Goal-oriented inference : theoretical foundations and application to carbon capture and storage

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2013.This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from department-submitted PDF version of thesis.Includes bibliographical references (p. 127-132).Many important engineering problems require computation of prediction output quantities of interest that depend on unknown distributed parameters of the governing partial differential equations. Examples include prediction of concentration levels in critical areas for contamination events in urban areas and prediction of trapped volume of supercritical carbon dioxide in carbon capture and storage. In both cases the unknown parameter is a distributed quantity that is to be inferred from indirect and sparse data in order to make accurate predictions of the quantities of interest. Traditionally parameter inference involves regularization in deterministic formulations or specification of a prior probability density in Bayesian statistical formulations to resolve the ill-posedness manifested in the many possible parameters giving rise to the same observed data. Critically, the final prediction requirements are not considered in the inference process. Goal-oriented inference, on the other hand, utilizes the prediction requirements to drive the inference process. Since prediction quantities of interest are often very low-dimensional, the same ill-posedness that stymies the inference process can be exploited when inference of the parameter is undertaken solely to obtain predictions. Many parameters give rise to the same predictions; as a result, resolving the parameter is not required in order to accurately make predictions. In goal-oriented inference, we exploit this fact to obtain fast and accurate predictions from experimental data by sacrificing accuracy in parameter estimation. When the governing models for experimental data and prediction quantities of interest depend linearly on the parameter, a linear algebraic analysis reveals a dimensionally-optimal parameter subspace within which inference proceeds. Parameter estimates are inaccurate but the resulting predictions are identical to those achieved by first performing inference in the full high-dimensional parameter space and then computing predictions. The analysis required to identify the parameter subspace reveals inefficiency in experiment and sources of uncertainty in predictions, which can also be utilized in experimental design. Linear goal-oriented inference is demonstrated on a model problem in contaminant source inversion and prediction. In the nonlinear setting, we focus on the Bayesian statistical inverse problem formulation where the target of our goal-oriented inference is the posterior predictive probability density function representing the relative likelihood of predictions given the observed experimental data. In many nonlinear settings, particularly those involving nonlinear partial differential equations, distributed parameter estimation remains an unsolved problem. We circumvent estimation of the parameter by establishing a statistical model for the joint density of experimental data and predictions using either a Gaussian mixture model or kernel density estimate derived from simulated experimental data and simulated predictions based on parameter samples from the prior distribution. When experiments are conducted and data are observed, the statistical model is conditioned on the observed data, and the posterior predictive probability density is obtained. Nonlinear goal-oriented inference is applied to a realistic application in carbon capture and storage.by Chad Lieberman.Ph.D

Parameter and state model reduction for Bayesian statistical inverse problems

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 113-118).Decisions based on single-point estimates of uncertain parameters neglect regions of significant probability. We consider a paradigm based on decision-making under uncertainty including three steps: identification of parametric probability by solution of the statistical inverse problem, propagation of that uncertainty through complex models, and solution of the resulting stochastic or robust mathematical programs. In this thesis we consider the first of these steps, solution of the statistical inverse problem, for partial differential equations (PDEs) parameterized by field quantities. When these field variables and forward models are discretized, the resulting system is high-dimensional in both parameter and state space. The system is therefore expensive to solve. The statistical inverse problem is one of Bayesian inference. With assumption on prior belief about the form of the parameter and an assignment of normal error in sensor measurements, we derive the solution to the statistical inverse problem analytically, up to a constant of proportionality. The parametric probability density, or posterior, depends implicitly on the parameter through the forward model. In order to understand the distribution in parameter space, we must sample. Markov chain Monte Carlo (MCMC) sampling provides a method by which a random walk is constructed through parameter space. By following a few simple rules, the random walk converges to the posterior distribution and the resulting samples represent draws from that distribution. This set of samples from the posterior can be used to approximate its moments.(cont.) In the multi-query setting, it is computationally intractable to utilize the full-order forward model to perform the posterior evaluations required in the MCMC sampling process. Instead, we implement a novel reduced-order model which reduces in parameter and state. The reduced bases are generated by greedy sampling. We iteratively sample the field in parameter space which maximizes the error in full-order and current reduced-order model outputs. The parameter is added to its basis and then a high-fidelity forward model is solved for the state, which is then added to the state basis. The reduction in state accelerates posterior evaluation while the reduction in parameter allows the MCMC sampling to be conducted with a simpler, non-adaptive 3 Metropolis-Hastings algorithm. In contrast, the full-order parameter space is high-dimensional and requires more expensive adaptive methods. We demonstrate for the groundwater inverse problem in 1-D and 2-D that the reduced-order implementation produces accurate results with a factor of three speed up even for the model problems of dimension N ~~500. Our complexity analysis demonstrates that the same approach applied to the large-scale models of interest (e.g. N > 10⁴) results in a speed up of three orders of magnitude.by Chad Eric Lieberman.S.M

Development of Glucose Regularted Protein 94-Selective Inhibitors Based on the Bnlm and Radamide Scaffold

Glucose regulated protein 94 (Grp94) is the endoplasmic reticulum resident of the heat shock protein 90 kDa (Hsp90) family of molecular chaperones. Grp94 associates with many proteins involved in cell adhesion and signaling, including integrins, Toll-like receptors, immunoglobulins, and mutant myocilin. Grp94 has been implicated as a target for several therapeutic areas including glaucoma, cancer metastasis, and multiple myeloma. While 85% identical to other Hsp90 isoforms, the N-terminal ATP-binding site of Grp94 possesses a unique hydrophobic pocket that was used to design isoform-selective inhibitors. Incorporation of a cis-amide bioisostere into the radamide scaffold led to development of the original Grp94-selective inhibitor, BnIm. Structure–activity relationship studies have now been performed on the aryl side chain of BnIm, which resulted in improved analogues that exhibit better potency and selectivity for Grp94. These analogues also manifest superior antimigratory activity in a metastasis model as well as enhanced mutant myocilin degradation in a glaucoma model compared to BnIm

