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This work aims to jointly estimate the arrival rate of customers to a market and the nested logit model that forecasts hierarchical customer choices from an assortment of products. The estimation is based on censored transactional data, where lost sales are not recorded. The goal is to determine the arrival rate, customer taste coefficients, and nest dissimilarity parameters that maximize the likelihood of the observed data. The problem is formulated as a maximum likelihood estimation model that addresses two prevailing challenges in the existing literature: Estimating demand fromdata with unobservable lost salesand capturingcustomer taste heterogeneity arising from hierarchical choices. However, the model is intractable to solve or analyze due to the nonconcavity of the likelihood function in both taste coefficients and dissimilarity parameters. We characterize conditions under which the model parameters are identifiable. Our results reveal that the parameter identification is influenced by thediversity of products and nests. We also develop a sequential minorization-maximization algorithm to solve the problem, by which the problem boils down to solving a series of convex optimization models with simple structures. Then, we show the convergence of the algorithm by leveraging the structural properties of these models. We evaluate the performance of the algorithm by comparing it with widely used benchmarks, using both synthetic and real data. Our findings show that the algorithm consistently outperforms the benchmarks in maximizing in-sample likelihood and ranks among the top two in out-of-sample prediction accuracy. Moreover, our algorithm is particularly effective in estimating nested logit models with low dissimilarity parameters, yielding higher profitability compared to the benchmarks. 

Abstract For next-generation neutrinoless double beta decay experiments, extremely low backgrounds are necessary. An understanding of in-situ cosmogenic backgrounds is critical to the design effort. In-situ cosmogenic backgrounds impose a depth requirement and especially impact the choice of host laboratory. Often, simulations are used to understand background effects, and these simulations can have large uncertainties. One way to characterize the systematic uncertainties is to compare unalike simulation programs. In this paper, a suite of neutron simulations with identical geometries and starting parameters have been performed with Geant4 and MCNP, using geometries relevant to the LEGEND-1000 experiment. This study is an important step in gauging the uncertainties of simulations-based estimates. To reduce project risks associated with simulation uncertainties, a novel alternative shield of methane-doped liquid argon is considered in this paper for LEGEND-1000, which could achieve large background reduction without requiring significant modification to the baseline design. 

Why the Challenger Deep, the deepest point on Earth’s solid surface, is so deep is unclear, but part of the reason must be the age and density of the downgoing plate. Northwest Pacific oceanic crust subducting in the Izu-Bonin-Mariana Trench is Cretaceous and Jurassic, but the age and nature of Pacific oceanic crust subducting in the southernmost Mariana Trench remains unknown. Here we present the first study of seafloor basalts recovered by the full-ocean-depth crewed submersible Fendouzhe from the deepest seafloor around the Challenger Deep, from both the overriding and downgoing plates. 40Ar/39Ar ages indicate that downgo¬ing basalts are Early Cretaceous (ca. 125 Ma), indicating they are part of the Pacific plate rather than the nearby Oligocene Caroline microplate. Downgoing-plate basalts are slightly enriched in incompatible elements but have similar trace element and Hf isotope compositions to other northwest Pacific mid-ocean ridge basalts (MORBs). They also have slightly enriched Sr-Nd-Pb isotope compositions like those of the Indian mantle domain. These features may have formed with contributions from plume-derived components via plume-ridge interac¬tions. One sample from the overriding plate gives an 40Ar/39Ar age of ca. 55 Ma, about the same age as subduction initiation, to form the Izu-Bonin-Mariana convergent margin. Our results suggest that 50%–90% of the Pb budget of Mariana arc magmas is derived from the subducted MORBs with Indian-type isotope affinity. 

Abstract While basaltic volcanism is dominant during rifting and continental breakup, felsic magmatism may be a significant component of some rift margins. During International Ocean Discovery Program (IODP) Expedition 396 on the continental margin of Norway, a graphite‐garnet‐cordierite bearing dacitic unit (the Mimir dacite) was recovered in two holes within early Eocene sediments on Mimir High (Site U1570), a marginal high on the Vøring Transform Margin. Here, we present a comprehensive textural, petrological, and geochemical study of the Mimir dacite in order to assess its origin and discuss the geodynamic implications. The major mineral phases (garnet, cordierite, quartz, plagioclase, alkali feldspar) are hosted in a fresh rhyolitic, vesicular, glassy matrix that is locally mingled with sediments. The major element chemistry of garnet and cordierite, the presence of zircon inclusions with inherited cores, and thermobarometric calculations all support an upper crustal metapelitic origin. While most magma‐rich margin models favor crustal anatexis in the lower crust, thermobarometric calculations performed here show that the Mimir dacite was produced at upper‐crustal depths (<5 kbar, 18 km depth) and high temperature (750–800°C) with up to 3 wt% water content. In situ U‐Pb analyses on zircon inclusions give a magmatic crystallization age of 54.6 ± 1.1 Ma, consistent with emplacement that post‐dates the Paleocene‐Eocene Thermal Maximum. Our results suggest that the opening of the Northeast Atlantic was associated with a phase of low‐pressure, high‐temperature crustal anatexis preceding the main phase of magmatism.