Robust importance sampling for error estimation in the context of optimal Bayesian transfer learning
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97 MATHEMATICS AND COMPUTING↗
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SU-E-T-144: Bayesian Inference of Local Relapse Data Using a Poisson-Based Tumour Control Probability Model
Purpose: The purpose of this project is to develop a robust method of parameter estimation for a Poisson-based TCP model using Bayesian inference. Methods: Bayesian inference was performed using the PyMC3 probabilistic programming framework written in Python. A Poisson-based TCP regression model that accounts for clonogen proliferation was fit to observed rates of local relapse as a function of equivalent dose in 2 Gy fractions for a population of 623 stage-I non-small-cell lung cancer patients. The Slice Markov Chain Monte Carlo sampling algorithm was used to sample the posterior distributions, and was initiated using the maximum of the posterior distributions found by optimization. The calculation of TCP with each sample step required integration over the free parameter α, which was performed using an adaptive 24-point Gauss-Legendre quadrature. Convergence was verified via inspection of the trace plot and posterior distribution for each of the fit parameters, as well as with comparisons of the most probable parameter values with their respective maximum likelihood estimates. Results: Posterior distributions for α, the standard deviation of α (σ), the average tumour cell-doubling time (Td), and the repopulation delay time (Tk), were generated assuming α/β = 10 Gy, and a fixed clonogen density of 10{sup 7} cm−{sup 3}. Posterior predictive plots generated from samples from these posterior distributions are in excellent agreement with the observed rates of local relapse used in the Bayesian inference. The most probable values of the model parameters also agree well with maximum likelihood estimates. Conclusion: A robust method of performing Bayesian inference of TCP data using a complex TCP model has been established.
60 APPLIED LIFE SCIENCES↗
Neural message-passing for objective-based uncertainty quantification and optimal experimental design
Various real-world scientific applications involve the mathematical modeling of complex uncertain systems with numerous unknown parameters. Accurate parameter estimation is often practically infeasible in such systems, as the available training data may be insufficient and the cost of acquiring additional data may be high. In such cases, based on a Bayesian paradigm, we can design robust operators retaining the best overall performance across all possible models and design optimal experiments that can effectively reduce uncertainty to enhance the performance of such operators maximally. While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) provides an effective means for quantifying uncertainty in complex systems, the high computational cost of estimating MOCU has been a challenge in applying it to real-world scientific/engineering problems. In this work, we propose a novel scheme to reduce the computational cost for objective-UQ via MOCU based on a data-driven approach. We adopt a neural message-passing model for surrogate modeling, incorporating a novel axiomatic constraint loss that penalizes an increase in the estimated system uncertainty. As an illustrative example, we consider the optimal experimental design (OED) problem for uncertain Kuramoto models, where the goal is to predict the experiments that can most effectively enhance robust synchronization performance through uncertainty reduction. We show that our proposed approach can accelerate MOCU-based OED by four to five orders of magnitude, without any visible performance loss compared to the state-of-the-art. The proposed approach applies to general OED tasks, beyond the Kuramoto model.
