Postprocessing of MCMC

Markov chain Monte Carlo is the engine of modern Bayesian statistics, being used to approximate the posterior and derived quantities of interest. Despite this, the issue of how the output from a Markov chain is postprocessed and reported is often overlooked. Convergence diagnostics can be used to control bias via burn-in removal, but these do not account for (common) situations where a limited computational budget engenders a bias-variance trade-off. The aim of this article is to review state-of-the-art techniques for postprocessing Markov chain output. Our review covers methods based on discrepancy minimization, which directly address the bias-variance trade-off, as well as general-purpose control variate methods for approximating expected quantities of interest. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Sensor Selection and State Estimation for Unobservable and Non-Linear System Models

To comply with the increasing complexity of new mechatronic systems and stricter safety regulations, advanced estimation algorithms are currently undergoing a transformation towards higher model complexity. However, more complex models often face issues regarding the observability and computational effort needed. Moreover, sensor selection is often still conducted pragmatically based on experience and convenience, whereas a more cost-effective approach would be to evaluate the sensor performance based on its effective estimation performance. In this work, a novel estimation and sensor selection approach is presented that is able to stabilise the estimator Riccati equation for unobservable and non-linear system models. This is possible when estimators only target some specific quantities of interest that do not necessarily depend on all system states. An Extended Kalman Filter-based estimation framework is proposed where the Riccati equation is projected onto an observable subspace based on a Singular Value Decomposition (SVD) of the Kalman observability matrix. Furthermore, a sensor selection methodology is proposed, which ranks the possible sensors according to their estimation performance, as evaluated by the error covariance of the quantities of interest. This allows evaluating the performance of a sensor set without the need for costly test campaigns. Finally, the proposed methods are evaluated on a numerical example, as well as an automotive experimental validation case.

Microdosimetry and Dose-Averaged LET Calculations of Protons in Liquid Water: A Novel Geant4-DNA Application

The spatial distribution of energy deposition events is an essential aspect in the determination of the radiobiological effects of ionizing radiation at the cellular level. Microdosimetry provides a theoretical framework for the description of these events, and has been used in several studies to address problems such as the characterization of Linear Energy Transfer (LET) and Relative Biological Effectiveness (RBE) of ion beams for proton therapy applications. Microdosimetry quantities and their distributions can be obtained by means of Monte Carlo simulations. In this work, we present a track structure Monte Carlo (MC) application, based on Geant4-DNA, for the computation of microdosimetric distributions of protons in liquid water. This application provides two sampling methods uniform and weighted, for the scoring of the quantities of interest in spherical sites, with diameters ranging from 1 to 10 μm. As an element of novelty, the work shows the approach followed to calculate, without resorting to dedicated simulations, the distribution of energy imparted to the site per electronic collision of the proton, which can be used to obtain the macroscopic dose-averaged LET as proposed by Kellerer. Furthermore, in this work the concept of effective mean chord length is proposed to take into account δ-ray influx and escape in the calculation of macroscopic dose-averaged LET for proton track segments and retrieve the agreement predicted by Kellerer’s formula. Finally, the results obtained demonstrate that our MC application is reliable and computational-efficient to perform calculations of microdosimetric distributions and dose-averaged LET of proton track segments in liquid water.

Hedge Fund Activism and Financial Performance

The magnitude of changes in observable quantities of interest at hedge fund activism targets are economically small and unimportant except when the company is up for sale. When it can facilitate the sale of companies, hedge fund activism is likely to benefit target shareholders, though investors must consider whether the companies acquiring the targets are also in their portfolios and merely overpaying, so that money is simply shifting from one part of their portfolio to another. But the rest of hedge fund activism finds itself sitting with past rounds of shareholder activism of which it is only the latest manifestation. Like those past forms of shareholder activism, it just doesn’t seem to matter much.

The maximum entropy method for data fusion and uncertainty quantification in multifunctional materials and structures

The quantification of uncertainty in intelligent material systems and structures requires methods to objectively compare complex models to measurements, where the majority of cases include multiple model outputs and quantities of interests given multiphysics coupling. This creates questions about constructing appropriate measures of uncertainty during fusion of data and comparisons between data and models. Novel materials with complex or poorly understood coupling can benefit from advanced statistical analysis to judge models in light of multiphysics data. Here, we apply the Maximum Entropy (ME) method to more complicated ferroelectric single crystals containing domain structures and soft electrostrictive membranes under both mechanical and electrical loading. Multiple quantities of interest are considered, which requires fusing heterogeneous information together when quantifying the uncertainty of lower fidelity models. We find that parameters, which were initially unidentifiable using a single quantity of interest, become identifiable using multiple quantities of interest. We also show that posterior densities may broaden or narrow when multiple data sets are fused together. This is likely due to conflict or agreement, respectively, between the different quantities of interest and the multiple model outputs. Such information is important to advance our predictions of intelligent materials and structures from multi-model inputs and heterogeneous data.

Static analysis model of a non-pneumatic tire with elastic spokes contacting with rigid ground

An analytical model of a non-pneumatic tire is proposed to study the static deformation responses of a non-pneumatic tire in contact with a rigid ground. The tire consists of a shear band which is formed by an annular beam, and elastic spokes that connect the shear band to the rigid hub of the tire. The shear band is modeled using a Timoshenko beam. The spokes are modeled by linear springs, which are distributed evenly in circumferential direction. Governing equations of the model were derived using a theoretical analysis. The shear band static deformation was obtained based on the discussion of the relationship between spoke stiffness and the parameters of the shear band. A finite element model was developed to verify the accuracy of the model. As a part of the results from this study, a parametric analysis of quantities of interest for the tire is presented, which can be used in improving the optimal design of non-pneumatic tires. This scheme offers a holonomic solution for the complicated differential equations and gives a computationally efficient tool for rapid analyzing and designing such systems.

Nuclear Data Sensitivity Study for the EBR-II Fast Reactor Benchmark Using SCALE with ENDF/B-VII.1 and ENDF/B-VIII.0

The EBR-II benchmark, which was recently included in the International Handbook of Evaluated Reactor Physics Benchmark Experiments, served as a basis for assessing the performance of the SCALE code system for fast reactor analyses. A reference SCALE model was developed based on the benchmark specifications. Great agreement was observed between the eigenvalue calculated with this SCALE model and the benchmark eigenvalue. To identify potential gaps and uncertainties of nuclear data for the simulation of various quantities of interest in fast spectrum systems, sensitivity and uncertainty analyses were performed for the eigenvalue, reactivity effects, and the radial power profile of EBR-II using the two most recent ENDF/B nuclear data library releases. While the nominal results are consistent between the calculations with the different libraries, the uncertainties due to nuclear data vary significantly. The major driver of observed uncertainties is the uncertainty of the 235U (n,γ) reaction. Since the uncertainty of this reaction is significantly reduced in the ENDF/B-VIII.0 library compared to ENDF/B-VII.1, the obtained output uncertainties tend to be smaller in ENDF/B-VIII.0 calculations, although the decrease is partially compensated by increased uncertainties in 235U fission and ν¯.