Testing for nonlinearity in mean and volatility for heteroskedastic models

A simple test for threshold nonlinearity in either the mean or volatility equation, or both, of a heteroskedastic time series model is proposed. The procedure extends current Bayesian Markov chain Monte Carlo methods and threshold modelling by employing a general double threshold GARCH model that allows for an explosive, non-stationary regime. Posterior credible intervals on model parameters are used to detect and specify threshold nonlinearity in the mean and/or volatility equations. Simulation experiments demonstrate that the method works favorably in identifying model specifications varying in complexity from the conventional GARCH up to the full double-threshold nonlinear GARCH model with an explosive regime, and is robust to over-specification in model orders.     

A novel hybrid learning algorithm for full Bayesian approach of artificial neural networks

The Bayesian neural networks are useful tools to estimate the functional structure in the nonlinear systems. However, they suffer from some complicated problems such as controlling the model complexity, the training time, the efficient parameter estimation, the random walk, and the stuck in the local optima in the high-dimensional parameter cases. In this paper, to alleviate these mentioned problems, a novel hybrid Bayesian learning procedure is proposed. This approach is based on the full Bayesian learning, and integrates Markov chain Monte Carlo procedures with genetic algorithms and the fuzzy membership functions. In the application sections, to examine the performance of proposed approach, nonlinear time series and regression analysis are handled separately, and it is compared with the traditional training techniques in terms of their estimation and prediction abilities.     

MCMC方法在生物逆问题求解中的应用

提出用马尔科夫链蒙特卡罗（MCMC）方法来求解生物逆问题。导出待求参数分布规律的后验概率密度函数;采用自适应Metropolis算法构造Markov链;然后截取收敛的链序列计算数学期望,成功估计出未知参数。数值实验结果表明,该方法具有很高的估计精度和较好的抗噪声性能。     

A hybrid modeling approach for forecasting the volatility of S&P 500 index return

Forecasting volatility is an essential step in many financial decision makings. GARCH family of models has been extensively used in finance and economics, particularly for estimating volatility. The motivation of this study is to enhance the ability of GARCH models in forecasting the return volatility. We propose two hybrid models based on EGARCH and Artificial Neural Networks to forecast the volatility of S&P 500 index. The estimates of volatility obtained by an EGARCH model are fed forward to a Neural Network. The input to the first hybrid model is complemented by historical values of other explanatory variables. The second hybrid model takes as inputs both series of the simulated data and explanatory variables. The forecasts obtained by each of those hybrid models have been compared with those of EGARCH model in terms of closeness to the realized volatility. The computational results demonstrate that the second hybrid model provides better volatility forecasts.     

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.     

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.     

Bayes网络学习的MCMC方法

基于Bayes统计理论, 提出了一种从数据样本中学习Bayes网络的Markov链Monte Carlo(MCMC)方法. 首先通过先验概率和数据样本的结合得到未归一化的后验概率, 然后使用此后验概率指导随机搜索算法寻找“好”的网络结构模型. 通过对Alarm网络的学习表明了本算法具有较好的性能.     

A Bayesian analysis of an agricultural field trial with three spatial dimensions

Modern technology now has the ability to generate large datasets over space and time. Such data typically exhibit high autocorrelations over all dimensions. The field trial data motivating the methods of this paper were collected to examine the behaviour of traditional cropping and to determine a cropping system which could maximise water use for grain production while minimising leakage below the crop root zone. They consist of moisture measurements made at 15 depths across 3 rows and 18 columns, in the lattice framework of an agricultural field.Bayesian conditional autoregressive (CAR) models are used to account for local site correlations. Conditional autoregressive models have not been widely used in analyses of agricultural data. This paper serves to illustrate the usefulness of these models in this field, along with the ease of implementation in WinBUGS, a freely available software package.The innovation is the fitting of separate conditional autoregressive models for each depth layer, the ‘layered CAR model’, while simultaneously estimating depth profile functions for each site treatment. Modelling interest also lies in how best to model the treatment effect depth profiles, and in the choice of neighbourhood structure for the spatial autocorrelation model. The favoured model fitted the treatment effects as splines over depth, and treated depth, the basis for the regression model, as measured with error, while fitting CAR neighbourhood models by depth layer. It is hierarchical, with separate conditional autoregressive spatial variance components at each depth, and the fixed terms which involve an errors-in-measurement model treat depth errors as interval-censored measurement error. The Bayesian framework permits transparent specification and easy comparison of the various complex models compared.     

