# Browsing by Subject "Bayesian inference"

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Item An evaluation of competing geoacoustic models and their applicability to sandy ocean sediments(2017-12-01) Bonomo, Anthony Lucas; Hamilton, Mark F.; Isakson, Marcia J.; Wilson, Preston S; Ghattas, Omar; Kallivokas, Loukas FShow more This dissertation studies five models that make up a cross section of the geoacoustic models that have been used to study sandy sediments: a simple fluid model, the effective density fluid model (EDFM) of Williams, the viscous grain-shearing (VGS[lambda]) model of Buckingham, the Biot-Stoll model, and the corrected and reparameterized extended Biot (CREB) model of Chotiros. The first objective is to use numerical experiments and model/data comparisons to determine the usefulness and assess the physical validity of these five models. The second objective is to ascertain the current state of knowledge of sandy sediments and describe what truths can be learned from model/data comparisons. To complete these objectives, the models' predictions of geoacoustic quantities such as wave speeds, attenuations, and bottom loss are compared with published measurements and to each other through Bayesian inference and computational studies. It is determined that while each model has its uses, no one model fully captures the wave physics of sandy sediments.Show more Item Bayesian approaches for modeling protein biophysics(2014-08) Hines, Keegan; Aldrich, R. W. (Richard W.)Show more Proteins are the fundamental unit of computation and signal processing in biological systems. A quantitative understanding of protein biophysics is of paramount importance, since even slight malfunction of proteins can lead to diverse and severe disease states. However, developing accurate and useful mechanistic models of protein function can be strikingly elusive. I demonstrate that the adoption of Bayesian statistical methods can greatly aid in modeling protein systems. I first discuss the pitfall of parameter non-identifiability and how a Bayesian approach to modeling can yield reliable and meaningful models of molecular systems. I then delve into a particular case of non-identifiability within the context of an emerging experimental technique called single molecule photobleaching. I show that the interpretation of this data is non-trivial and provide a rigorous inference model for the analysis of this pervasive experimental tool. Finally, I introduce the use of nonparametric Bayesian inference for the analysis of single molecule time series. These methods aim to circumvent problems of model selection and parameter identifiability and are demonstrated with diverse applications in single molecule biophysics. The adoption of sophisticated inference methods will lead to a more detailed understanding of biophysical systems.Show more Item A comparison of two Markov Chain Monte Carlo methods for sampling from unnormalized discrete distributions(2015-05) Gillett, Carlos Townes; Walker, Stephen G., 1945-; Scott, JamesShow more This report compares the convergence behavior of the Metropolis-Hastings and an alternative Markov Chain Monte Carlo sampling algorithm targeting unnormalized, discrete distributions with countably infinite sample spaces. The two methods are compared through a simulation study in which each is used to generate samples from a known distribution. We find that the alternative sampler generates increasingly independent samples as the scale parameter is increased, in contrast to the Metropolis-Hastings. These results suggest that, regardless of the target distribution, our alternative algorithm can generate Markov chains with less autocorrelation than even an optimally scaled Metropolis-Hastings algorithm. We conclude that this alternative algorithm represents a valuable addition to extant Markov Chain Monte Carlo Methods.Show more Item A computational framework for the solution of infinite-dimensional Bayesian statistical inverse problems with application to global seismic inversion(2015-08) Martin, James Robert, Ph. D.; Ghattas, Omar N.; Biros, George; Demkowicz, Leszek; Fomel, Sergey; Marzouk, Youssef; Moser, RobertShow more Quantifying uncertainties in large-scale forward and inverse PDE simulations has emerged as a central challenge facing the field of computational science and engineering. The promise of modeling and simulation for prediction, design, and control cannot be fully realized unless uncertainties in models are rigorously quantified, since this uncertainty can potentially overwhelm the computed result. While statistical inverse problems can be solved today for smaller models with a handful of uncertain parameters, this task is computationally intractable using contemporary algorithms for complex systems characterized by large-scale simulations and high-dimensional parameter spaces. In this dissertation, I address issues regarding the theoretical formulation, numerical approximation, and algorithms for solution of infinite-dimensional Bayesian statistical inverse problems, and apply the entire framework to a problem in global seismic wave propagation. Classical (deterministic) approaches to solving inverse problems attempt to recover the “best-fit” parameters that match given observation data, as measured in a particular metric. In the statistical inverse problem, we go one step further to return not only a point estimate