Scalable Bayesian computation for crossed and nested hierarchical models

We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and nested multilevel models, which are used ubiquitously in applied sciences. The posterior dependence in both classes is sparse: in crossed random effects models it resembles a random graph, whereas in nested multilevel models it is tree-structured. For each class we identify a framework for scalable computation, building on previous work. Methods for crossed models are based on extensions of appropriately designed collapsed Gibbs samplers, where we introduce the idea of local centering; while methods for nested models are based on sparse linear algebra (SLA) and data augmentation. We provide a theoretical analysis of the proposed algorithms in some simplified settings, including a comparison with previously proposed methodologies and an average-case analysis based on random graph theory. Numerical experiments, including two challenging real data analyses on predicting electoral results and real estate prices, compare with off-the-shelf Hamiltonian Monte Carlo, displaying drastic improvement in performance. The code for replicating the experiments in the article and for implementing our methods can be found at https://github.com/timsf/crossed-effects and https://github.com/timsf/nested-effects

Total synthesis of the Amaryllidaceae alkaloid clivonine

Two syntheses of the Amaryllidaceae alkaloid clivonine (1) are described. Both employ previously reported 7-arylhydrindane 6 as an intermediate but differ in the method employed for subsequent introduction of what becomes the ring-B lactone carbonyl carbon (C7). The synthesis featuring a Bischler–Napieralski reaction for this transformation constitutes the first asymmetric synthesis of natural (+)-clivonine. Crystal structures for compounds (±)-13, (±)-16, (−)-20 and (±)-28 are also reported

Исследование последовательности импульсов тормозного излучения малогабаритного бетатрона

Разработана имитационная модель потока импульсного тормозного излучения и реализована в подпрограмме на MathCad. Адаптирована модель потока импульсного тормозного излучения к имитационной модели формирования цифровых радиографических изображений. Исследовано влияние параметров исходного потока тормозного излучения на качество цифровых радиографических изображений. Проведён цикл натурных экспериментов по оценке изменения параметров потока импульсов регистрируемого излучения с цифровых детекторов на этапах формирования радиографического изображения на комплексе высокоэнергетической цифровой радиографии Томского политехнического университета.A simulation model of pulsed radiation flux and implemented in a subroutine on MathCad is available. Pulse bremsstrahlung flow model for a simulation model of digital radiographic image formation Adapted. Effect of source stream parameters. Experiments on the study of changes in the parameters of the pulse flux are recorded using digital detectors at the stages of radiographic image formation on the complexes of high-energy digital radiography of the Tomsk Polytechnic University