Multilevel Monte Carlo in approximate Bayesian computation

In the following article, we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.     

An optimization approach to adaptive multi-dimensional capital management

Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with multiple business lines including allocation. The individual capital reserve of each line can be represented by means of classical models, such as the conventional Cramér–Lundberg model, but the challenge lies in soundly modelling the correlations between the business lines. We propose a simple yet versatile approach that allows for dependence by introducing a common environmental factor. We present a novel Bayesian approach to calibrate the latent environmental state distribution based on observations concerning the claim processes. The calibration approach is adjusted for an environmental factor that changes over time. The convergence of the calibration procedure towards the true environmental state is deduced. We then point out how to determine the optimal initial capital of the different business lines under specific constraints on the ruin probability of subsets of business lines. Upon combining the above findings, we have developed an easy-to-implement approach to capital risk management in a multi-dimensional insurance risk model.     

Bayesian planning of step‐stress accelerated degradation tests under various optimality criteria

Step‐stress accelerated degradation testing (SSADT) has become a common approach to predicting lifetime for highly reliable products that are unlikely to fail in a reasonable time under use conditions or even elevated stress conditions. In literature, the planning of SSADT has been widely investigated for stochastic degradation processes, such as Wiener processes and gamma processes. In this paper, we model the optimal SSADT planning problem from a Bayesian perspective and optimize test plans by determining both stress levels and the allocation of inspections. Large‐sample approximation is used to derive the asymptotic Bayesian utility functions under 3 planning criteria. A revisited LED lamp example is presented to illustrate our method. The comparison with optimal plans from previous studies demonstrates the necessity of considering the stress levels and inspection allocations simultaneously.     

基于动态因子结构的贝叶斯分位面板协整研究

针对传统面板协整检验在建模过程中易受异常值影响以及其原假设设置的主观选择问题,本文利用动态公共因子刻画面板数据潜在的截面相关结构,提出基于动态因子的截面相关结构的贝叶斯分位面板协整检验,结合各个主要分位数水平下参数的条件后验分布,设计结合卡尔曼滤波的Gibbs抽样算法,进行贝叶斯分位面板协整检验;并进行Monte Carlo仿真实验验证贝叶斯分位面板协整检验的可行性与有效性。同时,采用中国各省金融发展和经济增长的面板数据进行实证研究,结果发现在各主要分位数水平下中国金融发展和经济增长之间具有协整关系。研究结果表明:贝叶斯分位面板协整检验方法避免了传统面板数据协整方法由于原假设设置不同而发生误判的问题,克服了异常值的影响,能够提供全面准确的模型参数估计和协整检验结果。     

Degradation modeling of 2 fatigue‐crack growth characteristics based on inverse Gaussian processes: A case study

Most modern products that are highly reliable are complex in their inner and outer structures. This situation indicates quality characterization by the interaction of multiple performance characteristics, which motivates the utilization of robust reliability models to obtain robust estimates. It is paramount to obtaining substantial information about a product's life cycle; therefore, when multiple performance characteristics are dependent, it is important to find models that address the joint distribution of performance degradation of such. In this paper, a reliability model for products with 2 fatigue‐crack growth characteristics related to 2 degradation processes is developed. The proposed model considers the dependence among degradation processes by using copula functions considering the marginal degradation processes as inverse Gaussian processes. The statistical inference is performed by using a Bayesian approach to estimate the parameters of the joint bivariate model. A time‐scale transformation is considered to assure monotone paths of the degradation trajectories. The comparison results of the reliability analysis, under both dependent and independent assumptions, are reported with the implementation of the proposed modeling in a case study, which consists of the crack propagation data of 2 terminals of an electronic device.     

AN ACCELERATION STRATEGY FOR RANDOMIZE-THEN-OPTIMIZE SAMPLING VIA DEEP NEURAL NETWORKS

Randomize-then-optimize (RTO) is widely used for sampling from posterior distribu-tions in Bayesian inverse problems.However,RTO can be computationally intensive for complexity problems due to repetitive evaluations of the expensive forward model and its gradient.In this work,we present a novel goal-oriented deep neural networks (DNN) sur-rogate approach to substantially reduce the computation burden of RTO.In particular,we propose to drawn the training points for the DNN-surrogate from a local approximated posterior distribution-yielding a flexible and efficient sampling algorithm that converges to the direct RTO approach.We present a Bayesian inverse problem governed by elliptic PDEs to demonstrate the computational accuracy and efficiency of our DNN-RTO ap-proach,which shows that DNN-RTO can significantly outperform the traditional RTO.     

Research on Flood Loss Distribution and Catastrophe Bond Pricing Based on Bayesian Inference

Taking flood catastrophe risk in China as the research background, aiming at the characteristics of flood loss ``low frequency and high loss', Bayesian inference method is used to fit the loss distribution, and Bayesian inference is used to obtain the loss frequency distribution and loss quota distribution of flood in China. On this basis, Monte Carlo simulation method is used to calculate the probability distribution of annual flood loss in China under different trigger conditions, and then CAPM is used to study the pricing of flood catastrophe bonds in China. It is concluded that under different trigger conditions, as the trigger value increases gradually, the corresponding trigger is triggered. Comparing the three types of bonds, it can be found that the price of bonds decreases with the decrease of principal guarantee ratio and the increase of principal loss ratio, that is, the investment risk is directly proportional to the return, which provides reference for issuing flood catastrophe bonds in China.     

泊松逆高斯回归模型的贝叶斯统计推断

本文研究泊松逆高斯回归模型的贝叶斯统计推断.基于应用Gibbs抽样,Metropolis-Hastings算法以及Multiple-Try Metropolis算法等MCMC统计方法计算模型未知参数和潜变量的联合贝叶斯估计,并引入两个拟合优度统计量来评价提出的泊松逆高斯回归模型的合理性.若干模拟研究与一个实证分析说明方法的可行性.     

Bayes in the sky: Bayesian inference and model selection in cosmology

The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more traditional statistical tools, offering the advantage of higher efficiency and of a consistent conceptual basis for dealing with the problem of induction in the presence of uncertainty. This trend is likely to continue in the future, when the way we collect, manipulate and analyse observations and compare them with theoretical models will assume an even more central role in cosmology.

This review is an introduction to Bayesian methods in cosmology and astrophysics and recent results in the field. I first present Bayesian probability theory and its conceptual underpinnings, Bayes' Theorem and the role of priors. I discuss the problem of parameter inference and its general solution, along with numerical techniques such as Monte Carlo Markov Chain methods. I then review the theory and application of Bayesian model comparison, discussing the notions of Bayesian evidence and effective model complexity, and how to compute and interpret those quantities. Recent developments in cosmological parameter extraction and Bayesian cosmological model building are summarised, highlighting the challenges that lie ahead.     

���ն����ı�Ҷ˹���Ƽ���ͳ�Ʒ���

??The Bayesian model are established for the VaR and related risk measurements. The relationship between VaR and other risk measurements including expect shortfall, tail condition expectation and conditional value at risk are discussed. Furthermore, the Bayesian estimates and Bayesian predictors of these risk measurement are derived. Thirdly, the consistency and asymptotic normality in the exponential risk model are proved. Finally, the numerical simulation method is used to verify the convergence rate under different sample sizes.