of the best medium properties, but also a complete statistical description of the uncertain parameters. The result is a posterior probability distribution that describes our state of knowledge after learning from the available data, and provides a complete description of parameter uncertainty. In this dissertation, a computational framework for such problems is described that wraps around the existing forward solvers, as long as they are appropriately equipped, for a given physical problem. Then a collection of tools, insights and numerical methods may be applied to solve the problem, and interrogate the resulting posterior distribution, which describes our final state of knowledge. We demonstrate the framework with numerical examples, including inference of a heterogeneous compressional wavespeed field for a problem in global seismic wave propagation with 10⁶ parameters.Show more Item Computational methods for understanding genetic variations from next generation sequencing data(2018-05) Ahn, Soyeon, Ph. D.; Vikalo, Haris; de Veciana, Gustavo; Vishwanath, Sriram; Soloveichik, David; Savran, CagriShow more Studies of human genetic variation reveal critical information about genetic and complex diseases such as cancer, diabetes and heart disease, ultimately leading towards improvements in health and quality of life. Moreover, understanding genetic variations in viral population is of utmost importance to virologists and helps in search for vaccines. Next-generation sequencing technology is capable of acquiring massive amounts of data that can provide insight into the structure of diverse sets of genomic sequences. However, reconstructing heterogeneous sequences is computationally challenging due to the large dimension of the problem and limitations of the sequencing technology.This dissertation is focused on algorithms and analysis for two problems in which we seek to characterize genetic variations: (1) haplotype reconstruction for a single individual, so-called single individual haplotyping (SIH) or haplotype assembly problem, and (2) reconstruction of viral population, the so-called quasispecies reconstruction (QSR) problem. For the SIH problem, we have developed a method that relies on a probabilistic model of the data and employs the sequential Monte Carlo (SMC) algorithm to jointly determine type of variation (i.e., perform genotype calling) and assemble haplotypes. For the QSR problem, we have developed two algorithms. The first algorithm combines agglomerative hierarchical clustering and Bayesian inference to reconstruct quasispecies characterized by low diversity. The second algorithm utilizes tensor factorization framework with successive data removal to reconstruct quasispecies characterized by highly uneven frequencies of its components. Both algorithms outperform existing methods in both benchmarking tests and real data.Show more Item The effects of three different priors for variance parameters in the normal-mean hierarchical model(2010-05) Chen, Zhu, 1985-; Greenberg, Betsy S.; Sager, Thomas W.Show more Many prior distributions are suggested for variance parameters in the hierarchical model. The “Non-informative” interval of the conjugate inverse-gamma prior might cause problems. I consider three priors – conjugate inverse-gamma, log-normal and truncated normal for the variance parameters and do the numerical analysis on Gelman’s 8-schools data. Then with the posterior draws, I compare the Bayesian credible intervals of parameters using the three priors. I use predictive distributions to do predictions and then discuss the differences of the three priors suggested.Show more Item Forward and inverse modeling of fire physics towards fire scene reconstructions(2013-05) Overholt, Kristopher James; Ezekoye, Ofodike A.Show more Fire models are routinely used to evaluate life safety aspects of building design projects and are being used more often in fire and arson investigations as well as reconstructions of firefighter line-of-duty deaths and injuries. A fire within a compartment effectively leaves behind a record of fire activity and history (i.e., fire signatures). Fire and arson investigators can utilize these fire signatures in the determination of cause and origin during fire reconstruction exercises. Researchers conducting fire experiments can utilize this record of fire activity to better understand the underlying physics. In all of these applications, the fire heat release rate (HRR), location of a fire, and smoke production are important parameters that govern the evolution of thermal conditions within a fire compartment. These input parameters can be a large source of uncertainty in fire models, especially in scenarios in which experimental data or detailed information on fire behavior are not available. To better understand fire behavior indicators related to soot, the deposition of soot onto surfaces was considered. Improvements to a soot deposition submodel were implemented in a computational fluid dynamics (CFD) fire model. To better understand fire behavior indicators related to fire size, an inverse HRR methodology was developed that calculates a transient HRR in a compartment based on measured temperatures resulting from a fire source. To address issues related to the uncertainty of input parameters, an inversion framework was developed that has applications towards fire scene reconstructions. Rather than using point