Bayesian Item Response Modeling in R with brms and Stan

Item Response Theory (IRT) is widely applied in the human sciences to model persons' responses on a set of items measuring one or more latent constructs. While several R packages have been developed that implement IRT models, they tend to be restricted to respective prespecified classes of models. Further, most implementations are frequentist while the availability of Bayesian methods remains comparably limited. We demonstrate how to use the R package brms together with the probabilistic programming language Stan to specify and fit a wide range of Bayesian IRT models using flexible and intuitive multilevel formula syntax. Further, item and person parameters can be related in both a linear or non-linear manner. Various distributions for categorical, ordinal, and continuous responses are supported. Users may even define their own custom response distribution for use in the presented framework. Common IRT model classes that can be specified natively in the presented framework include 1PL and 2PL logistic models optionally also containing guessing parameters, graded response and partial credit ordinal models, as well as drift diffusion models of response times coupled with binary decisions. Posterior distributions of item and person parameters can be conveniently extracted and post-processed. Model fit can be evaluated and compared using Bayes factors and efficient cross-validation procedures.Comment: 54 pages, 16 figures, 3 table

Asymptotic Redundancies for Universal Quantum Coding

Clarke and Barron have recently shown that the Jeffreys' invariant prior of Bayesian theory yields the common asymptotic (minimax and maximin) redundancy of universal data compression in a parametric setting. We seek a possible analogue of this result for the two-level {\it quantum} systems. We restrict our considerations to prior probability distributions belonging to a certain one-parameter family, $q(u)$, $-\infty < u < 1$. Within this setting, we are able to compute exact redundancy formulas, for which we find the asymptotic limits. We compare our quantum asymptotic redundancy formulas to those derived by naively applying the classical counterparts of Clarke and Barron, and find certain common features. Our results are based on formulas we obtain for the eigenvalues and eigenvectors of $2^n \times 2^n$ (Bayesian density) matrices, $\zeta_{n}(u)$. These matrices are the weighted averages (with respect to $q(u)$) of all possible tensor products of $n$ identical $2 \times 2$ density matrices, representing the two-level quantum systems. We propose a form of {\it universal} coding for the situation in which the density matrix describing an ensemble of quantum signal states is unknown. A sequence of $n$ signals would be projected onto the dominant eigenspaces of \ze_n(u)

Photon counting statistics of a microwave cavity

The development of microwave photon detectors is paving the way for a wide range of quantum technologies and fundamental discoveries involving single photons. Here, we investigate the photon emission from a microwave cavity and find that distribution of photon waiting times contains information about few-photon processes, which cannot easily be extracted from standard correlation measurements. The factorial cumulants of the photon counting statistics are positive at all times, which may be intimately linked with the bosonic quantum nature of the photons. We obtain a simple expression for the rare fluctuations of the photon current, which is helpful in understanding earlier results on heat transport statistics and measurements of work distributions. Under non-equilibrium conditions, where a small temperature gradient drives a heat current through the cavity, we formulate a fluctuation-dissipation relation for the heat noise spectra. Our work suggests a number of experiments for the near future, and it offers theoretical questions for further investigation.Comment: 16 pages, 3 figures, final version as published in Phys. Rev.

The economics of copyright law: a stocktake of the literature

This article is a survey of publications by economists writing on copyright law. It begins with a general overview of how economists analyse these questions; the distinction is made between the economics of copying and the economic aspects of copyright law as analysed in law and economics. It then continues with sections on research on the effects of copying and downloading and the effects of unauthorised use (‘piracy’) and ends with an overall evaluation of the economics of copyright in the light of recent technological changes. Economists have always been, and still are, somewhat sceptical about copyright and question what alternatives there are to it. On balance, most accept the role of copyright law in the creative industries while urging caution about its becoming too strong. And although European authors’ rights are different in legal terms from the Anglo-American copyright, the economic analysis of these laws is essentially the same

On the role of the Jeffreys'sheltering mechanism in the sustain of extreme water waves

The effect of the wind on the sustain of extreme water waves is investigated experimentally and numerically. A series of experiments conducted in the Large Air-Sea Interactions Facility (LASIF) showed that a wind blowing over a strongly nonlinear short wave group due to the linear focusing of a modulated wave train may increase the life time of the extreme wave event. The expriments suggested that the air flow separation that occurs on the leeward side of the steep crests may sustain longer the maximum of modulation of the focusing-defocusing cycle. Based on a Boundary-Integral Equation Method and a pressure distribution over the steep crests given by the Jeffreys'sheltering theory, similar numerical simulations have confirmed the experimental resultsComment: accept\'{e} pour publication 200