A Riemannian-Stein Kernel Method

This paper presents a theoretical analysis of numerical integration based on interpolation with a Stein kernel. In particular, the case of integrals with respect to a posterior distribution supported on a general Riemannian manifold is considered and the asymptotic convergence of the estimator in this context is established. Our results are considerably stronger than those previously reported, in that the optimal rate of convergence is established under a basic Sobolev-type assumption on the integrand. The theoretical results are empirically verified on $\mathbb{S}^2$

Stein Point Markov Chain Monte Carlo

An important task in machine learning and statistics is the approximation of a probability measure by an empirical measure supported on a discrete point set. Stein Points are a class of algorithms for this task, which proceed by sequentially minimising a Stein discrepancy between the empirical measure and the target and, hence, require the solution of a non-convex optimisation problem to obtain each new point. This paper removes the need to solve this optimisation problem by, instead, selecting each new point based on a Markov chain sample path. This significantly reduces the computational cost of Stein Points and leads to a suite of algorithms that are straightforward to implement. The new algorithms are illustrated on a set of challenging Bayesian inference problems, and rigorous theoretical guarantees of consistency are established

FLOW ANALYSIS AND MODELING OF THE LAKE ÁGUA PRETA: WATER SOURCE OF THE BELÉM METROPOLITAN AREA

The natural conditions of water resources can be modified with the unsustainable use of them. For example, in Belém, capital of Pará State, Água Preta Lake has a history of degradation jeopardize the drinking water supply in Belém. Thus, the main contribution of this work is to develop a study on modeling hydrodynamic study of Água Preta Lake. Such study is carried through the bathymetric of 2009 performed with an ADCP. The bathymetry and substrate data that composes the Lake and its boundary. The bathymetry data are used to construct the digital elevation model, with the coordinates x, y and z in UTM; while the composition of the substrate is used for the determination of the Manning coefficient. The coordinates x, y, z and Manning coefficient are used in the hydrodynamic model. This one is the classic model of Saint-Venant. In this case, a vertical integration is applied to the three-dimensional equations of Navier-Stokes for incompressible flow with outline conditions, of bottom and of liquid and solid surface, included. Thus, the problem becomes two-dimensional (2D) and the values obtained for velocities are medium in the vertical direction. The velocities are the input data for the many models, such as pollutant dispersion sediment transport and aquatic fauna and flora habitats. Thus, besides of hydrodynamic model explains the patterns of flow in the lake, it can be employed for the others models of the Lake Água Preta

Bone Mineral Density and Trabecular Bone Score Changes throughout Menopause in Women with HIV

Objective: The objectives of this study were to describe the trajectories of bone mineral density (BMD) and trabecular bone score (TBS) changes throughout pre-menopause (reproductive phase and menopausal transition) and post-menopause (early and late menopause) in women with HIV (WWH) undergoing different antiretroviral therapies (ARTs) and explore the risk factors associated with those changes. Methods: This was an observational longitudinal retrospective study in WWH with a minimum of two DEXA evaluations comprising BMD and TBS measurements, both in the pre-menopausal and post-menopausal periods. Menopause was determined according to the STRAW+10 criteria, comprising four periods: the reproductive period, menopausal transition, and early- and late-menopausal periods. Mixed-effects models were fitted to estimate the trajectories of the two outcomes (BMD and TBS) over time. Annualized lumbar BMD and TBS absolute and percentage changes were calculated in each STRAW+10 time window. A backward elimination procedure was applied to obtain the final model, including the predictors that affected the trajectories of BMD or TBS over time. Results: A total of 202 WWH, all Caucasian, were included. In detail, 1954 BMD and 195 TBS data were analyzed. The median number of DEXA evaluations per woman was 10 (IQR: 7, 12). The median observation periods per patient were 12.0 years (IQR = 8.9-14.4) for BMD and 6.0 years (IQR: 4.3, 7.9) for TBS. The prevalence of osteopenia (63% vs. 76%; p < 0.001) and osteoporosis (16% vs. 36%; p < 0.001) increased significantly between the pre-menopausal and post-menopausal periods. Both BMD (1.03 (+/- 0.14) vs. 0.92 (+/- 0.12) g/cm2; p < 0.001) and TBS (1.41 (IQR: 1.35, 1.45) vs. 1.32 (IQR: 1.28, 1.39); p < 0.001) decreased significantly between the two periods. The trend in BMD decreased across the four STRAW+10 periods, with a slight attenuation only in the late-menopausal period when compared with the other intervals. The TBS slope did not significantly change throughout menopause. The delta mean values of TBS in WWH were lower between the menopausal transition and reproductive period compared with the difference between menopause and menopausal transition. Conclusions: Both BMD and TBS significantly decreased over time. The slope of the change in BMD and TBS significantly decreased in the menopausal transition, suggesting that this period should be considered by clinicians as a key time during which to assess bone health and modifiable risk factors in WWH

Stein’s Method Meets Computational Statistics: A Review of Some Recent Developments

peer reviewedStein’s method compares probability distributions through the study of a class of linear operators called Stein operators.While mainly studied in probability and used to underpin theoretical statistics, Stein’s method has led to significant advances in computational statistics in recent years. The goal of this survey is to bring together some of these recent developments, and in doing so, to stimulate further research into the successful field of Stein’s method and statistics. The topics we discuss include tools to benchmark and compare sampling methods such as approximate Markov chain Monte Carlo, deterministic alternatives to sampling methods, control variate techniques, parameter estimation and goodness-of-fit testin

Female Behaviour Drives Expression and Evolution of Gustatory Receptors in Butterflies

Secondary plant compounds are strong deterrents of insect oviposition and feeding, but may also be attractants for specialist herbivores. These insect-plant interactions are mediated by insect gustatory receptors (Grs) and olfactory receptors (Ors). An analysis of the reference genome of the butterfly Heliconius melpomene, which feeds on passion-flower vines (Passiflora spp.), together with whole-genome sequencing within the species and across the Heliconius phylogeny has permitted an unprecedented opportunity to study the patterns of gene duplication and copy-number variation (CNV) among these key sensory genes. We report in silico gene predictions of 73 Gr genes in the H. melpomene reference genome, including putative CO2, sugar, sugar alcohol, fructose, and bitter receptors. The majority of these Grs are the result of gene duplications since Heliconius shared a common ancestor with the monarch butterfly or the silkmoth. Among Grs but not Ors, CNVs are more common within species in those gene lineages that have also duplicated over this evolutionary time-scale, suggesting ongoing rapid gene family evolution. Deep sequencing (∼1 billion reads) of transcriptomes from proboscis and labial palps, antennae, and legs of adult H. melpomene males and females indicates that 67 of the predicted 73 Gr genes and 67 of the 70 predicted Or genes are expressed in these three tissues. Intriguingly, we find that one-third of all Grs show female-biased gene expression (n = 26) and nearly all of these (n = 21) are Heliconius-specific Grs. In fact, a significant excess of Grs that are expressed in female legs but not male legs are the result of recent gene duplication. This difference in Gr gene expression diversity between the sexes is accompanied by a striking sexual dimorphism in the abundance of gustatory sensilla on the forelegs of H. melpomene, suggesting that female oviposition behaviour drives the evolution of new gustatory receptors in butterfly genomes