Revisiting the Gelman-Rubin Diagnostic

Gelman and Rubin's (1992) convergence diagnostic is one of the most popular methods for terminating a Markov chain Monte Carlo (MCMC) sampler. Since the seminal paper, researchers have developed sophisticated methods for estimating variance of Monte Carlo averages. We show that these estimators find immediate use in the Gelman-Rubin statistic, a connection not previously established in the literature. We incorporate these estimators to upgrade both the univariate and multivariate Gelman-Rubin statistics, leading to improved stability in MCMC termination time. An immediate advantage is that our new Gelman-Rubin statistic can be calculated for a single chain. In addition, we establish a one-to-one relationship between the Gelman-Rubin statistic and effective sample size. Leveraging this relationship, we develop a principled termination criterion for the Gelman-Rubin statistic. Finally, we demonstrate the utility of our improved diagnostic via examples

Freund-Rubin Revisited

We utilise the duality between M theory and Type IIA string theory to show the existence of Freund-Rubin compactifications of M theory on 7-manifolds with singularities supporting chiral fermions. This leads to a concrete way to study phenomenologically interesting quantum gravity vacua using a holographically dual three dimensional field theory.Comment: reference adde

Tamagawa defect of Euler systems

As remarked in [Kolyvagin systems, by Barry Mazur and Karl Rubin] Proposition 6.2.6 and Buyukboduk[ arXiv:0706.0377v1 ] Remark 3.25 one does not expect the Kolyvagin system obtained from an Euler system for a p-adic Galois representation T to be primitive (in the sense of [Kolyvagin systems, by Barry Mazur and Karl Rubin] Definition 4.5.5) if p divides a Tamagawa number at a prime \ell different from p; thus fails to compute the correct size of the relevant Selmer module. In this paper we obtain a lower bound for the size of the cokernel of the Euler system to Kolyvagin system map (see Theorem 3.2.4 of [Kolyvagin systems, by Barry Mazur and Karl Rubin] for a definition of this map) in terms of the Tamagawa numbers of T, refining [Kolyvagin systems, by Barry Mazur and Karl Rubin] Propostion 6.2.6. We show how this partially accounts for the missing Tamagawa factors in Kato's calculations with his Euler system.Comment: 20 page

Exactly Distribution-free Inference in Instrumental Variables Regression with Possibly Weak Instruments

This paper introduces a rank-based test for the instrumental variables regression model that dominates the Anderson-Rubin test in terms of finite sample size and asymptotic power in certain circumstances. The test has correct size for any distribution of the errors with weak or strong instruments. The test has noticeably higher power than the Anderson-Rubin test when the error distribution has thick tails and comparable power otherwise. Like the Anderson-Rubin test, the rank tests considered here perform best, relative to other available tests, in exactly-identified models.Aligned ranks, Anderson-Rubin statistic, categorical covariates, exact size, normal scores, rank test, weak instruments, Wilcoxon scores

Are Private Automobile Insurance Companies Replacing Workers’ Compensation Coverage When the Employee/Insured is Injured in the Course and Scope of Employment by a Third-Party Tortfeasor?: Rubin v. State Farm Mutual Automobile Insurance Company

[Excerpt] “Multiple sources for recovery are available for an employee who is physically injured by a third-party tortfeasor in the course and scope of employment. This is especially true when the physical injury triggers coverage under a health insurance policy or other type of insurance policy for medical benefits. First, assuming that the employer participates in workers’ compensation insurance, the employee is entitled to receive workers’ compensation benefits for medical expenses. Second, the employee can also recover payments for medical benefits from the third-party tortfeasor in a common-law negligence lawsuit. Third, the employee, who in this context would be considered “the insured,” can also make a claim for medical benefits under a private health insurance policy, private automobile insurance policy, or some other variety of private insurance. […] In 2002, the Nevada Supreme Court held in Rubin v. State Farm Mutual Automobile Company that a workers’ compensation exclusionary clause in a private insurance contract does not apply where an injured employee subsequently recovers damages from a third-party tortfeasor. The recovery the employee receives from the third-party tortfeasor, however, is to be reimbursed to the workers’ compensation carrier until workers’ compensation is made whole. Finally, the Rubin court also allows the employee/insured to recover payments for medical benefits under the insured’s med-pay clause of his private automobile insurance policy. This Note contends that under Rubin when an employee recovers medical benefits from both workers’ compensation and the employee’s own private insurance, the insured employee should either not be entitled to med-pay benefits from the private insurance company, or the private automobile insurance company should be permitted to subrogate against the third-party tortfeasor for med-pay benefits already paid to the insured. Many other jurisdictions support this approach. This Note concedes, however, that Rubin was correctly decided under Nevada law since subrogation of med-pay benefits in Nevada is against public policy. Although some states have allowed the same result as the decision in Rubin, the opposing view is better because it serves the purpose of no-fault med-pay benefits, discourages the windfall of a double recovery, and requires that physical injuries sustained in the course and scope of employment are primarily covered by workers’ compensation. Part II of this Note will provide background information on no-fault medical benefits, subrogation and offsetting, and the collateral source rule as they relate to med-pay benefits. Part III of this Note will report the facts, procedural history, and reasoning of the Rubin decision. Part IV will analyze the Rubin decision using explanations from other jurisdictions that have reached similar results. Part V will explain the problems associated with the Rubin situation, and offer alternate solutions, as reached in jurisdictions other than Nevada. Part VI will briefly conclude this Note.

Solitary and compact-like shear waves in the bulk of solids

We show that a model proposed by Rubin, Rosenau, and Gottlieb [J. Appl. Phys. 77 (1995) 4054], for dispersion caused by an inherent material characteristic length, belongs to the class of simple materials. Therefore, it is possible to generalize the idea of Rubin, Rosenau, and Gottlieb to include a wide range of material models, from nonlinear elasticity to turbulence. Using this insight, we are able to fine-tune nonlinear and dispersive effects in the theory of nonlinear elasticity in order to generate pulse solitary waves and also bulk travelling waves with compact support

Shale Play: Poems and Photographs from the Fracking Fields by Julia Spicher Kasdorf and Steven Rubin

Review of Julia Spicher Kasdorf and Steven Rubin\u27s Shale Play: Poems and Photographs from the Fracking Field