Bayesian testing for non-linearity in volatility modeling

Neural networks provide a tool for describing non-linearity in volatility processes of financial data and help to answer the question “how much” non-linearity is present in the data. Non-linearity is studied under three different specifications of the conditional distribution: Gaussian, Student-t and mixture of Gaussians. To rank the volatility models, a Bayesian framework is adopted to perform a Bayesian model selection within the different classes of models. In the empirical analysis, the return series of the Dow Jones Industrial Average index, FTSE 100 and NIKKEI 225 indices over a period of 16 years are studied. The results show different behavior across the three markets. In general, if a statistical model accounts for non-normality and explains most of the fat tails in the conditional distribution, then there is less need for complex non-linear specifications.     

基于Copula的贝叶斯分类器

利用Copula的理论提出了基于Copula贝叶斯分类算法,克服了一般的朴素贝叶斯分类器要求属性独立性假设的不足,进一步扩展了朴素贝叶斯分类器,实验结果表明,基于Copula贝叶斯算法取得了较好的分类效果。     

CPU load prediction using neuro-fuzzy and Bayesian inferences

Ensuring adequate use of the computing resources for highly fluctuating availability in multi-user computational environments requires effective prediction models, which play a key role in achieving application performance for large-scale distributed applications. Predicting the processor availability for scheduling a new process or task in a distributed environment is a basic problem that arises in many important contexts. The present paper aims at developing a model for single-step-ahead CPU load prediction that can be used to predict the future CPU load in a dynamic environment. Our prediction model is based on the control of multiple Local Adaptive Network-based Fuzzy Inference Systems Predictors (LAPs) via the Naïve Bayesian Network inference between clusters states of CPU load time points obtained by the C-means clustering process. Experimental results show that our model performs better and has less overhead than other approaches reported in the literature.     

Being Bayesian About Network Structure. A Bayesian Approach to Structure Discovery in Bayesian Networks

In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have non-negligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior landscape. We present empirical results on synthetic and real-life datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a non-Bayesian bootstrap approach.     

Linking Bayesian networks and PLS path modeling for causal analysis

Causal knowledge based on causal analysis can advance the quality of decision-making and thereby facilitate a process of transforming strategic objectives into effective actions. Several creditable studies have emphasized the usefulness of causal analysis techniques. Partial least squares (PLS) path modeling is one of several popular causal analysis techniques. However, one difficulty often faced when we commence research is that the causal direction is unknown due to the lack of background knowledge. To solve this difficulty, this paper proposes a method that links the Bayesian network and PLS path modeling for causal analysis. An empirical study is presented to illustrate the application of the proposed method. Based on the findings of this study, conclusions and implications for management are discussed.     

On copulas and their diagonals

We formulate the necessary and sufficient conditions for a function δ:[0,1]→[0,1] to be the diagonal section of a multivariate absolutely continuous copula. Moreover we provide some simple analytic formulas for copulas having given diagonal section or given distribution functions of order statistics.     

A Bayesian approach to model-based clustering for binary panel probit models

Considering latent heterogeneity is of special importance in nonlinear models in order to gauge correctly the effect of explanatory variables on the dependent variable. A stratified model-based clustering approach is adapted for modeling latent heterogeneity in binary panel probit models. Within a Bayesian framework an estimation algorithm dealing with the inherent label switching problem is provided. Determination of the number of clusters is based on the marginal likelihood and a cross-validation approach. A simulation study is conducted to assess the ability of both approaches to determine on the correct number of clusters indicating high accuracy for the marginal likelihood criterion, with the cross-validation approach performing similarly well in most circumstances. Different concepts of marginal effects incorporating latent heterogeneity at different degrees arise within the considered model setup and are directly at hand within Bayesian estimation via MCMC methodology. An empirical illustration of the methodology developed indicates that consideration of latent heterogeneity via latent clusters provides the preferred model specification over a pooled and a random coefficient specification.     

A Bayesian multilevel model for fMRI data analysis

Bayesian approaches have been proposed by several functional magnetic resonance imaging (fMRI) researchers in order to overcome the fundamental limitations of the popular statistical parametric mapping method. However, the difficulties associated with subjective prior elicitation have prevented the widespread adoption of the Bayesian methodology by the neuroimaging community. In this paper, we present a Bayesian multilevel model for the analysis of brain fMRI data. The main idea is to consider that all the estimated group effects (fMRI activation patterns) are exchangeable. This means that all the collected voxel time series are considered manifestations of a few common underlying phenomena. In contradistinction to other Bayesian approaches, we think of the estimated activations as multivariate random draws from the same distribution without imposing specific prior spatial and/or temporal information for the interaction between voxels. Instead, a two-stage empirical Bayes prior approach is used to relate voxel regression equations through correlations between the regression coefficient vectors. The adaptive shrinkage properties of the Bayesian multilevel methodology are exploited to deal with spatial variations, and noise outliers. The characteristics of the proposed model are evaluated by considering its application to two real data sets.     