estimates of input parameters, a statistical inversion framework based on the Bayesian inference approach was used to determine probability distributions of input parameters. These probability distributions contain uncertainty information about the input parameters and can be propagated through fire models to obtain uncertainty information about predicted quantities of interest. The Bayesian inference approach was applied to various fire problems and coupled with zone and CFD fire models to extend the physical capability and accuracy of the inversion framework. Example applications include the estimation of both steady-state and transient fire sizes in a compartment, material properties related to pyrolysis, and the location of a fire in a compartment.Show more Item Machine learning via particle optimization(2020-08-14) Wang, Dilin; Liu, Qiang, (Ph.D. in computer science); Bajaj, Chandrajit; Huang, Qixing; Pan, Zhigang; Zhou, MingyuanShow more A variety of machine learning problems can be unifiedly viewed as optimizing a set of variables that are invariant to permutations (a.k.a. particles). This includes, for example, finding particle-based approximations of intractable distributions for uncertainty quantification and Bayesian inference, and learning mixture models or neural networks in which the mixture components or neurons in the same layers are permutable. In this dissertation, we take this unified particle optimization view and develop a variety of novel steepest descent algorithms for particle optimization, providing powerful tools for various challenging tasks, including salable and automatic approximate inference, learning diversified mixture models and energy-efficient neural architecture optimization. Part I: By viewing sampling from distributions as optimization of particles, we develop a non-parametric, particle-based variational inference algorithm for approximate inference of intractable distributions. Our algorithm works by moving a set of particles iteratively to form increasingly better approximation of a given target distribution in the sense that KL divergence between the empirical particle distribution and the target distribution is minimized. Our new algorithms greatly increase the scalability of Bayesian inference for both big data and complex models. Part II: By viewing mixture components as particles, we develop a novel and efficient algorithm for learning diversity-promoting mixture models. We leverage an entropy functional to encourage exploration in the parameter space. This diversity-promoting algorithm enables us to build accurate density models of complex data, yielding quantitatively improved explanatory representations of the data. Part III: By viewing the neurons in deep neural networks as particles and investigating new mechanisms for adaptively introducing new particles by splitting existing particles, we develop a new architecture learning framework to progressively grow neural architectures. Our framework efficiently optimizes the loss function, allowing us to learn neural network architectures that are both accurate in prediction and efficient in computational and energy cost.Show more Item Mixtures of triangular densities with applications to Bayesian mode regressions(2014-08) Ho, Chi-San; Damien, Paul, 1960-Show more The main focus of this thesis is to develop full parametric and semiparametric Bayesian inference for data arising from triangular distributions. A natural consequence of working with such distributions is it allows one to consider regression models where the response variable is now the mode of the data distribution. A new family of nonparametric prior distributions is developed for a certain class of convex densities of particular relevance to mode regressions. Triangular distributions arise in several contexts such as geosciences, econometrics, finance, health care management, sociology, reliability engineering, decision and risk analysis, etc. In many fields, experts, typically, have a reasonable idea about the range and most likely values that define a data distribution. Eliciting these quantities is thus, generally, easier than eliciting moments of other commonly known distributions. Using simulated and actual data, applications of triangular distributions, with and without mode regressions, in some of the aforementioned areas are tackled.Show more Item Modeling unobserved heterogeneity of spatially correlated count data using finite-mixture random parameters(2015-05) Buddhavarapu, Prasad Naga Venkata Siva Rama; Scott, James (Statistician); Prozzi, Jorge AShow more The main goal of this research is to propose a specification to model the unobserved heterogeneity in count outcomes. A negative binomial likelihood is utilized for modeling count data. Unobserved heterogeneity is modeled using random model parameters with finite multi-variate normal mixture prior structure. The model simultaneously accounts for potential spatial correlation of crash counts from neighboring units. The model extracts the inherent groups of road segments with crash counts that are equally sensitive to the road attributes on an average; the heterogeneity within these groups is also allowed in the proposed framework. This research employs a computationally efficient Bayesian estimation framework to perform statistical inference of the proposed model. A Markov Chain Monte Carlo (MCMC) sampling strategy is