On model selection criteria for climate change impact studies

Climate change impact studies inform policymakers on the estimated damages of future climate change on economic, health and other outcomes. In most studies, an annual outcome variable is observed, e.g. annual mortality rate, along with higher-frequency regressors, e.g. daily temperature and precipitation. Practitioners use summaries of the higher-frequency regressors in fixed effects panel models. The choice over summary statistics amounts to model selection. Some practitioners use Monte Carlo cross-validation (MCCV) to justify a particular specification. However, conventional implementation of MCCV with fixed testing-to-full sample ratios tends to select over-fit models. This paper presents conditions under which MCCV, and also information criteria, can deliver consistent model selection. Previous work has established that the Bayesian information criterion (BIC) can be inconsistent for non-nested selection. We illustrate that the BIC can also be inconsistent in our framework, when all candidate models are misspecified. Our results have practical implications for empirical conventions in climate change impact studies. Specifically, they highlight the importance of a priori information provided by the scientific literature to guide the models considered for selection. We emphasize caution in interpreting model selection results in settings where the scientific literature does not specify the relationship between the outcome and the weather variables.Comment: Additional simulation results available from authors by reques

Spectral properties of photon pairs generated by spontaneous four wave mixing in inhomogeneous photonic crystal fibers

The photonic crystal fiber (PCF) is one of the excellent media for generating photon pairs via spontaneous four wave mixing. Here we study how the inhomogeneity of PCFs affect the spectral properties of photon pairs from both the theoretical and experimental aspects. The theoretical model shows that the photon pairs born in different place of the inhomogeneous PCF are coherently superposed, and a modulation in the broadened spectrum of phase matching function will appear, which prevents the realization of spectral factorable photon pairs. In particular, the inhomogeneity induced modulation can be examined by measuring the spectrum of individual signal or idler field when the asymmetric group velocity matching is approximately fulfilled. Our experiments are performed by tailoring the spectrum of pulsed pump to satisfy the specified phase matching condition. The observed spectra of individual signal photons, which are produced from different segments of the 1.9 m inhomogeneous PCF, agree with the theoretical predictions. The investigations are not only useful for fiber based quantum state engineering, but also provide a dependable method to test the homogeneity of PCF.Comment: to appear in Phys. Rev.

Possible discovery of the r-process characteristics in the abundances of metal-rich barium stars

We study the abundance distributions of a sample of metal-rich barium stars provided by Pereira et al. (2011) to investigate the s- and r-process nucleosynthesis in the metal-rich environment. We compared the theoretical results predicted by a parametric model with the observed abundances of the metal-rich barium stars. We found that six barium stars have a significant r-process characteristic, and we divided the barium stars into two groups: the r-rich barium stars ($C_r>5.0$, [La/Nd]\,$<0$) and normal barium stars. The behavior of the r-rich barium stars seems more like that of the metal-poor r-rich and CEMP-r/s stars. We suggest that the most possible formation mechanism for these stars is the s-process pollution, although their abundance patterns can be fitted very well when the pre-enrichment hypothesis is included. The fact that we can not explain them well using the s-process nucleosynthesis alone may be due to our incomplete knowledge on the production of Nd, Eu, and other relevant elements by the s-process in metal-rich and super metal-rich environments (see details in Pereira et al. 2011).Comment: 5 pages, 5 figures, accepted for publication in A&

Entropy and specific heat for open systems in steady states

The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics can be built. In this paper, we show that the Boltzmann distribution in general can not describe the steady state of open system. Based on the effective Hamiltonian approach, we calculate the specific heat, the free energy and the entropy for an open system in steady states. Examples are illustrated and discussed.Comment: 4 pages, 7 figure