使用Oracle Spatial进行空间数据建模研究

介绍了空间数据建模和管理的常用方法,重点讨论Oracle Spatial的对象关系建模,分析了使用Oracle Spatial组织管理空间数据的特点。基于Oracle Spatial进行空间数据建模,可以降低专业性,提高空间数据的标准化共享能力。     

Bayesian zero-order TSK fuzzy system modeling

Different from the existing TSK fuzzy system modeling methods, a novel zero-order TSK fuzzy modeling method called Bayesian zero-order TSK fuzzy system (B-ZTSK-FS) is proposed from the perspective of Bayesian inference in this paper. The proposed method B-ZTSK-FS constructs zero-order TSK fuzzy system by using the maximum a posteriori (MAP) framework to maximize the corresponding posteriori probability. First, a joint likelihood model about zero-order TSK fuzzy system is defined to derive a new objective function which can assure that both antecedents and consequents of fuzzy rules rather than only their antecedents of the most existing TSK fuzzy systems become interpretable. The defined likelihood model is composed of three aspects: clustering on the training set for antecedents of fuzzy rules, the least squares (LS) error for consequent parameters of fuzzy rules, and a Dirichlet prior distribution for fuzzy cluster memberships which is considered to not only automatically match the “sum-to-one” constraints on fuzzy cluster memberships, but also make the proposed method B-ZTSK-FS scalable for large-scale datasets by appropriately setting the Dirichlet index. This likelihood model indeed indicates that antecedent and consequent parameters of fuzzy rules can be linguistically interpreted and simultaneously optimized by the proposed method B-ZTSK-FS which is based on the MAP framework with the iterative sampling algorithm, which in fact implies that fuzziness and probability can co-jointly work for TSK fuzzy system modeling in a collaborative rather than repulsive way. Finally, experimental results on 28 synthetic and real-world datasets are reported to demonstrate the effectiveness of the proposed method B-ZTSK-FS in the sense of approximation accuracy, interpretability and scalability.     

Approximate Bayesian inference in spatial GLMM with skew normal latent variables

Spatial generalized linear mixed models are common in applied statistics. Most users are satisfied using a Gaussian distribution for the spatial latent variables in this model, but it is unclear whether the Gaussian assumption holds. Wrong Gaussian assumptions cause bias in the parameter estimates and affect the accuracy of spatial predictions. Thus, there is a need for more flexible priors for the latent variables, and to perform efficient inference and spatial prediction in the resulting models. In this paper we use a skew normal prior distribution for the spatial latent variables. We propose new approximate Bayesian methods for the inference and spatial prediction in this model. A key ingredient in our approximations is using the closed skew normal distribution to approximate the full conditional for the latent variables. Our approximate inference and spatial prediction methods are fast and deterministic, using no sampling based strategies. The results indicate that the skew normal prior model can give better predictions than the normal model, while avoiding overfitting.     

可变参数的有理分形插值曲线建模

为了有效地处理复杂真实现象中的不规则数据,提出一种利用有理分形插值进行分形曲线建模的方法.首先,基于传统的具有形状参数的有理样条,构造了一类具有函数尺度因子的有理迭代函数系统,并定义了有理分形插值曲线.然后,研究了有理分形曲线的一些重要性质,包括光滑性、稳定性以及收敛性.最后,估计了有理分形曲线计盒维数的上下界.提出的...     

Bayesian network modeling of strokes and their relationships for on-line handwriting recognition

In this paper, we propose a Bayesian network framework for explicitly modeling strokes and their relationships of characters. A character is modeled as a composition of stroke models, and a stroke as a composition of point models. A point is modeled with 2-D Gaussian distribution for its X-Y position. Relationships between points and strokes are modeled as their positional dependencies. All the models and relationships are represented probabilistically in Bayesian networks. The recognition experiment with on-line handwritten digits showed promising results; the recognition errors of the proposed system were greatly reduced by dependency modeling, and its recognition rates were higher than those of previous methods.     