proposed that leverages recent theoretical developments in data-augmentation algorithms, and elegantly sidesteps many of the computational difficulties usually associated with Bayesian inference of count models.Show more Item Novel algorithms for Uncertainty Quantification in large scale systems(2020-05-07) Wahal, Siddhant; Biros, George; Marzouk, Youssef; Ghattas, Omar N; Moser, Robert D; Mueller, PeterShow more Uncertainty Quantification (UQ) algorithms are of increasing significance in science and engineering. The process of modeling physical reality on computers is rife with uncertainties. These uncertainties get propagated through the computer model, leading to uncertain outputs. As decision-makers from every facet of society come to increasingly rely on computer predictions, the need to characterize this uncertainty has never been greater. However, doing so efficiently remains challenging. This is primarily because computer models are often time consuming to run and because their inputs live in high-dimensional spaces that are difficult to explore. In this thesis, we seek to address this challenge in the context of two UQ problems. In the first UQ problem, we study rare-event simulation: given a smooth non-linear map with uncertain inputs, what is the probability that the output evaluates inside a specified interval? Standard statistical approaches for computing this probability, such as the Monte Carlo method, become computationally inefficient as the event under consideration becomes rare. To address this inefficiency, we present two Importance Sampling (IS) algorithms. Our first algorithm, called the Bayesian Inverse Monte Carlo (BIMC) method, relies on solving a fictitious Bayesian inverse problem. The solution of the inverse problem yields a posterior PDF, a local Gaussian approximation to which serves as the importance sampling density. We subject BIMC to rigorous theoretical and experimental analysis, which establishes that BIMC can lead to speedups of several orders-of-magnitude (over the Monte Carlo method) when the forward map is nearly affine, or weakly non-linear. When these conditions are violated, that is, when the forward map is significantly nonlinear, BIMC leads to a poor-quality IS distribution. Motivated by these limitations, we propose modifications to BIMC. The modified algorithm, which we term Adaptive-BIMC (A-BIMC), proceeds in two stages. The first stage roughly identifies those regions in input space that trigger a rare event. The second stage then refines the approximation from the first stage of the algorithm. We study A-BIMC’s performance on synthetic problems and demonstrate that its performance doesn’t depend on how small the target probability is. Rather it depends on the nonlinearity of the input-output map. Through these experiments, we also find that A-BIMC’s performance deteriorates with increasing ambient dimensionality of the problem. To address this issue, we lay the foundation for a general dimension reduction strategy for rare-event probability estimation. The second UQ problem concerns the statistical calibration of model inputs from observed data, with the ultimate aim of issuing uncertainty-equipped predictions of a Quantity-of- Interest (QoI). The physical system that we study here is a hydrocarbon reservoir containing geological faults. Operational decisions concerning the reservoir rely on predictions of financial summaries of the reservoir, such as its Net Present Value. These summaries depend on the nature of fluid flow within the reservoir, which is itself controlled by the extent to which an individual fault inhibits or facilitates flow. This fault property, known as the fault transmissibility, isn’t directly measurable and must be calibrated using production data. Here, we design and analyze a complete data-to-prediction workflow to quantify post-calibration uncertainties. We also discuss how these uncertainties change under different reservoir conditions.Show more Item On a transform for modeling skewness(2020-05-07) Kang, Li, Ph. D.; Walker, Stephen G., 1945-; Damien, Paul, 1960-; Zhou, Mingyuan; Brockett, PatrickShow more In many applications, data exhibit skewness, such as finance, economics and bio-medicine, the outcome variable's data do not stem from symmetric distributions. This thesis is going to present a transform providing skewness, along similar lines to which one would use transforms within a class of density to obtain location and scale. Hence, in order to model data to include location, scale, skewness and shape, one needs only to find a family of densities exhibiting a variety of shapes, since the location, scale and skewness are taken care of via the transformations. The chosen class of density with the variety of shape is the simplest available and presented in the thesis. Multivariate extension and application in regressions are also discussed in this thesis, along with simulation and real data analysis.Show more Item On the representation of model inadequacy : a stochastic operator approach(2016-05) Morrison, Rebecca Elizabeth; Moser, Robert deLancey; Oden, John Tinsley; Ghattas, Omar; Henkelman, Graeme; Oliver, Todd A; Simmons, Christopher SShow more Mathematical models of physical systems are subject to many sources of uncertainty such as measurement errors and uncertain initial and boundary conditions. After accounting for these uncertainties, it is often revealed