulation (Shuliang Li & Jim Zheng Li) A framework, model and software prototype for modelling and simulation for deshopping behaviour and how companies respond (Shawkat Rahman & Shuliang Li) Integrating multiple agents, simulation, knowledge bases and fuzzy logic for international marketing decision making (Shuliang Li & Jim Zheng Li) A Web-based hybrid intelligent system for combined conventional, digital, mobile, social media and mobile marketing strategy formulation (Shuliang Li & Jim Zheng Li) A hybrid intelligent model for Web & social media dynamics, and evolutionary and adaptive branding (Shuliang Li) A hybrid paradigm for modelling, simulation and analysis of brand virality in social media (Shuliang Li & Jim Zheng Li) Network configuration management: attack paradigms and architectures for computer network survivability (Tero Karvinen & Shuliang Li)

An Investigation into the Use of Computer-based Simulation Games for Learning and Teaching in Business Management Courses

Computer-based simulation games (CSG) are a form of innovation in learning and teaching. CGS are used more pervasively in various ways such as a class activity (formative exercises) and as part of summative assessments (Leemkuil and De Jong, 2012; Zantow et al., 2005). This study investigates the current and potential use of CGS in Worcester Business School’s (WBS) Business Management undergraduate programmes. The initial survey of off-the-shelf simulation reveals that there are various categories of simulations, with each offering varying levels of complexity and learning opportunities depending on the field of study. The findings suggest that whilst there is marginal adoption of the use CSG in learning and teaching, there is significant opportunity to increase the use of CSG in enhancing learning and learner achievement, especially in Level 5 modules. The use of CSG is situational and its adoption should be undertaken on a case-by-case basis. WBS can play a major role by creating an environment that encourages and supports the use of CSG as well as other forms of innovative learning and teaching methods. Thus the key recommendation involves providing module teams further support in embedding and integrating CSG into their modules.

Methods for Hypothesis Testing in Animal Carcinogenicity Experiments

Thesis (Ph.D.)--University of Washington, 2016-08

Evaluating New Matrix Pooled Testing Methods for Detecting HIV Treatment Failure with and without Covariate Information

Thesis (Master's)--University of Washington, 2016-08

Vehicle Distance Threshold for Quayside Operations of Container Terminals

Thesis (Master's)--University of Washington, 2016-08

Likelihood-Based Inference for Partially Observed Multi-Type Markov Branching Processes

Thesis (Ph.D.)--University of Washington, 2016-08

DIRECT NUMERICAL SIMULATION OF INCOMPRESSIBLE MULTIPHASE FLOW WITH PHASE CHANGE

Phase change problems arise in many practical applications such as air-conditioning and refrigeration, thermal energy storage systems and thermal management of electronic devices. The physical phenomenon in such applications are complex and are often difficult to be studied in detail with the help of only experimental techniques. The efforts to improve computational techniques for analyzing two-phase flow problems with phase change are therefore gaining momentum. The development of numerical methods for multiphase flow has been motivated generally by the need to account more accurately for (a) large topological changes such as phase breakup and merging, (b) sharp representation of the interface and its discontinuous properties and (c) accurate and mass conserving motion of the interface. In addition to these considerations, numerical simulation of multiphase flow with phase change introduces additional challenges related to discontinuities in the velocity and the temperature fields. Moreover, the velocity field is no longer divergence free. For phase change problems, the focus of developmental efforts has thus been on numerically attaining a proper conservation of energy across the interface in addition to the accurate treatment of fluxes of mass and momentum conservation as well as the associated interface advection. Among the initial efforts related to the simulation of bubble growth in film boiling applications the work in \cite{Welch1995} was based on the interface tracking method using a moving unstructured mesh. That study considered moderate interfacial deformations. A similar problem was subsequently studied using moving, boundary fitted grids \cite{Son1997}, again for regimes of relatively small topological changes. A hybrid interface tracking method with a moving interface grid overlapping a static Eulerian grid was developed \cite{Juric1998} for the computation of a range of phase change problems including, three-dimensional film boiling \cite{esmaeeli2004computations}, multimode two-dimensional pool boiling \cite{Esmaeeli2004} and film boiling on horizontal cylinders \cite{Esmaeeli2004a}. The handling of interface merging and pinch off however remains a challenge with methods that explicitly track the interface. As large topological changes are crucial for phase change problems, attention has turned in recent years to front capturing methods utilizing implicit interfaces that are more effective in treating complex interface deformations. The VOF (Volume of Fluid) method was adopted in \cite{Welch2000} to simulate the one-dimensional Stefan problem and the two-dimensional film boiling problem. The approach employed a specific model for mass transfer across the interface involving a mass source term within cells containing the interface. This VOF based approach was further coupled with the level set method in \cite{Son1998}, employing a smeared-out Heaviside function to avoid the numerical instability related to the source term. The coupled level set, volume of fluid method and the diffused interface approach was used for film boiling with water and R134a at the near critical pressure condition \cite{Tomar2005}. The effect of superheat and saturation pressure on the frequency of bubble formation were analyzed with this approach. The work in \cite{Gibou2007} used the ghost fluid and the level set methods for phase change simulations. A similar approach was adopted in \cite{Son2008} to study various boiling problems including three-dimensional film boiling on a horizontal cylinder, nucleate boiling in microcavity \cite{lee2010numerical} and flow boiling in a finned microchannel \cite{lee2012direct}. The work in \cite{tanguy2007level} also used the ghost fluid method and proposed an improved algorithm based on enforcing continuity and divergence-free condition for the extended velocity field. The work in \cite{sato2013sharp} employed a multiphase model based on volume fraction with interface sharpening scheme and derived a phase change model based on local interface area and mass flux. Among the front capturing methods, sharp interface methods have been found to be particularly effective both for implementing sharp jumps and for resolving the interfacial velocity field. However, sharp velocity jumps render the solution susceptible to erroneous oscillations in pressure and also lead to spurious interface velocities. To implement phase change, the work in \cite{Hardt2008} employed point mass source terms derived from a physical basis for the evaporating mass flux. To avoid numerical instability, the authors smeared the mass source by solving a pseudo time-step diffusion equation. This measure however led to mass conservation issues due to non-symmetric integration over the distributed mass source region. The problem of spurious pressure oscillations related to point mass sources was also investigated by \cite{Schlottke2008}. Although their method is based on the VOF, the large pressure peaks associated with sharp mass source was observed to be similar to that for the interface tracking method. Such spurious fluctuation in pressure are essentially undesirable because the effect is globally transmitted in incompressible flow. Hence, the pressure field formation due to phase change need to be implemented with greater accuracy than is reported in current literature. The accuracy of interface advection in the presence of interfacial mass flux (mass flux conservation) has been discussed in \cite{tanguy2007level,tanguy2014benchmarks}. The authors found that the method of extending one phase velocity to entire domain suggested by Nguyen et al. in \cite{nguyen2001boundary} suffers from a lack of mass flux conservation when the density difference is high. To improve the solution, the authors impose a divergence-free condition for the extended velocity field by solving a constant coefficient Poisson equation. The approach has shown good results with enclosed bubble or droplet but is not general for more complex flow and requires additional solution of the linear system of equations. In current thesis, an improved approach that addresses both the numerical oscillation of pressure and the spurious interface velocity field is presented by featuring (i) continuous velocity and density fields within a thin interfacial region and (ii) temporal velocity correction steps to avoid unphysical pressure source term. Also I propose a general (iii) mass flux projection correction for improved mass flux conservation. The pressure and the temperature gradient jump condition are treated sharply. A series of one-dimensional and two-dimensional problems are solved to verify the performance of the new algorithm. Two-dimensional and cylindrical film boiling problems are also demonstrated and show good qualitative agreement with the experimental observations and heat transfer correlations. Finally, a study on Taylor bubble flow with heat transfer and phase change in a small vertical tube in axisymmetric coordinates is carried out using the new multiphase, phase change method.

