24,445 research outputs found
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, , . 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 (Bayesian density) matrices,
. These matrices are the weighted averages (with respect to
) of all possible tensor products of identical 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 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 (âpiracyâ) 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 authorsâ 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
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