that there remains some discrepancy between the model output and the observations; if so, the model is said to be inadequate. In practice, the inadequate model may be the best that is available or tractable, and so despite its inadequacy the model may be used to make predictions of unobserved quantities. In this case, a representation of the inadequacy is necessary, so the impact of the observed discrepancy can be determined. We investigate this problem in the context of chemical kinetics and propose a new technique to account for model inadequacy that is both probabilistic and physically meaningful. Chemical reactions are generally modeled by a set of nonlinear ordinary differential equations (ODEs) for the concentrations of the species and temperature. In this work, a stochastic inadequacy operator S is introduced which includes three parts. The first is represented by a random matrix which is embedded within the ODEs of the concentrations. The matrix is required to satisfy several physical constraints, and its most general form exhibits some useful properties, such as having only non-positive eigenvalues. The second is a smaller but specific set of nonlinear terms that also modifies the species’ concentrations, and the third is an operator that properly accounts for changes to the energy equation due to the previous changes. The entries of S are governed by probability distributions, which in turn are characterized by a set of hyperparameters. The model parameters and hyperparameters are calibrated using high-dimensional hierarchical Bayesian inference, with data from a range of initial conditions. This allows the use of the inadequacy operator on a wide range of scenarios, rather than correcting any particular realization of the model with a corresponding data set. We apply the method to typical problems in chemical kinetics including the reaction mechanisms of hydrogen and methane combustion. We also study how the inadequacy representation affects an unobserved quantity of interest— the flamespeed of a one-dimensional hydrogen laminar flame.Show more Item Quantifying and mitigating wind power variability(2015-12) Niu, Yichuan; Santoso, Surya; Arapostathis, Aristotle; Baldick, Ross; Longoria, Raul G.; Tiwari, MohitShow more Understanding variability and unpredictability of wind power is essential for improving power system reliability and energy dispatch in transmission and distribution systems. The research presented herein intends to address a major challenge in managing and utilizing wind energy with mitigated fluctuation and intermittency. Caused by the varying wind speed, power variability can be explained as power imbalances. These imbalances create power surplus or deficiency in respect to the desired demand. To ameliorate the aforementioned issue, the fluctuating wind energy needs to be properly quantified, controlled, and re-distributed to the grid. The first major study in this dissertations is to develop accurate wind turbine models and model reductions to generate wind power time-series in a laboratory time-efficient manner. Reliable wind turbine models can also perform power control events and acquire dynamic responses more realistic to a real-world condition. Therefore, a Type 4 direct-drive wind turbine with power electronic converters has been modeled and designed with detailed aerodynamic and electric parameters based on a given generator. Later, using averaging and approximation techniques for power electronic circuits, the order of the original model is lowered to boost the computational efficiency for simulating long-term wind speed data. To quantify the wind power time-series, efforts are made to enhance adaptability and robustness of the original conditional range metric (CRM) algorithm that has been proposed by literatures for quantitatively assessing the power variability within a certain time frame. The improved CRM performs better under scarce and noisy time-series data with a reduced computational complexity. Rather than using a discrete probability model, the improved method implements a continuous gamma distribution with parameters estimated by the maximum likelihood estimators. With the leverage from the aforementioned work, a wind farm level behavior can be revealed by analyzing the data through long-term simulations using individual wind turbine models. Mitigating the power variability by reserved generation sources is attempted and the generation scenarios are generalized using an unsupervised machine learning algorithm regarding power correlations of those individual wind turbines. A systematic blueprint for reducing intra-hour power variations via coordinating a fast- and a slow- response energy storage systems (ESS) has been proposed. Methods for sizing, coordination control, ESS regulation, and power dispatch schemes are illustrated in detail. Applying the real-world data, these methods have been demonstrated desirable for reducing short-term wind power variability to an expected level.Show more Item The relationships between crime rate and income inequality : evidence from China(2013-08) Zhang, Wenjie, active 2013; Scott, James (Statistician)Show more The main purpose of this study is to determine if a Bayesian approach can better capture and provide reasonable predictions for the complex linkage between crime and income inequality. In this research, we conduct a model comparison between classical