Magnetic moment predictions of odd-A nuclei with the Bayesian neural network approach

The Bayesian neural network approach has been employed to improve the nuclear magnetic moment predictions of odd-A nuclei. The Schmidt magnetic moment obtained from the extreme single-particle shell model makes large root-mean-square (rms) deviations from data, i.e., 0.949 \begin{document}$ \mu_\mathrm{N} $\end{document} and 1.272 \begin{document}$ \mu_\mathrm{N} $\end{document} for odd-neutron nuclei and odd-proton nuclei, respectively. By including the dependence of the nuclear spin and Schmidt magnetic moment, the machine-learning approach precisely describes the magnetic moments of odd-A nuclei with rms deviations of 0.036 \begin{document}$ \mu_\mathrm{N} $\end{document} for odd-neutron nuclei and 0.061 \begin{document}$ \mu_\mathrm{N} $\end{document} for odd-proton nuclei. Furthermore, the evolution of magnetic moments along isotopic chains, including the staggering and sudden jump trend, which are difficult to describe using nuclear models, have been well reproduced by the Bayesian neural network (BNN) approach. The magnetic moments of doubly closed-shell \begin{document}$ \pm1 $\end{document} nuclei, for example, isoscalar and isovector magnetic moments, have been well studied and compared with the corresponding non-relativistic and relativistic calculations.     

EcoQBNs: First Application of Ecological Modeling with Quantum Bayesian Networks

A recent advancement in modeling was the development of quantum Bayesian networks (QBNs). QBNs generally differ from BNs by substituting traditional Bayes calculus in probability tables with the quantum amplification wave functions. QBNs can solve a variety of problems which are unsolvable by, or are too complex for, traditional BNs. These include problems with feedback loops and temporal expansions; problems with non-commutative dependencies in which the order of the specification of priors affects the posterior outcomes; problems with intransitive dependencies constituting the circular dominance of the outcomes; problems in which the input variables can affect each other, even if they are not causally linked (entanglement); problems in which there may be >1 dominant probability outcome dependent on small variations in inputs (superpositioning); and problems in which the outcomes are nonintuitive and defy traditional probability calculus (Parrondo’s paradox and the violation of the Sure Thing Principle). I present simple examples of these situations illustrating problems in prediction and diagnosis, and I demonstrate how BN solutions are infeasible, or at best require overly-complex latent variable structures. I then argue that many problems in ecology and evolution can be better depicted with ecological QBN (EcoQBN) modeling. The situations that fit these kinds of problems include noncommutative and intransitive ecosystems responding to suites of disturbance regimes with no specific or single climax condition, or that respond differently depending on the specific sequence of the disturbances (priors). Case examples are presented on the evaluation of habitat conditions for a bat species, representing state-transition models of a boreal forest under disturbance, and the entrainment of auditory signals among organisms. I argue that many current ecological analysis structures—such as state-and-transition models, predator–prey dynamics, the evolution of symbiotic relationships, ecological disturbance models, and much more—could greatly benefit from a QBN approach. I conclude by presenting EcoQBNs as a nascent field needing the further development of the quantum mathematical structures and, eventually, adjuncts to existing BN modeling shells or entirely new software programs to facilitate model development and application.     

Message Passing-Based Inference for Time-Varying Autoregressive Models

Time-varying autoregressive (TVAR) models are widely used for modeling of non-stationary signals. Unfortunately, online joint adaptation of both states and parameters in these models remains a challenge. In this paper, we represent the TVAR model by a factor graph and solve the inference problem by automated message passing-based inference for states and parameters. We derive structured variational update rules for a composite “AR node” with probabilistic observations that can be used as a plug-in module in hierarchical models, for example, to model the time-varying behavior of the hyper-parameters of a time-varying AR model. Our method includes tracking of variational free energy (FE) as a Bayesian measure of TVAR model performance. The proposed methods are verified on a synthetic data set and validated on real-world data from temperature modeling and speech enhancement tasks.     

Variationally Inferred Sampling through a Refined Bound

In this work, a framework to boost the efficiency of Bayesian inference in probabilistic models is introduced by embedding a Markov chain sampler within a variational posterior approximation. We call this framework “refined variational approximation”. Its strengths are its ease of implementation and the automatic tuning of sampler parameters, leading to a faster mixing time through automatic differentiation. Several strategies to approximate evidence lower bound (ELBO) computation are also introduced. Its efficient performance is showcased experimentally using state-space models for time-series data, a variational encoder for density estimation and a conditional variational autoencoder as a deep Bayes classifier.     