97 MATHEMATICS AND COMPUTING↗
THE BOLOCAM GALACTIC PLANE SURVEY. VIII. A MID-INFRARED KINEMATIC DISTANCE DISCRIMINATION METHOD
We present a new distance estimation method for dust-continuum-identified molecular cloud clumps. Recent (sub-)millimeter Galactic plane surveys have cataloged tens of thousands of these objects, plausible precursors to stellar clusters, but detailed study of their physical properties requires robust distance determinations. We derive Bayesian distance probability density functions (DPDFs) for 770 objects from the Bolocam Galactic Plane Survey in the Galactic longitude range 7. Degree-Sign 5 {<=} l {<=} 65 Degree-Sign . The DPDF formalism is based on kinematic distances, and uses any number of external data sets to place prior distance probabilities to resolve the kinematic distance ambiguity (KDA) for objects in the inner Galaxy. We present here priors related to the mid-infrared absorption of dust in dense molecular regions and the distribution of molecular gas in the Galactic disk. By assuming a numerical model of Galactic mid-infrared emission and simple radiative transfer, we match the morphology of (sub-)millimeter thermal dust emission with mid-infrared absorption to compute a prior DPDF for distance discrimination. Selecting objects first from (sub-)millimeter source catalogs avoids a bias towards the darkest infrared dark clouds (IRDCs) and extends the range of heliocentric distance probed by mid-infrared extinction and includes lower-contrast sources. We derive well-constrained KDA resolutions for 618 molecular cloud clumps, with approximately 15% placed at or beyond the tangent distance. Objects with mid-infrared contrast sufficient to be cataloged as IRDCs are generally placed at the near kinematic distance. Distance comparisons with Galactic Ring Survey KDA resolutions yield a 92% agreement. A face-on view of the Milky Way using resolved distances reveals sections of the Sagittarius and Scutum-Centaurus Arms. This KDA-resolution method for large catalogs of sources through the combination of (sub-)millimeter and mid-infrared observations of molecular cloud clumps is generally applicable to other dust-continuum Galactic plane surveys.
79 ASTRONOMY AND ASTROPHYSICS↗
Pedestal main ion particle transport inference through gas puff modulation with experimental source measurements
Abstract Transport in the DIII-D high confinement mode (H-mode) pedestal is investigated through a periodic edge gas puff modulation (GPM) which perturbs the deuterium density and source profiles. By using absolutely calibrated experimental edge ionization profile measurements, radial profiles of diffusion ( D ) and convection ( v ) are calculated into the pedestal region without depending on modeling the edge ionization source. An analytic approach with closed-form expressions for the D and v profiles and a more advanced Bayesian approach show evidence of an inward particle convection on the order of 1 m s −1 extending to normalized poloidal flux ( Ψ N ) of 0.98. Meanwhile, diffusion reaches a minimum value of ( 0.03 ± 0.02 ) m 2 s −1 in the pedestal region. Notably, the Bayesian approach, which utilizes the Aurora 1.5 D forward model inside the IMPRAD OMFIT module, provides radially resolved transport profiles with associated uncertainty without requiring an explicit form for the perturbation to the density profile or source. The combination of experimental ionization measurements and Bayesian inference provides an enhanced robust framework for investigating edge particle transport coefficients to experimentally test transport physics in order to improve predictive capabilities in the tokamak edge.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Bayesian analysis of (3 +1)D relativistic nuclear dynamics with the RHIC beam energy scan data
This work presents a Bayesian inference study for relativistic heavy-ion collisions in the beam energy scan program at the BNL Relativistic Heavy-Ion Collider. The theoretical model simulates event-by-event (3+1)-dimensional [(3+1)D] collision dynamics using hydrodynamics and hadronic transport theory. We analyze the model's 20-dimensional posterior distributions obtained using three model emulators with different accuracy and demonstrate the essential role of training an accurate model emulator in the Bayesian analysis. Our analysis provides robust constraints on the quark-gluon plasma's transport properties and various aspects of (3+1)D relativistic nuclear dynamics. By running full model simulations with 100 parameter sets sampled from the posterior distribution, we make predictions for p T -differential observables and estimate their systematic theory uncertainty. Here, a sensitivity analysis is performed to elucidate how individual experimental observables respond to different model parameters, providing useful physics insights into the phenomenological model for heavy-ion collisions.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Light-quark connected intermediate-window contributions to the muon 𝑔 − 2 hadronic vacuum polarization from lattice QCD
