Global consensus Monte Carlo

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples

In Defense of the Foundation Stone: Deterring Post-Election Abuse of the Legal Process

The COVID-19 pandemic has upended the American way oflife and revolutionized the way we vote. Record voter turnout in2020, including among first-time voters and voters of color, wasmet with unprecedented legal challenges seeking to nullifymillions of votes. A coordinated effort to amplify groundlessaccusations of voting fraud, shorthanded as “the Big Lie,” wasadvanced in multiple states through scores of lawsuits.Although the cases themselves were dismissed as lacking meritand as failing to state actionable claims, their impact uponpublic confidence in free and fair elections was palpable andthe resources of the courts and defending parties were severelytaxed. As a self-regulating profession, lawyers and courts haveboth the tools and the duty to hold litigants and their counselaccountable for unethical and unfounded attacks on votes afterthey have been cast. Rule 11 sanctions, statutory remedies, andother consequences must be employed when litigants baselesslychallenge election results, or the courts will find themselvesregularly enlisted in efforts to confer false legitimacy onmisinformation campaigns. Firm, fair accountability in thepresent is crucial to deter those who would use litigation topoison the democratic well in the future