inference and Bayesian inference. The conventional studies on the relationship between crime and income inequality usually employ regression analysis to demonstrate whether these two issues are associated. However, there seems to be lack of use of Bayesian approaches in regard to this matter. Studying the panel data of China from 1993 to 2009, we found that in addition to a linear mixed effects model, a Bayesian hierarchical model with informative prior is also a good model to describe the linkage between crime rate and income inequality. The choice of models really depends on the research needs and data availability.Show more Item Safe and efficient inverse reinforcement learning(2020-08) Brown, Daniel Sundquist; Niekum, Scott David; Stone, Peter; Topcu, Ufuk; Dragan, AncaShow more As robots and other autonomous agents enter our homes, hospitals, schools, and workplaces, it is important that they can safely and efficiently infer and adapt to human preferences. One common way to teach human preferences to robots and other autonomous agents is through imitation learning, where an agent learns by observing demonstrations of how to perform a task. Imitation learning has the potential to allow everyday users the ability to program and adapt the behavior of an autonomous agent simply by showing it how to perform a task. However, for imitation learning algorithms to be deployed in complex, possibly high-risk situations, it is important that these algorithms can provide practical, high-confidence bounds on performance. If a robot is to reason effectively about its performance when learning from demonstrations, it needs to infer the goals and intent of the demonstrator. One common way to infer goals and intentions from demonstrations is through inverse reinforcement learning, where the goal is to infer the reward function of the demonstrator. However, most inverse reinforcement learning algorithms have limited real-world applicability because they do not provide practical assessments of safety, often require large numbers of demonstrations, and have high computational costs. This dissertation addresses these shortcomings by developing efficient inverse reinforcement learning algorithms that allow autonomous agents to provide high-confidence bounds on performance when learning from demonstrations. We first formalize the problem of safe imitation learning via high-confidence performance bounds. We then present a general Bayesian framework for computing tight high-confidence performance bounds on any evaluation policy when the true reward function is unknown and must be inferred from demonstrations. The method we propose is sample-efficient, but is computationally inefficient for learning in complex, high-dimensional tasks. To address this computational inefficiency, we first introduce a computationally efficient algorithm for reward learning via ranked demonstrations. We show that preference rankings over demonstrations enable reward inference algorithms to scale to high-dimensional imitation learning tasks such as learning to play Atari games with no access to the score, but with access to a few suboptimal, ranked demonstrations. We also show that preference rankings allow for better-than-demonstrator performance and that rankings over demonstrations can sometimes be obtained automatically, without requiring access to explicit preference labels. Furthermore, we leverage the computational efficiency of reward learning via preferences to scale high-confidence policy evaluation to complex imitation learning settings with high-dimensional, visual demonstrations. While our work on high-confidence policy evaluation gives efficient bounds on the performance of an imitation learning agent, it does not answer the question of what an agent should do to learn a policy that is safe with high probability. The final contributions of this dissertation are two different approaches for robust policy optimization for imitation learning. We first derive an algorithm that directly optimizes a policy to balance risk and expected return under a reward function posterior given a fixed set of demonstrations. Second, we address the problem of robust policy optimization via active learning. We present a sample-efficient, active inverse reinforcement learning algorithm that generates risk-aware queries that enable robust policy improvement via repeated interactions with a demonstrator.Show more Item Scalable and causal Bayesian inference(2021-08-30) Chavez, Omar Demian; Williamson, Sinead; Daniels, Michael J; Linero, Antonio; Shively, TomShow more This thesis will focus on two facets of Bayesian estimation. First, we propose methods that can improve parameter estimation in particle filtering when making use of a distributed computing environment by allowing for periodic communication between compute nodes. The periodic communication can improve the embarrassingly parallel version of our particle filter without dramatically increasing the computational costs. Our method is intended for use on data with large N or in streaming settings where latent parameters are changing over time. Secondly, we propose a method for estimating heterogeneous treatment effects in observational studies using transformed response variables via a modification to Bayesian additive regression trees that incorporates a mixture model in the regression error terms.Show more Item Selection, calibration, and