We present a lattice-QCD calculation of the light-quark connected contribution to window observables associated with the leading-order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, $a^{HVP,LO}_μ$. We employ the MILC Collaboration’s isospin-symmetric QCD gauge-field ensembles, which contain four flavors of dynamical highly improved staggered quarks with four lattice spacings between $a ≈ 0.06-0.15$ fm and close-to-physical quark masses. We consider several effective-field-theory-based schemes for finite volume and other lattice corrections and combine the results via Bayesian model averaging to obtain robust estimates of the associated systematic uncertainties. After unblinding, our final results for the intermediate and "W2" windows are $a^{U,W}_μ$(conn) = 206.6(1.0) x 10 -10 and $a^{U,W2}_μ$ (conn) = 100.7(3.2) x 10 -10 , respectively
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Deep Learning and Likelihood Approaches for Viral Phylogeography Converge on the Same Answers Whether the Inference Model Is Right or Wrong
Abstract Analysis of phylogenetic trees has become an essential tool in epidemiology. Likelihood-based methods fit models to phylogenies to draw inferences about the phylodynamics and history of viral transmission. However, these methods are often computationally expensive, which limits the complexity and realism of phylodynamic models and makes them ill-suited for informing policy decisions in real-time during rapidly developing outbreaks. Likelihood-free methods using deep learning are pushing the boundaries of inference beyond these constraints. In this paper, we extend, compare, and contrast a recently developed deep learning method for likelihood-free inference from trees. We trained multiple deep neural networks using phylogenies from simulated outbreaks that spread among 5 locations and found they achieve close to the same levels of accuracy as Bayesian inference under the true simulation model. We compared robustness to model misspecification of a trained neural network to that of a Bayesian method. We found that both models had comparable performance, converging on similar biases. We also implemented a method of uncertainty quantification called conformalized quantile regression that we demonstrate has similar patterns of sensitivity to model misspecification as Bayesian highest posterior density (HPD) and greatly overlap with HPDs, but have lower precision (more conservative). Finally, we trained and tested a neural network against phylogeographic data from a recent study of the SARS-Cov-2 pandemic in Europe and obtained similar estimates of region-specific epidemiological parameters and the location of the common ancestor in Europe. Along with being as accurate and robust as likelihood-based methods, our trained neural networks are on average over 3 orders of magnitude faster after training. Our results support the notion that neural networks can be trained with simulated data to accurately mimic the good and bad statistical properties of the likelihood functions of generative phylogenetic models.
Evolutionary Biology↗
Planck intermediate results: XVI. Profile likelihoods for cosmological parameters
We explore the 2013 Planck likelihood function with a high-precision multi-dimensional minimizer (Minuit). This allows a refinement of the CDM best-fit solution with respect to previously-released results, and the construction of frequentist confidence intervals using profile likelihoods. The agreement with the cosmological results from the Bayesian framework is excellent, demonstrating the robustness of the Planck results to the statistical methodology. We investigate the inclusion of neutrino masses, where more significant differences may appear due to the non-Gaussian nature of the posterior mass distribution. By applying the Feldman-Cousins prescription, we again obtain results very similar to those of the Bayesian methodology. However, the profile-likelihood analysis of the cosmic microwave background (CMB) combination ( Planck +WP+highL) reveals a minimum well within the unphysical negative-mass region. We show that inclusion of the Planck CMB-lensing information regularizes this issue, and provide a robust frequentist upper limit Σ$m_v$ ≤0:26 eV (95% confidence) from the CMB+lensing+BAO data combination.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Privacy policy robustness to reverse engineering
Differential privacy policies allow one to preserve data privacy while sharing and analyzing data. However, these policies are susceptible to an array of attacks. In particular, often a portion of the data desired to be privacy protected is exposed online. Access to these pre-privacy protected data samples can then be used to reverse engineer the privacy policy. With knowledge of the generating privacy policy, an attacker can use machine learning to approximate the full set of originating data. Bayesian inference is one method for reverse engineering both model and model parameters. We present a methodology for evaluating and ranking privacy policy robustness to Bayesian inference-based reverse engineering, and demonstrated this method across data with a variety of temporal trends.