International consensus on (ICON) anaphylaxis

ICON: Anaphylaxis provides a unique perspective on the principal evidence-based anaphylaxis guidelines developed and published independently from 2010 through 2014 by four allergy/immunology organizations. These guidelines concur with regard to the clinical features that indicate a likely diagnosis of anaphylaxis -- a life-threatening generalized or systemic allergic or hypersensitivity reaction. They also concur about prompt initial treatment with intramuscular injection of epinephrine (adrenaline) in the mid-outer thigh, positioning the patient supine (semi-reclining if dyspneic or vomiting), calling for help, and when indicated, providing supplemental oxygen, intravenous fluid resuscitation and cardiopulmonary resuscitation, along with concomitant monitoring of vital signs and oxygenation. Additionally, they concur that H1-antihistamines, H2-antihistamines, and glucocorticoids are not initial medications of choice. For self-management of patients at risk of anaphylaxis in community settings, they recommend carrying epinephrine auto-injectors and personalized emergency action plans, as well as follow-up with a physician (ideally an allergy/immunology specialist) to help prevent anaphylaxis recurrences. ICON: Anaphylaxis describes unmet needs in anaphylaxis, noting that although epinephrine in 1 mg/mL ampules is available worldwide, other essentials, including supplemental oxygen, intravenous fluid resuscitation, and epinephrine auto-injectors are not universally available. ICON: Anaphylaxis proposes a comprehensive international research agenda that calls for additional prospective studies of anaphylaxis epidemiology, patient risk factors and co-factors, triggers, clinical criteria for diagnosis, randomized controlled trials of therapeutic interventions, and measures to prevent anaphylaxis recurrences. It also calls for facilitation of global collaborations in anaphylaxis research. In addition to confirming the alignment of major anaphylaxis guidelines, ICON: Anaphylaxis adds value by including summary tables and citing 130 key references. It is published as an information resource about anaphylaxis for worldwide use by healthcare professionals, academics, policy-makers, patients, caregivers, and the public

Vertebroplasty and kyphoplasty: a comparative review of efficacy and adverse events

Vertebroplasty and kyphoplasty have become common surgical techniques for the treatment of vertebral compression fractures. Vertebroplasty involves the percutaneous injection of bone cement into the cancellous bone of a vertebral body with the goals of pain alleviation and preventing further loss of vertebral body height. Kyphoplasty utilizes an inflatable balloon to create a cavity for the cement with the additional potential goals of restoring height and reducing kyphosis. Vertebroplasty and kyphoplasty are effective treatment options for the reduction of pain associated with vertebral body compression fractures. Biomechanical studies demonstrate that kyphoplasty is initially superior for increasing vertebral body height and reducing kyphosis, but these gains are lost with repetitive loading. Complications secondary to extravasation of cement include compression of neural elements and venous embolism. These complications are rare but more common with vertebroplasty. Vertebroplasty and kyphoplasty are both safe and effective procedures for the treatment of vertebral body compression fractures

Microduplications of 16p11.2 are associated with schizophrenia

Recurrent microdeletions and microduplications of a 600-kb genomic region of chromosome 16p11.2 have been implicated in childhood-onset developmental disorders1,2,3. We report the association of 16p11.2 microduplications with schizophrenia in two large cohorts. The microduplication was detected in 12/1,906 (0.63%) cases and 1/3,971 (0.03%) controls (P = 1.2 × 10−5, OR = 25.8) from the initial cohort, and in 9/2,645 (0.34%) cases and 1/2,420 (0.04%) controls (P = 0.022, OR = 8.3) of the replication cohort. The 16p11.2 microduplication was associated with a 14.5-fold increased risk of schizophrenia (95% CI (3.3, 62)) in the combined sample. A meta-analysis of datasets for multiple psychiatric disorders showed a significant association of the microduplication with schizophrenia (P = 4.8 × 10−7), bipolar disorder (P = 0.017) and autism (P = 1.9 × 10−7). In contrast, the reciprocal microdeletion was associated only with autism and developmental disorders (P = 2.3 × 10−13). Head circumference was larger in patients with the microdeletion than in patients with the microduplication (P = 0.0007)

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo

Nonlinear Goal-Oriented Bayesian Inference: Application to Carbon Capture and Storage

In many engineering problems, unknown parameters of a model are inferred in order to make predictions, to design controllers, or to optimize the model. When parameters are distributed (continuous) or very high-dimensional (discrete) and quantities of interest are low-dimensional, parameters need not be fully resolved to make accurate estimates of quantities of interest. In this work, we extend goal-oriented inference---the process of estimating predictions from observed data without resolving the parameter, previously justified theoretically in the linear setting---to Bayesian statistical inference problem formulations with nonlinear experimental and prediction processes. We propose to learn the joint density of data and predictions offline using Gaussian mixture models. When data are observed online, we condition the representation to arrive at a probabilistic description of predictions given observed data. Our approach enables real-time estimation of uncertainty in quantities of interest and renders tractable high-dimensional PDE-constrained Bayesian inference when there exist low-dimensional output quantities of interest. We demonstrate the method on a realistic problem in carbon capture and storage for which existing methods of Bayesian parameter estimation are intractable.United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-09-0613)United States. Dept. of Energy (DiaMonD MMICC