Comparison of different methods to detect genetic barriers in a small mammal population

Habitat fragmentation and the consequently the loss of connectivity between populations can reduce the individuals interchange and gene flow, increasing the chances of inbreeding, and the increase the risk of local extinction. Landscape genetics is providing more and better tools to identify genetic barriers.. To our knowledge, no comparison of methods in terms of consistency has been made with observed data and species with low dispersal ability. The aim of this study is to examine the consistency of the results of five methods to detect barriers to gene flow in a Mediterranean pine vole population Microtus duodecimcostatus: F-statistics estimations, Non-Bayesian clustering, Bayesian clustering, Boundary detection and Simple/Partial Mantel tests. All methods were consistent in detecting the stream as a non-genetic barrier. However, no consistency in results among the methods were found regarding the role of the highway as a genetic barrier. Fst, Bayesian clustering assignment test and Partial Mantel test identifyed the highway as a filter to individual interchange. The Mantel tests were the most sensitive method. Boundary detection method (Monmonier’s Algorithm) and Non-Bayesian approaches did not detect any genetic differentiation of the pine vole due to the highway. Based on our findings we recommend that the genetic barrier detection in low dispersal ability populations should be analyzed with multiple methods such as Mantel tests, Bayesian clustering approaches because they show more sensibility in those scenarios and with boundary detection methods by having the aim of detect drastic changes in a variable of interest between the closest individuals. Although simulation studies highlight the weaknesses and the strengths of each method and the factors that promote some results, tests with real data are needed to increase the effectiveness of genetic barrier detection.

A new age of fuel performance code criteria studied through advanced atomistic simulation techniques

A fundamental step in understanding the effects of irradiation on metallic uranium and uranium dioxide ceramic fuels, or any material, must start with the nature of radiation damage on the atomic level. The atomic damage displacement results in a multitude of defects that influence the fuel performance. Nuclear reactions are coupled, in that changing one variable will alter others through feedback. In the field of fuel performance modeling, these difficulties are addressed through the use of empirical models rather than models based on first principles. Empirical models can be used as a predictive code through the careful manipulation of input variables for the limited circumstances that are closely tied to the data used to create the model. While empirical models are efficient and give acceptable results, these results are only applicable within the range of the existing data. This narrow window prevents modeling changes in operating conditions that would invalidate the model as the new operating conditions would not be within the calibration data set. This work is part of a larger effort to correct for this modeling deficiency. Uranium dioxide and metallic uranium fuels are analyzed through a kinetic Monte Carlo code (kMC) as part of an overall effort to generate a stochastic and predictive fuel code. The kMC investigations include sensitivity analysis of point defect concentrations, thermal gradients implemented through a temperature variation mesh-grid, and migration energy values. In this work, fission damage is primarily represented through defects on the oxygen anion sublattice. Results were also compared between the various models. Past studies of kMC point defect migration have not adequately addressed non-standard migration events such as clustering and dissociation of vacancies. As such, the General Utility Lattice Program (GULP) code was utilized to generate new migration energies so that additional non-migration events could be included into kMC code in the future for more comprehensive studies. Defect energies were calculated to generate barrier heights for single vacancy migration, clustering and dissociation of two vacancies, and vacancy migration while under the influence of both an additional oxygen and uranium vacancy.