Kusne, Aaron Gilad↗
Bayesian High-Rank Hankel Matrix Completion for Nonlinear Synchrophasor Data Recovery
Phasor measurement units (PMUs) provide high temporal-resolution synchrophasor measurements for power system monitoring and control. The frequent data quality issues, such as missing and bad data, prevent the incorporation of synchrophasor data in real-time operations. Most existing data-driven data recovery methods assume the power system dynamics can be approximated by a linear dynamical system, and the recovery performance degrades significantly when the power system is experiencing nonlinear dynamics during significant events. Here, this paper proposes a data-driven Bayesian nonlinear synchrophasor data recovery method (Ba-NSDR) that can recover a consecutive time period of simultaneous data losses or errors across all channels, even when the underlying system is highly nonlinear. The idea is to lift the Hankel matrix of the spatial-temporal synchrophasor data to a higher dimension such that the lifted Hankel matrix is low-rank in that space and can be processed with the kernel trick. Our proposed Bayesian method then infers the probabilistic distributions of synchrophasor from the partial observations. Some distinctive features of Ba-NSDR include an uncertainty index to measure the accuracy of the recovery result and the robustness to parameter selections. Our method is verified on both synthetic and recorded event datasets.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Cosmic Inference: Constraining Parameters with Observations and a Highly Limited Number of Simulations
We look at cosmological probes that pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters that characterize the underlying physical system-our universe, from these observations and theoretical forward-modeling. The only way to accurately forward-model physical behavior on small scales is via expensive numerical simulations, which are further “emulated” due to their high cost. Emulators are commonly built with a set of simulations covering the parameter space with Latin hypercube sampling and an interpolation procedure; the aim is to establish an approximately constant prediction error across the hypercube. In this paper, we provide a description of a novel statistical framework for obtaining accurate parameter constraints. The proposed framework uses multi-output Gaussian process emulators that are adaptively constructed using Bayesian optimization methods with the goal of maintaining a low emulation error in the region of the hypercube preferred by the observational data. In this paper, we compare several approaches for constructing multi-output emulators that enable us to take possible inter-output correlations into account while maintaining the efficiency needed for inference. Using a Lyα forest flux power spectrum, we demonstrate that our adaptive approach requires considerably fewer-by a factor of a few in the Lyα P(k) case considered here-simulations compared to the emulation based on Latin hypercube sampling, and that the method is more robust in reconstructing parameters and their Bayesian credible intervals.
79 ASTRONOMY AND ASTROPHYSICS↗
Large-Scale Optimization for Bayesian Inference in Complex Systems
The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT₋Sandia component of the SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas₋Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as "reduce then sample" and "sample then reduce." In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.
97 MATHEMATICS AND COMPUTING↗
Low Energy Analysis of NuclEar Reactions v0.0.1
This is a lightweight, easy to use Python analysis package for analyzing public low-energy nuclear reaction data relevant to understanding basic nuclear processes, often of relevance to Solar Fusion, to improve our theoretical understanding of them, and enable connections with input from lattice QCD. It performs the analysis in a Bayesian Framework and supports Bayesian Model Averaging to provide a robust uncertainty quantification.
Walker-Loud, André↗
Nature Versus Nurture: A Bayesian Framework for Assessing Apparent Correlations between Planetary Orbital Properties and Stellar Ages
Many exoplanets have orbital characteristics quite different from those seen in our own solar system, including planets locked in orbital resonances and planets on orbits that are elliptical or highly inclined from their host star’s spin axis. It is debated whether the wide variety in system architecture is primarily due to differences in formation conditions (nature) or due to evolution over time (nurture). Identifying trends between planetary and stellar properties, including stellar age, can help distinguish between these competing theories and offer insights as to how planets form and evolve. However, it can be challenging to determine whether observed trends between planetary properties and stellar age are driven by the age of the system—pointing to evolution over time being an important factor—or other parameters to which the age may be related, such as stellar mass or stellar temperature. The situation is complicated further by the possibilities of selection biases, small number statistics, uncertainties in stellar age, and orbital evolution timescales that are typically much shorter than the range of observed ages. Here, we develop a Bayesian statistical framework to assess the robustness of such observed correlations and to determine whether they are indeed due to evolutionary processes, are more likely to reflect different formation scenarios, or are merely coincidental. We apply this framework to reported trends between stellar age and 2:1 orbital resonances, spin–orbit misalignments, and hot Jupiters’ orbital eccentricities. We find strong support for the nurture hypothesis only in the final case.
