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

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

ERISA Subrogation and the Controversy over Sereboff: Silencing the Critics, the Divided Bench Is a Legitimate Standard

ERISA protects employees in the administration ofemployer-sponsored benefit plans. When a party is injuredby third parties and a health and welfare benefit plangoverned by ERISA pays benefits, conflicts have arisenbetween insurers seeking subrogation and individualsseeking full recovery. Injured parties claim they shouldnot have to reimburse insurers while insurers denyresponsibility for damage caused by third parties. TheSupreme Court set the standard for plan fiduciary rightsto ERISA subrogation in Sereboff v. Mid Atlantic MedicalServices, Inc. Sereboff held that the plain wording of 29U.S.C. § 1132(a)(3) means equitable relief available underthe historically divided courts of law and equity. TheCourt reasoned that the statute specifies only equitablerelief\u27 rather than specific categories of equitable relief,such as constructive trusts and equitable liens.Controversy continues as scholars criticize the standard asunsupported by ERISA and contrary to ERISA\u27s purposes.This Note asserts that the standard is supported by statuteand precedent: Mertens v. Hewitt Associates and Great-West Life & Annuity Insurance Co. v. Knudson. ThisNote concludes that the Court established a workablestandard, the ultimate legitimacy of which lies in theequitable balance it achieves between fiduciary rights to enforce ERISA plan subrogation provisions and theprotection of beneficiaries. The critics should accept theCourt\u27s equitable solution: equitable relief under thedivided bench

Long-Range Coupling in an Allosteric Receptor Revealed by Mutant Cycle Analysis

The functional coupling of residues that are far apart in space is the quintessential property of allosteric proteins. For example, in Cys-loop receptors, the gating of an intrinsic ion channel is allosterically regulated by the binding of small molecule neurotransmitters 50–60 Å from the channel gate. Some residues near the binding site must have as their primary function the communication of the binding event to the gating region. These gating pathway residues are essential to function, but their identification and characterization can be challenging. This work introduces a simple strategy, derived from mutant cycle analysis, for identifying gating pathway residues using macroscopic measurements alone. In the exemplar Cys-loop receptor, the nicotinic acetylcholine receptor, a well-characterized reporter mutation (βL9′S) known to impact gating, was combined with mutations of target residues in the ligand-binding domain hypothesized or previously found to be functionally significant. A mutant cycle analysis of the macroscopic EC50 measurements can then provide insights into the role of the target residue. This new method, elucidating long-range functional coupling in allosteric receptors, can be applied to several reporter mutations in a wide variety of receptors to identify previously characterized and novel mutations that impact the gating pathway. We support our interpretation of macroscopic data with single-channel studies. Elucidating long-range functional coupling in allosteric receptors should be broadly applicable to determining functional roles of residues in allosteric receptors

PARENTS' DESCRIPTIONS OF BARRIERS FACED AND STRATEGIES USED TO OBTAIN DENTAL CARE *

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65428/1/j.1752-7325.1974.tb00670.x.pd