Bayesian inference for stable Lévy–driven stochastic differential equations with high‐frequency data

In this paper, we consider parametric Bayesian inference for stochastic differential equations driven by a pure‐jump stable Lévy process, which is observed at high frequency. In most cases of practical interest, the likelihood function is not available; hence, we use a quasi‐likelihood and place an associated prior on the unknown parameters. It is shown under regularity conditions that there is a Bernstein–von Mises theorem associated to the posterior. We then develop a Markov chain Monte Carlo algorithm for Bayesian inference, and assisted with theoretical results, we show how to scale Metropolis–Hastings proposals when the frequency of the data grows, in order to prevent the acceptance ratio from going to zero in the large data limit. Our algorithm is presented on numerical examples that help verify our theoretical findings.     

Bayesian estimation of the efficient frontier

In this paper, we consider the estimation of the three determining parameters of the efficient frontier, the expected return, and the variance of the global minimum variance portfolio and the slope parameter, from a Bayesian perspective. Their posterior distribution is derived by assigning the diffuse and the conjugate priors to the mean vector and the covariance matrix of the asset returns and is presented in terms of a stochastic representation. Furthermore, Bayesian estimates together with the standard uncertainties for all three parameters are provided, and their asymptotic distributions are established. All obtained findings are applied to real data, consisting of the returns on assets included into the S&P 500. The empirical properties of the efficient frontier are then examined in detail.     

部分状态可见的隐马尔可夫模型状态序列的估计方法

本文考虑了部分状态可见的隐马尔可夫模型的状态序列估计问题,在分析了现有算法无法合理估计状态路径之后,以状态转移概率、观测概率和可见状态作为先验信息,通过贝叶斯分析计算可见状态前后向状态的后验概率,并给出初始条件和递推公式,运用动态规划递推得到每个观测值对应的最可能状态以及最可能的状态路径。最后,本文给出一个系统故障识别的应用例子,验证了所设计算法的可行性。     

Model selection for factor analysis: Some new criteria and performance comparisons

This paper derives Akaike information criterion (AIC), corrected AIC, the Bayesian information criterion (BIC) and Hannan and Quinn’s information criterion for approximate factor models assuming a large number of cross-sectional observations and studies the consistency properties of these information criteria. It also reports extensive simulation results comparing the performance of the extant and new procedures for the selection of the number of factors. The simulation results show the di?culty of determining which criterion performs best. In practice, it is advisable to consider several criteria at the same time, especially Hannan and Quinn’s information criterion, Bai and Ng’s IC_p2 and BIC₃, and Onatski’s and Ahn and Horenstein’s eigenvalue-based criteria. The model-selection criteria considered in this paper are also applied to Stock and Watson’s two macroeconomic data sets. The results differ considerably depending on the model-selection criterion in use, but evidence suggesting five factors for the first data and five to seven factors for the second data is obtainable.     

Accurate estimation for extra-Poisson variability assuming random effect models

In this study, the components of extra-Poisson variability are estimated assuming random effect models under a Bayesian approach. A standard existing methodology to estimate extra-Poisson variability assumes a negative binomial distribution. The obtained results show that using the proposed random effect model it is possible to get more accurate estimates for the extra-Poisson variability components when compared to the use of a negative binomial distribution where it is possible to estimate only one component of extra-Poisson variability. Some illustrative examples are introduced considering real data sets.     

Regression models to dependence for exceedance

Extreme Value Theory (EVT) aims to study the tails of probability distributions in order to measure and quantify extreme events of maximum and minimum. In river flow data, an extreme level of a river may be related to the level of a neighboring river that flows into it. In this type of data, it is very common for flooding of a location to have been caused by a very large flow from an affluent river that is tens or hundreds of kilometers from this location. In this sense, an interesting approach is to consider a conditional model for the estimation of a multivariate model. Inspired by this idea, we propose a Bayesian model to describe the dependence of exceedance between rivers, where we considered a conditionally independent structure. In this model, the dependence between rivers is captured by modeling the excess marginally of one river as a consequence of linear functions of the other rivers. The results showed that there is a strong and positive connection between excesses in one river caused by the excesses of the other rivers.     

Prediction of tumour pathological subtype from genomic profile using sparse logistic regression with random effects

The purpose of this study is to highlight the application of sparse logistic regression models in dealing with prediction of tumour pathological subtypes based on lung cancer patients'' genomic information. We consider sparse logistic regression models to deal with the high dimensionality and correlation between genomic regions. In a hierarchical likelihood (HL) method, it is assumed that the random effects follow a normal distribution and its variance is assumed to follow a gamma distribution. This formulation considers ridge and lasso penalties as special cases. We extend the HL penalty to include a ridge penalty (called ‘HLnet’) in a similar principle of the elastic net penalty, which is constructed from lasso penalty. The results indicate that the HL penalty creates more sparse estimates than lasso penalty with comparable prediction performance, while HLnet and elastic net penalties have the best prediction performance in real data. We illustrate the methods in a lung cancer study.     

Varieties of political support in emerging democracies: A cross-national analysis

Political support is a multidimensional construct encompassing evaluations of political leaders and institutions (specific support) as well as adherence to basic regime principles (diffuse support). Scholars have traditionally assumed that diffuse and specific support are driven by different forces and evolve largely independently. Prior empirical work, however, has struggled to untangle the two support dimensions and focused predominantly on cross-national differences, ignoring their dynamics. This paper develops an analytical and empirical approach to examine the levels and dynamic interplay of both support dimensions and estimate their determinants, applying it to South American democracies between 1996 and 2015. Contrary to received wisdom, we show that both dimensions are quite volatile and closely linked in this region. In particular, negative economic shocks not only undermine support for government actors, but also fuel democratic disenchantment. Nonetheless, while regime support is rather fickle in South America, it can be ultimately resistant to performance fluctuations.     

Estimating the effects of network covariates on subgroup insularity with a hierarchical mixed membership stochastic blockmodel

Social networks describe the relationships and interactions among a group of individuals. In many peer relationships, individuals tend to associate more often with some members than others, forming subgroups or clusters. Subgroup structure varies across networks; subgroups may be insular, appearing distinct and isolated from one another, or subgroups may be so integrated that subgroup structure is not visually apparent, and there are numerous ways of quantifying these types of structures. We propose a new model that relates the amount of subgroup integration to network attributes, building on the mixed membership stochastic blockmodel (Airoldi et al., 2008) and subsequent work by Sweet and Zheng (2017) and Sweet et al. (2014). We explore some of the operating characteristics of this model with simulated data and apply this model to determine the relationship between teachers’ instructional practices and their classrooms’ peer network subgroup structure.     

Probabilistic population projections for countries with generalized HIV/AIDS epidemics

In 2015, the United Nations (UN) issued probabilistic population projections for all countries up to 2100, by simulating future levels of total fertility and life expectancy and combining the results using a standard cohort component projection method. For the 40 countries with generalized HIV/AIDS epidemics, the mortality projections used the Spectrum/Estimation and Projection Package (EPP) model, a complex, multistate model designed for short-term projections of policy-relevant quantities for the epidemic. We propose a simpler approach that is more compatible with existing UN projection methods for other countries. Changes in life expectancy are projected probabilistically using a simple time series regression and then converted to age- and sex-specific mortality rates using model life tables designed for countries with HIV/AIDS epidemics. These are then input to the cohort component method, as for other countries. The method performed well in an out-of-sample cross-validation experiment. It gives similar short-run projections to Spectrum/EPP, while being simpler and avoiding multistate modelling.