79 ASTRONOMY AND ASTROPHYSICS↗
BAYESIAN ESTIMATION OF THERMONUCLEAR REACTION RATES
The problem of estimating non-resonant astrophysical S -factors and thermonuclear reaction rates, based on measured nuclear cross sections, is of major interest for nuclear energy generation, neutrino physics, and element synthesis. Many different methods have been applied to this problem in the past, almost all of them based on traditional statistics. Bayesian methods, on the other hand, are now in widespread use in the physical sciences. In astronomy, for example, Bayesian statistics is applied to the observation of extrasolar planets, gravitational waves, and Type Ia supernovae. However, nuclear physics, in particular, has been slow to adopt Bayesian methods. We present astrophysical S -factors and reaction rates based on Bayesian statistics. We develop a framework that incorporates robust parameter estimation, systematic effects, and non-Gaussian uncertainties in a consistent manner. The method is applied to the reactions d(p, γ ){sup 3}He, {sup 3}He({sup 3}He,2p){sup 4}He, and {sup 3}He( α , γ ){sup 7}Be, important for deuterium burning, solar neutrinos, and Big Bang nucleosynthesis.
79 ASTRONOMY AND ASTROPHYSICS↗
Model-Form Epistemic Uncertainty Quantification for Modeling with Differential Equations: Application to Epidemiology
Modeling real-world phenomena to any degree of accuracy is a challenge that the scientific research community has navigated since its foundation. Lack of information and limited computational and observational resources necessitate modeling assumptions which, when invalid, lead to model-form error (MFE). The work reported herein explored a novel method to represent model-form uncertainty (MFU) that combines Bayesian statistics with the emerging field of universal differential equations (UDEs). The fundamental principle behind UDEs is simple: use known equational forms that govern a dynamical system when you have them; then incorporate data-driven approaches – in this case neural networks (NNs) – embedded within the governing equations to learn the interacting terms that were underrepresented. Utilizing epidemiology as our motivating exemplar, this report will highlight the challenges of modeling novel infectious diseases while introducing ways to incorporate NN approximations to MFE. Prior to embarking on a Bayesian calibration, we first explored methods to augment the standard (non-Bayesian) UDE training procedure to account for uncertainty and increase robustness of training. In addition, it is often the case that uncertainty in observations is significant; this may be due to randomness or lack of precision in the measurement process. This uncertainty typically manifests as “noisy” observations which deviate from a true underlying signal. To account for such variability, the NN approximation to MFE is endowed with a probabilistic representation and is updated using available observational data in a Bayesian framework. By representing the MFU explicitly and deploying an embedded, data-driven model, this approach enables an agile, expressive, and interpretable method for representing MFU. In this report we will provide evidence that Bayesian UDEs show promise as a novel framework for any science-based, data-driven MFU representation; while emphasizing that significant advances must be made in the calibration of Bayesian NNs to ensure a robust calibration procedure.
97 MATHEMATICS AND COMPUTING↗
Robust Spectral Unmixing of Sparse Multispectral Lidar Waveforms using Gamma Markov Random Fields
Here, this paper presents a new Bayesian spectral un-mixing algorithm to analyse remote scenes sensed via sparse multispectral Lidar measurements. To a first approximation, in the presence of a target, each Lidar waveform consists of a main peak, whose position depends on the target distance and whose amplitude depends on the wavelength of the laser source considered (i.e, on the target reflectivity). Besides, these temporal responses are usually assumed to be corrupted by Poisson noise in the low photon count regime. When considering multiple wavelengths, it becomes possible to use spectral information in order to identify and quantify the main materials in the scene, in addition to estimation of the Lidar-based range profiles. Due to its anomaly detection capability, the proposed hierarchical Bayesian model, coupled with an efficient Markov chain Monte Carlo algorithm, allows robust estimation of depth images together with abundance and outlier maps associated with the observed 3D scene. The proposed methodology is illustrated via experiments conducted with real multispectral Lidar data acquired in a controlled environment. The results demonstrate the possibility to unmix spectral responses constructed from extremely sparse photon counts (less than 10 photons per pixel and band).
97 MATHEMATICS AND COMPUTING↗