30,429 research outputs found
Approximating Cross-validatory Predictive P-values with Integrated IS for Disease Mapping Models
An important statistical task in disease mapping problems is to identify out-
lier/divergent regions with unusually high or low residual risk of disease.
Leave-one-out cross-validatory (LOOCV) model assessment is a gold standard for
computing predictive p-value that can flag such outliers. However, actual LOOCV
is time-consuming because one needs to re-simulate a Markov chain for each
posterior distribution in which an observation is held out as a test case. This
paper introduces a new method, called iIS, for approximating LOOCV with only
Markov chain samples simulated from a posterior based on a full data set. iIS
is based on importance sampling (IS). iIS integrates the p-value and the
likelihood of the test observation with respect to the distribution of the
latent variable without reference to the actual observation. The predictive
p-values computed with iIS can be proved to be equivalent to the LOOCV
predictive p-values, following the general theory for IS. We com- pare iIS and
other three existing methods in the literature with a lip cancer dataset
collected in Scotland. Our empirical results show that iIS provides predictive
p-values that are al- most identical to the actual LOOCV predictive p-values
and outperforms the existing three methods, including the recently proposed
ghosting method by Marshall and Spiegelhalter (2007).Comment: 21 page
Weak Measurement of Qubit Oscillations with Strong Response Detectors: Violation of the Fundamental Bound Imposed on Linear Detectors
We investigate the continuous weak measurement of a solid-state qubit by
single electron transistors in nonlinear response regime. It is found that the
signal-to-noise ratio can violate the universal upper bound imposed quantum
mechanically to any linear response detectors. We understand the violation by
means of the cross-correlation of the detector currents.Comment: 4 pages, 4 figure
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