Reliable inference for complex models by discriminative composite likelihood estimation

Composite likelihood estimation has an important role in the analysis of multivariate data for which the full likelihood function is intractable. An important issue in composite likelihood inference is the choice of the weights associated with lower-dimensional data sub-sets, since the presence of incompatible sub-models can deteriorate the accuracy of the resulting estimator. In this paper, we introduce a new approach for simultaneous parameter estimation by tilting, or re-weighting, each sub-likelihood component called discriminative composite likelihood estimation (D-McLE). The data-adaptive weights maximize the composite likelihood function, subject to moving a given distance from uniform weights; then, the resulting weights can be used to rank lower-dimensional likelihoods in terms of their influence in the composite likelihood function. Our analytical findings and numerical examples support the stability of the resulting estimator compared to estimators constructed using standard composition strategies based on uniform weights. The properties of the new method are illustrated through simulated data and real spatial data on multivariate precipitation extremes.Comment: 29 pages, 4 figure

Aziridinium lead iodide: a stable, low bandgap hybrid halide perovskite for photovoltaics

The low ionization energy of an $A$ site molecule is a very important factor, which determines the thermodynamical stability of $A$PbI$_3$ hybrid halide perovskites, while the size of the molecule governs the stable phase at room temperature and, eventually, the bandgap. It is challenging to achieve both a low ionization energy and the reasonable size for the PbI$_3$ cage to circumvent the stability issue inherent to hybrid halide perovskites. Here we propose a new three-membered charged ring radical, which demonstrates a low ionization energy that renders a good stability for its corresponding perovskite and a reasonable cation size that translates into a suitable bandgap for the photovoltaic application. We use ab initio calculations to evaluate a polymorphism of the crystal structure of the proposed halide hybrid perovskite, its stability and electronic properties in comparison to the mainstream perovskites, such as the methylammonium and formamidinium lead iodide. Our results highlight the importance of van der Waals interactions for predicting a correct polymorphism of the perovskite vs hexagonal crystal structure.Comment: 22 pages, 5 figures, 5 table