连续属性一阶贝叶斯衍生分类器学习与集成

依据copula和贝叶斯网络理论,将高斯copula函数、引入平滑参数的高斯核函数和以分类器的分类准确性为标准的属性父结点贪婪选择等相结合,综合考虑效率和可靠性,进行连续属性一阶贝叶斯衍生分类器学习、优化和集成。使用UCI数据库中连续属性分类数据进行实验,结果显示,经过优化和集成的一阶连续属性贝叶斯衍生分类器具有良好的分类准确性。     

应用色彩空间聚类方法实现道路建模

通过图像对交通事故进行识别、处理,需要将卷入交通事故的车辆等目标从交通事故场景图像中分离出来,因此建立准确的道路模型十分重要.传统的道路建模方法大都基于灰度空间,忽略了图像中的彩色信息,不适合复杂的交通环境.针对道路像素分布的非参数化特点和后续处理中对彩色信息的需求,提出一种基于色彩空间聚类的非参数化道路模型,将道路模型的建立抽象为时间轴上的色彩空间聚类过程.根据颜色变化理论,设置聚类区间为RGB颜色空间中以聚类中心和原点连线为轴的圆柱体,并通过聚类中心特征值的不同自适应来调整聚类半径.同时,对于每个像素位置,根据场景复杂程度和变化频率的不同自适应地选取聚类中心数目,获得较为准确的背景模型,在提高检测精度的同时也保证了检测效率.     

A Bayesian approach for analyzing a cluster-randomized trial with adjustment for risk misclassification

Bayesian hierarchical modelling techniques have some advantages over classic methods for the analysis of cluster-randomized trial. Bayesian approach is also becoming more popular to deal with measurement error and misclassification problems. We propose a Bayesian approach to analyze a cluster-randomized trial with adjusting for misclassification in a binary covariate in the random effect logistic model when a gold standard is not available. This Markov chain Monte Carlo (MCMC) approach uses two imperfect measures of a dichotomous exposure under the assumptions of conditional independence and non-differential misclassification. Both simulated numerical example and real clinical example are given to illustrate the proposed approach. The Bayesian approach has great potential to be used in misclassification problem in generalized linear mixed model (GLMM) since it allow us to fit complex models and identify all the parameters. Our results suggest that Bayesian approach for analyzing cluster-randomized trial and adjusting for misclassification in GLMM is flexible and powerful.     

GARCH dependence in extreme value models with Bayesian inference

Extreme value methods are widely used in financial applications such as risk analysis, forecasting and pricing models. One of the challenges with their application in finance is accounting for the temporal dependence between the observations, for example the stylised fact that financial time series exhibit volatility clustering. Various approaches have been proposed to capture the dependence. Commonly a two-stage approach is taken, where the volatility dependence is removed using a volatility model like a GARCH (or one of its many incarnations) followed by application of standard extreme value models to the assumed independent residual innovations.This study examines an alternative one stage approach, which makes parameter estimation and accounting for the associated uncertainties more straightforward than the two-stage approach. The location and scale parameters of the extreme value distribution are defined to follow a conditional autoregressive heteroscedasticity process. Essentially, the model implements GARCH volatility via the extreme value model parameters. Bayesian inference is used and implemented via Markov chain Monte Carlo, to permit all sources of uncertainty to be accounted for. The model is applied to both simulated and empirical data to demonstrate performance in extrapolating the extreme quantiles and quantifying the associated uncertainty.     

Development of an internet based system for modeling biotin metabolism using Bayesian networks

Biotin is an essential water-soluble vitamin crucial for maintaining normal body functions. The importance of biotin for human health has been under-appreciated but there is plenty of opportunity for future research with great importance for human health. Currently, carrying out predictions of biotin metabolism involves tedious manual manipulations. In this paper, we report the development of BiotinNet, an internet based program that uses Bayesian networks to integrate published data on various aspects of biotin metabolism. Users can provide a combination of values on the levels of biotin related metabolites to obtain the predictions on other metabolites that are not specified. As an inherent feature of Bayesian networks, the uncertainty of the prediction is also quantified and reported to the user. This program enables convenient in silico experiments regarding biotin metabolism, which can help researchers design future experiments while new data can be continuously incorporated.     

Variational Bayesian methods for spatial data analysis

With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. However, fitting spatial models often involves expensive matrix decompositions, whose computational complexity increases in cubic order with the number of spatial locations. This situation is aggravated in Bayesian settings where such computations are required once at every iteration of the Markov chain Monte Carlo (MCMC) algorithms. In this paper, we describe the use of Variational Bayesian (VB) methods as an alternative to MCMC to approximate the posterior distributions of complex spatial models. Variational methods, which have been used extensively in Bayesian machine learning for several years, provide a lower bound on the marginal likelihood, which can be computed efficiently. We provide results for the variational updates in several models especially emphasizing their use in multivariate spatial analysis. We demonstrate estimation and model comparisons from VB methods by using simulated data as well as environmental data sets and compare them with inference from MCMC.