Approximate Bayesian computation via the energy statistic

Approximate Bayesian computation (ABC) has become an essential part of the Bayesian toolbox for addressing problems in which the likelihood is prohibitively expensive or entirely unknown, making it intractable. ABC defines a pseudo-posterior by comparing observed data with simulated data, traditionally based on some summary statistics, the elicitation of which is regarded as a key difficulty. Recently, using data discrepancy measures has been proposed in order to bypass the construction of summary statistics. Here we propose to use the importance-sampling ABC (IS-ABC) algorithm relying on the so-called two-sample energy statistic. We establish a new asymptotic result for the case where both the observed sample size and the simulated data sample size increase to infinity, which highlights to what extent the data discrepancy measure impacts the asymptotic pseudo-posterior. The result holds in the broad setting of IS-ABC methodologies, thus generalizing previous results that have been established only for rejection ABC algorithms. Furthermore, we propose a consistent V-statistic estimator of the energy statistic, under which we show that the large sample result holds, and prove that the rejection ABC algorithm, based on the energy statistic, generates pseudo-posterior distributions that achieves convergence to the correct limits, when implemented with rejection thresholds that converge to zero, in the finite sample setting. Our proposed energy statistic based ABC algorithm is demonstrated on a variety of models, including a Gaussian mixture, a moving-average model of order two, a bivariate beta and a multivariate $g$-and-$k$ distribution. We find that our proposed method compares well with alternative discrepancy measures.Comment: 25 pages, 6 figures, 5 table

Truth Bounties: A Market Solution to Fake News

False information poses a threat to individuals, groups, and society. Many people struggle to judge the veracity of the information around them, whether that information travels through newspapers, talk radio, TV, or social media. Concerned with the spread of misinformation and harmful falsehoods, much of the policy, popular, and scholarly conversation today revolves around proposals to expand the regulation of individuals, platforms, and the media. While more regulation may seem inevitable, it faces constitutional and political hurdles. Furthermore, regulation can have undesirable side effects and be ripe for abuse by powerful actors, public and private. This Article presents an alternative for fighting misinformation that avoids many pitfalls of regulation: truth bounties. We develop a contractual mechanism that would enable individuals, media, and others to pledge money to support the credibility of their communications. Any person could claim the bounty by presenting evidence of the falsity of the communication before a dedicated body of private arbitrators. Under the system we envision, anyone consuming information on the internet would know immediately ifa given communication had a bounty attached, whether the communication had been challenged, and whether the challenge succeeded orfailed. As John Stuart Mill recognized, we can trust our grasp of the truth only by putting it to the fire of challenge. Truth bounties open the challenge to all

Annealed Flow Transport Monte Carlo

Annealed Importance Sampling (AIS) and its Sequential Monte Carlo (SMC) extensions are state-of-the-art methods for estimating normalizing constants of probability distributions. We propose here a novel Monte Carlo algorithm, Annealed Flow Transport (AFT), that builds upon AIS and SMC and combines them with normalizing flows (NFs) for improved performance. This method transports a set of particles using not only importance sampling (IS), Markov chain Monte Carlo (MCMC) and resampling steps - as in SMC, but also relies on NFs which are learned sequentially to push particles towards the successive annealed targets. We provide limit theorems for the resulting Monte Carlo estimates of the normalizing constant and expectations with respect to the target distribution. Additionally, we show that a continuous-time scaling limit of the population version of AFT is given by a Feynman--Kac measure which simplifies to the law of a controlled diffusion for expressive NFs. We demonstrate experimentally the benefits and limitations of our methodology on a variety of applications

Probing Individual Environmental Bacteria for Viruses by Using Microfluidic Digital PCR

Viruses may very well be the most abundant biological entities on the planet. Yet neither metagenomic studies nor classical phage isolation techniques have shed much light on the identity of the hosts of most viruses. We used a microfluidic digital polymerase chain reaction (PCR) approach to physically link single bacterial cells harvested from a natural environment with a viral marker gene. When we implemented this technique on the microbial community residing in the termite hindgut, we found genus-wide infection patterns displaying remarkable intragenus selectivity. Viral marker allelic diversity revealed restricted mixing of alleles between hosts, indicating limited lateral gene transfer of these alleles despite host proximity. Our approach does not require culturing hosts or viruses and provides a method for examining virus-bacterium interactions in many environments

Chaotic to ordered state transition of cathode-sheath instabilities in DC glow discharge plasmas

Transition from chaotic to ordered state has been observed during the initial stage of a discharge in a cylindrical dc glow discharge plasma. Initially it shows a chaotic behavior but increasing the discharge voltage changes the characteristics of the discharge glow and shows a period substraction of order 7 period $\to$ 5 period $\to$3 period $\to$1 period i.e. the system goes to single mode through odd cycle subtraction. On further increasing the discharge voltage, the system goes through period doubling, like 1 period $\to$ 2 period $\to$ 4 period. On further increasing the voltage, the system goes to stable state without having any oscillations.Comment: chathode-sheath, instabilities, chaos, period-subtraction, bifurcation, dc-discharg

Stationary solutions of the one-dimensional nonlinear Schroedinger equation: II. Case of attractive nonlinearity

All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box or periodic boundary conditions are presented in analytic form for the case of attractive nonlinearity. A companion paper has treated the repulsive case. Our solutions take the form of bounded, quantized, stationary trains of bright solitons. Among them are two uniquely nonlinear classes of nodeless solutions, whose properties and physical meaning are discussed in detail. The full set of symmetry-breaking stationary states are described by the $C_{n}$ character tables from the theory of point groups. We make experimental predictions for the Bose-Einstein condensate and show that, though these are the analog of some of the simplest problems in linear quantum mechanics, nonlinearity introduces new and surprising phenomena.Comment: 11 pages, 9 figures -- revised versio

Exact closed form analytical solutions for vibrating cavities

For one-dimensional vibrating cavity systems appearing in the standard illustration of the dynamical Casimir effect, we propose an approach to the construction of exact closed-form solutions. As new results, we obtain solutions that are given for arbitrary frequencies, amplitudes and time regions. In a broad range of parameters, a vibrating cavity model exhibits the general property of exponential instability. Marginal behavior of the system manifests in a power-like growth of radiated energy.Comment: 17 pages, 7 figure

Stationary solutions of the one-dimensional nonlinear Schroedinger equation: I. Case of repulsive nonlinearity

All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the attractive case. Our solutions take the form of stationary trains of dark or grey density-notch solitons. Real stationary states are in one-to-one correspondence with those of the linear Schr\"odinger equation. Complex stationary states are uniquely nonlinear, nodeless, and symmetry-breaking. Our solutions apply to many physical contexts, including the Bose-Einstein condensate and optical pulses in fibers.Comment: 11 pages, 7 figures -- revised versio

Stability of stationary states in the cubic nonlinear Schroedinger equation: applications to the Bose-Einstein condensate

The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a harmonic potential. Our comprehensive studies emphasize physical interpretations useful to experimentalists. Perturbation by stochastic white noise, phase engineering, and higher order nonlinearity are considered. We treat both attractive and repulsive nonlinearity and illustrate the soliton-train nature of the stationary states.Comment: 9 pages, 11 figure