validation of coarse-grained models of atomistic systems(2015-05) Farrell, Kathryn Anne; Oden, J. Tinsley (John Tinsley), 1936-; Prudhomme, Serge M.; Babuska, Ivo; Bui-Thanh, Tan; Demkowicz, Leszek; Elber, RonShow more This dissertation examines the development of coarse-grained models of atomistic systems for the purpose of predicting target quantities of interest in the presence of uncertainties. It addresses fundamental questions in computational science and engineering concerning model selection, calibration, and validation processes that are used to construct predictive reduced order models through a unified Bayesian framework. This framework, enhanced with the concepts of information theory, sensitivity analysis, and Occam's Razor, provides a systematic means of constructing coarse-grained models suitable for use in a prediction scenario. The novel application of a general framework of statistical calibration and validation to molecular systems is presented. Atomistic models, which themselves contain uncertainties, are treated as the ground truth and provide data for the Bayesian updating of model parameters. The open problem of the selection of appropriate coarse-grained models is addressed through the powerful notion of Bayesian model plausibility. A new, adaptive algorithm for model validation is presented. The Occam-Plausibility ALgorithm (OPAL), so named for its adherence to Occam's Razor and the use of Bayesian model plausibilities, identifies, among a large set of models, the simplest model that passes the Bayesian validation tests, and may therefore be used to predict chosen quantities of interest. By discarding or ignoring unnecessarily complex models, this algorithm contains the potential to reduce computational expense with the systematic process of considering subsets of models, as well as the implementation of the prediction scenario with the simplest valid model. An application to the construction of a coarse-grained system of polyethylene is given to demonstrate the implementation of molecular modeling techniques; the process of Bayesian selection, calibration, and validation of reduced-order models; and OPAL. The potential of the Bayesian framework for the process of coarse graining and of OPAL as a means of determining a computationally conservative valid model is illustrated on the polyethylene example.Show more Item Stochastic SIR-based Examination of the Policy Effects on the COVID-19 Spread in the U.S. States(2020) Song, Mina; Belle, Macy; Mendlovitz, Aaron; Han, DavidShow more Since the global outbreak of the novel COVID-19, many research groups have studied the epidemiology of the virus for short-term forecasts and to formulate the effective disease containment and mitigation strategies. The major challenge lies in the proper assessment of epidemiological parameters over time and of how they are modulated by the effect of any publicly announced interventions. Here we attempt to examine and quantify the effects of various (legal) policies/orders in place to mandate social distancing and to flatten the curve in each of the U.S. states. Through Bayesian inference on the stochastic SIR models of the virus spread, the effectiveness of each policy on reducing the magnitude of the growth rate of new infections is investigated statistically. This will inform the public and policymakers, and help them understand the most effective actions to fight against the current and future pandemics. It will aid the policy-makers to respond more rapidly (select, tighten, and/or loosen appropriate measures) to stop/mitigate the pandemic early on.Show more Item Value of information and the accuracy of discrete approximations(2010-08) Ramakrishnan, Arjun; Bickel, J. Eric; Lake, Larry W.Show more Value of information is one of the key features of decision analysis. This work deals with providing a consistent and functional methodology to determine VOI on proposed well tests in the presence of uncertainties. This method strives to show that VOI analysis with the help of discretized versions of continuous probability distributions with conventional decision trees can be very accurate if the optimal method of discrete approximation is chosen rather than opting for methods such as Monte Carlo simulation to determine the VOI. This need not necessarily mean loss of accuracy at the cost of simplifying probability calculations. Both the prior and posterior probability distributions are assumed to be continuous and are discretized to find the VOI. This results in two steps of discretizations in the decision tree. Another interesting feature is that there lies a level of decision making between the two discrete approximations in the decision tree. This sets it apart from conventional discretized models since the accuracy in this case does not follow the rules and conventions that normal discrete models follow because of the decision between the two discrete approximations. The initial part of the work deals with varying the number of points chosen in the discrete model to test their accuracy against different correlation coefficients between the information and the actual values. The latter part deals more with comparing different methods of existing discretization methods and establishing conditions under which each is optimal. The problem is comprehensively dealt with in the cases of both a risk neutral and a risk averse decision maker.Show more