Asymptotic Properties of Approximate Bayesian Computation

Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, its limiting shape, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.Comment: This 31 pages paper is a revised version of the paper, including supplementary materia

Western Oklahoma Irrigation Water and Energy Audits: Findings, Recommendations and Educational Materials

Interim Report to the OSU Water Center, March 17, 2017USGS104b Water Grants ProgramStart Date: (03/1/2016)End Date: (02/28/2018)Congressional District: (Oklahoma Congressional District 3 for University and all project sites)Focus Category: IG, WU, AG, GW, ECON, METDescriptors: Applied Research, Irrigation Efficiency, Water and Energy Nexus, Water Conservation, Aquifer Management, Life Cycle Assessment, Climate Change, Water Availability, Drought, Producers.Students: Total

Liquid encapsulated float zone process and apparatus

The process and apparatus for growing crystals using float zone techniques are described. A rod of crystalline materials is disposed in a cylindrical container, leaving a space between the rod and container walls. This space is filled with an encapsulant, selected to have a slightly lower melting point than the crystalline material. The rod is secured to a container end cap at one end and to a shaft at its other end. A piston slides over the rod and provides pressure to prevent loss of volatile components upon melting of the rod. Prior to melting the rod the container is first heated to melt the encapsulant, with any off-gas from this step being vented to a cavity behind the piston. The piston moves slightly forward owing to volume change upon melting of the encapsulant, and the vent passageway is closed. The container is then moved longitudinally through a heated zone to progressively melt sections of the rod as in conventional float zone processes. The float zone technique may be used in the microgravity environment of space

Solid-state NMR Analysis of Adhesive Bondlines in Pilot Scale Flakeboards

This work demonstrates the application of solid-state NMR to the analysis of adhesive bondlines in pilot scale flakeboards. A comparison to laboratory scale experiments is also made. Phenol-formaldehyde resin is easily detected by using labeled formaldehyde. However, resin washout can occasionally prevent detection in pilot scale composites. The relative degree of resin cure is determined by measuring corrected signal areas and also by measuring proton longitudinal relaxation in the rotating frame. Such relaxation measurements were effective in laboratory scale experiments, but were much less useful for pilot scale tests. The degree of phenol-formaldehyde polymerization was not affected by changes in wood furnish moisture content; the range of furnish moisture was 13 and 24%. This suggests that phenol-formaldehyde moisture intolerance is not related to polymerization retardation by water. This work demonstrates the feasibility of performing detailed bondline analyses on pilot and possibly industrial scale composites

Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models

A computationally simple approach to inference in state space models is proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation of an intractable likelihood by matching summary statistics for the observed data with statistics computed from data simulated from the true process, based on parameter draws from the prior. Draws that produce a 'match' between observed and simulated summaries are retained, and used to estimate the inaccessible posterior. With no reduction to a low-dimensional set of sufficient statistics being possible in the state space setting, we define the summaries as the maximum of an auxiliary likelihood function, and thereby exploit the asymptotic sufficiency of this estimator for the auxiliary parameter vector. We derive conditions under which this approach - including a computationally efficient version based on the auxiliary score - achieves Bayesian consistency. To reduce the well-documented inaccuracy of ABC in multi-parameter settings, we propose the separate treatment of each parameter dimension using an integrated likelihood technique. Three stochastic volatility models for which exact Bayesian inference is either computationally challenging, or infeasible, are used for illustration. We demonstrate that our approach compares favorably against an extensive set of approximate and exact comparators. An empirical illustration completes the paper.Comment: This paper is forthcoming at the Journal of Computational and Graphical Statistics. It also supersedes the earlier arXiv paper "Approximate Bayesian Computation in State Space Models" (arXiv:1409.8363

On the use of adjoint-based sensitivity estimates to control local mesh refinement

Journal ArticleThe goal of efficient and robust error control, through local mesh adaptation in the computational solution of partial differential equations, is predicated on the ability to identify in an a posteriori way those localized regions whose refinement will lead to the most significant reductions in the error. The development of a posteriori error estimation schemes and of a refinement infrastructure both facilitate this goal, however they are incomplete in the sense that they do not provide an answer as to where the maximal impact of refinement may be gained or what type of refinement - elemental partitioning (h-refinement) or polynomial enrichment (p-refinement) - will best lead to that gain. In essence, one also requires knowledge of the sensitivity of the error to both the location and the type of refinement. In this communication we propose the use of adjoint-based sensitivity analysis to discriminate both where and how to refine. We present both an adjoint-based and an algebraic perspective on defining and using sensitivities, and then demonstrate through several one-dimensional model problem experiments the feasibility and benefits of our approach

Calibrated Generalized Bayesian Inference

We provide a simple and general solution to the fundamental open problem of inaccurate uncertainty quantification of Bayesian inference in misspecified or approximate models, and of generalized Bayesian posteriors more generally. While existing solutions are based on explicit Gaussian posterior approximations, or computationally onerous post-processing procedures, we demonstrate that correct uncertainty quantification can be achieved by substituting the usual posterior with an alternative posterior that conveys the same information. This solution applies to both likelihood-based and loss-based posteriors, and we formally demonstrate the reliable uncertainty quantification of this approach. The new approach is demonstrated through a range of examples, including generalized linear models, and doubly intractable models.Comment: This paper is a substantially revised version of arXiv:2302.06031v1. This revised version has a slightly different focus, additional examples, and theoretical results, as well as different author