Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models

Structured additive regression provides a general framework for complex Gaussian and non-Gaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying coefficients, random effects and further regression terms. The large flexibility of structured additive regression makes function selection a challenging and important task, aiming at (1) selecting the relevant covariates, (2) choosing an appropriate and parsimonious representation of the impact of covariates on the predictor and (3) determining the required interactions. We propose a spike-and-slab prior structure for function selection that allows to include or exclude single coefficients as well as blocks of coefficients representing specific model terms. A novel multiplicative parameter expansion is required to obtain good mixing and convergence properties in a Markov chain Monte Carlo simulation approach and is shown to induce desirable shrinkage properties. In simulation studies and with (real) benchmark classification data, we investigate sensitivity to hyperparameter settings and compare performance to competitors. The flexibility and applicability of our approach are demonstrated in an additive piecewise exponential model with time-varying effects for right-censored survival times of intensive care patients with sepsis. Geoadditive and additive mixed logit model applications are discussed in an extensive appendix

Fluctuations of radiation from a chaotic laser below threshold

Radiation from a chaotic cavity filled with gain medium is considered. A set of coupled equations describing the photon density and the population of gain medium is proposed and solved. The spectral distribution and fluctuations of the radiation are found. The full noise is a result of a competition between positive correlations of photons with equal frequencies (due to stimulated emission and chaotic scattering) which increase fluctuations, and a suppression due to interaction with a gain medium which leads to negative correlations between photons. The latter effect is responsible for a pronounced suppression of the photonic noise as compared to the linear theory predictions.Comment: 7 pages, 5 figures; expanded version, to appear in Phys. Rev.

Ferromagnetice exchange in bichloride bridged Cu(II) chains: magnetostructural correlations between ordered and disordered systems

The synthesis, structure, magnetic properties, and theoretical analysis of a new phase of dichloro(2-thlaro-3-methylpyridine)copper(II) (2) and its isomorphous analogue dichloro(2bromo-3-methylpyridine)copper(II) (3) are reported. Both complexes crystallize in the orthorhombic space group Pbca and present square pyramidal Cu(II) ions bridged into chains by chloride ions with each,copper(II)-bearing a single pyridine ligand. Variable temperature magnetic Susceptibility measurements were well fit by a uniform one-dimensional ferromagnetic chain model with,2) J = 69.0(7) K, C = 0.487 emu-K/mol-Oe; 3, J = 73.9(4) K, C = 0.463 emu-K/mol-Oe = Hamiltonian). The experimental J-values were confirmed-via theOretical calculations. Comparison to a known disordered polymorph of dichloro(2-chloro-3-inethylpyridine)copper(II), 1, shows marked differences as there are significant antiferromagnetic next-nearest neighbor interactions, in 1 in addition to randomness induced by the disorder which provide a distinctly different magnetic response. The differences in magnetic behavior are attributed principally to the structural difference in the Cu(II) coordination sphere, 1 being significantly closer to trigonal-bipyramidal, whose difference changes both the nearest and next-nearest neighbor interactions