5,400 research outputs found
Well-Posedness of Measurement Error Models for Self-Reported Data
It is widely admitted that the inverse problem of estimating the distribution of a latent variable X* from an observed sample of X, a contaminated measurement of X*, is ill-posed. This paper shows that a property of self-reporting errors, observed from validation studies, is that the probability of reporting the truth is nonzero conditional on the true values, and furthermore, this property implies that measurement error models for self-reporting data are in fact well-posed. We also illustrate that the classical measurement error models may in fact be conditionally well-posed given prior information on the distribution of the latent variable X*.
Well-posedness of measurement error models for self-reported data
It is widely admitted that the inverse problem of estimating the distribution of a latent variable X* from an observed sample of X, a contaminated measurement of X*, is ill-posed. This paper shows that measurement error models for self-reporting data are well-posed, assuming the probability of reporting truthfully is nonzero, which is an observed property in validation studies. This optimistic result suggests that one should not ignore the point mass at zero in the error distribution when modeling measurement errors in self-reported data. We also illustrate that the classical measurement error models may in fact be conditionally well-posed given prior information on the distribution of the latent variable X*. By both a Monte Carlo study and an empirical application, we show that failing to account for the property can lead to significant bias on estimation of distribution of X*.
Generalized Turing Patterns and Their Selective Realization in Spatiotemporal Systems
We consider the pattern formation problem in coupled identical systems after
the global synchronized state becomes unstable. Based on analytical results
relating the coupling strengths and the instability of each spatial mode
(pattern) we show that these spatial patterns can be selectively realized by
varying the coupling strengths along different paths in the parameter space.
Furthermore, we discuss the important role of the synchronized state (fixed
point versus chaotic attractor) in modulating the temporal dynamics of the
spatial patterns.Comment: 9 pages, 3 figure
Energy spread and current-current correlation in quantum systems
We consider energy (heat) transport in quantum systems, and establish a
relationship between energy spread and energy current-current correlation
function. The energy current-current correlation is related to thermal
conductivity by the Green-Kubo formula, and thus this relationship allows us to
study conductivity directly from the energy spread process. As an example, we
investigate a spinless fermion model; the numerical results confirm the
relationship.Comment: 5 pages, 2 figure
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