BayesWHAM: A Bayesian approach for free energy estimation,reweighting, and uncertainty quantification in the weighted histogram analysis method

The weighted histogram analysis method (WHAM) is a powerful approach to estimate molecular free energy surfaces (FES) from biased simulation data. Bayesian reformulations of WHAM are valuable in proving statistically optimal use of the data and providing a transparent means to incorporate regularizing priors and estimate statistical uncertainties. In this work, we develop a fully Bayesian treatment of WHAM to generate statistically optimal FES estimates in any number of biasing dimensions under arbitrary choices of the Bayes prior. Rigorous uncertainty estimates are generated by Metropolis‐Hastings sampling from the Bayes posterior. We also report a means to project the FES and its uncertainties into arbitrary auxiliary order parameters beyond those in which biased sampling was conducted. We demonstrate the approaches in applications of alanine dipeptide and the unthreading of a synthetic mimic of the astexin‐3 lasso peptide. Open‐source MATLAB and Python implementations of our codes are available for free public download. © 2017 Wiley Periodicals, Inc.     

Towards analytical model optimization in atmospheric tomography

Modern ground‐based telescopes rely on a technology called adaptive optics in order to compensate for the loss of angular resolution caused by atmospheric turbulence. Next‐generation adaptive optics systems designed for a wide field of view require a stable and high‐resolution reconstruction of the turbulent atmosphere. By introducing a novel Bayesian method, we address the problem via reconstructing the atmospheric turbulence strength profile and the turbulent layers simultaneously, where we only use wavefront measurements of incoming light from guide stars. Most importantly, we demonstrate how this method can be used for model optimization as well. We propose two different algorithms for solving the maximum a posteriori estimate: the first approach is based on alternating minimization and has the advantage of integrability into existing atmospheric tomography methods. In the second approach, we formulate a convex non‐differentiable optimization problem, which is solved by an iterative thresholding method. This approach clearly illustrates the underlying sparsity‐enforcing mechanism for the strength profile. By introducing a tuning/regularization parameter, an automated model reduction of the layer structure of the atmosphere is achieved. Using numerical simulations, we demonstrate the performance of our method in practice. Copyright © 2016 John Wiley & Sons, Ltd.     

基于分层贝叶斯时空模型的雾霾天气过程计数分析

本文以北京市8个行政区(东城区、西城区、石景山区、海淀区、朝阳区、昌平区、顺义区、怀柔区)的PM2.5指数计算各区逐月雾霞天气过程计数频数为研究对象,选择考虑包括地表温度、相对湿度、平均风速、SO_2质量浓度和NO_2质量浓度在内的5个影响因素。本文定义雾霾天气过程,构建分层贝叶斯时空模型,在一个统计模型中对诸多影响因素进行分析,并从计数分析的角度对北京市雾霾天气现象的时空分布、影响因素进行深入讨论。通过分析得出,温度、湿度、污染物浓度对于雾霾天气过程发生具有促进作用,平均风速对于雾霾天气过程发生具有抑制作用。从时空角度分析,从时间维度上看雾霾天气过程的发生具有明显的季节性特征,冬季(1月、2月)以及3月雾霾天气过程发生次数最高,春季(4月、5月)发生次数最低,秋季发生次数略高于夏季。从空间维度上来看,中心城区(东城区、西城区、石景山、海淀区、朝阳区)雾霾天气过程发生次数明显高于郊区(顺义、昌平、怀柔),以东城区、西城区和朝阳区最为严重。     

基于混合模型对地震巨灾风险的分析

POT模型常被用于分析巨灾风险,然而在应用POT模型时,阀值的估计及选择存在很多困难。本文提出用混合模型对巨灾风险进行估计,并讨论混合模型的贝叶斯统计分析。基于混合模型及贝叶斯统计方法,本文对我国1966年至2014年问GDP调整后的地震直接经济损失进行分析,并根据最终模型计算出不同置信度水平下的VaR值和ES值,为我国地震巨灾风险管理提供了理论依据。     

An admissibility criterion for inference rules with metavariables in the modal logic <Emphasis Type="Italic">S</Emphasis>4.<Emphasis Type="Italic">α</Emphasis><Subscript><Emphasis Type="Italic">N</Emphasis></Subscript>

Using the criterion of this paper, we solve the substitution problem and obtain an algorithm for determining the solvability of logical equations in the modal logic S4.α _N . Another corollary of the criterion is the solvability of the corresponding quasiequational theory of the free modal algebra whose signature is enriched with constants for the free generators.     

加权平衡熵损失函数下Poisson分布参数的Bayes估计

首先, 基于平衡损失函数的形式, 给出一个加权平衡熵损失函数, 并将其应用到Poisson分布中, 得到了该损失函数下参数的Bayes估计. 其次, 在先验分布为Gamma分布的条件下, 给出估计量的显式表达式, 证明估计量的相合性, 并利用QQ图的方法检验估计量的渐近正态性.