Estimating light absorption by chlorophyll, leaf and canopy in a deciduous broadleaf forest using MODIS data and a radiative transfer model

In this paper, we present a theoretical and modeling framework to estimate the fractions of photosynthetically active radiation (PAR) absorbed by vegetation canopy (FAPAR_canopy), leaf (FAPAR_leaf ), and chlorophyll (FAPAR_chl), respectively. FAPAR_canopy is an important biophysical variable and has been used to estimate gross and net primary production. However, only PAR absorbed by chlorophyll is used for photosynthesis, and therefore there is a need to quantify FAPAR_chl. We modified and coupled a leaf radiative transfer model (PROSPECT) and a canopy radiative transfer model (SAIL-2), and incorporated a Markov Chain Monte Carlo (MCMC) method (the Metropolis algorithm) for model inversion, which provides probability distributions of the retrieved variables. Our two-step procedure is: (1) to retrieve biophysical and biochemical variables using coupled PROSPECT + SAIL-2 model (PROSAIL-2), combined with multiple daily images (five spectral bands) from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor; and (2) to calculate FAPAR_canopy, FAPAR_leaf and FAPAR_chl with the estimated model variables from the first step. We evaluated our approach for a temperate forest area in the Northeastern US, using MODIS data from 2001 to 2003. The inverted PROSAIL-2 fit the observed MODIS reflectance data well for the five MODIS spectral bands. The estimated leaf area index (LAI) values are within the range of field measured data. Significant differences between FAPAR_canopy and FAPAR_chl are found for this test case. Our study demonstrates the potential for using a model such as PROSAIL-2, combined with an inverse approach, for quantifying FAPAR_chl, FAPAR_leaf, FAPAR_canopy, biophysical variables, and biochemical variables for deciduous broadleaf forests at leaf- and canopy-levels over time.     

Bayesian Treed Models

When simple parametric models such as linear regression fail to adequately approximate a relationship across an entire set of data, an alternative may be to consider a partition of the data, and then use a separate simple model within each subset of the partition. Such an alternative is provided by a treed model which uses a binary tree to identify such a partition. However, treed models go further than conventional trees (e.g. CART, C4.5) by fitting models rather than a simple mean or proportion within each subset. In this paper, we propose a Bayesian approach for finding and fitting parametric treed models, in particular focusing on Bayesian treed regression. The potential of this approach is illustrated by a cross-validation comparison of predictive performance with neural nets, MARS, and conventional trees on simulated and real data sets.     

基于马尔可夫链蒙特卡罗采样的双密钥盲水印算法

为了更好地提高水印算法的安全性,提出了一种基于两种形式密钥的强鲁棒盲水印算法。首先对水印加密,然后将每块载体的第一个奇异值组成矩阵Q再分块离散小波变换(DWT)获得四个子带,通过对四个子带进行马尔可夫链蒙特卡罗(MCMC)采样决定第k个水印位量化嵌入到矩阵Q的第k块低频、水平、垂直和高频子带中的一个并记录当前嵌入子带的密钥位,这样做不仅使水印位随机分配,而且提高了水印算法的安全性。实验结果表明,所提算法在满足不可见性的条件下,不仅对常规的图像攻击具备较强的鲁棒性,而且在水印嵌入过程中通过MCMC采样实现了用不同的密钥嵌入,提高了水印算法的安全性。     

一种基于吉布斯抽样的MUSIC多维参数联合估计算法

将马尔可夫蒙特卡罗(MCMC)方法与多重子空间分类(MUSIC)方法估计相结合,提出一种用于联合估计多个目标的频率、方位和俯仰,基于吉布斯抽样的MUSIC多维参数联合估计新方法。该方法将MUSIC方法的谱函数作为频率、方位和俯仰的联合概率密度函数,采用MCMC吉布斯抽样方法对该联合概率密度函数进行采样。理论分析和仿真实验表明:在目标个数较少时,该方法不仅保持了常规MUSIC方法的高分辨能力,而且减少了计算量和存储量     

Association Models for Web Mining

We describe how statistical association models and, specifically, graphical models, can be usefully employed to model web mining data. We describe some methodological problems related to the implementation of discrete graphical models for web mining data. In particular, we discuss model selection procedures.     

基于运动补偿和MCMC算法的视频目标跟踪

针对视频目标跟踪领域摄像头运动等问题,提出一种基于二次观测模型的马尔科夫链蒙特卡洛(MCMC)粒子滤波算法。第1次观测通过计算相邻2帧的光流场对运动模型实时修正使其逼近真实的运动方程,第2次观测MCMC粒子滤波步骤。二次观测模型利用图像中的光流信息进行运动补偿实现跟踪。时变的运动模型可以有效提高MCMC方法的效率,减少无效的粒子点数,使其能更快速地收敛到真实值。实验表明对MCMC进行运动补偿可以有效处理摄像头运动问题。     

Bayesian MLP neural networks for image analysis

We demonstrate the advantages of using Bayesian multi-layer perceptron (MLP) neural networks for image analysis. The Bayesian approach provides consistent way to do inference by combining the evidence from the data to prior knowledge from the problem. A practical problem with MLPs is to select the correct complexity for the model, i.e., the right number of hidden units or correct regularization parameters. The Bayesian approach offers efficient tools for avoiding overfitting even with very complex models, and facilitates estimation of the confidence intervals of the results. In this contribution we review the Bayesian methods for MLPs and present comparison results from two case studies. In the first case, MLPs were used to solve the inverse problem in electrical impedance tomography. The Bayesian MLP provided consistently better results than other methods. In the second case, the goal was to locate trunks of trees in forest scenes. With Bayesian MLP it was possible to use large number of potentially useful features and prior for determining the relevance of the features automatically.     

A Bayesian propensity score adjustment for latent variable modeling and MCMC algorithm

The estimation of the differences among groups in observational studies is frequently inaccurate owing to a bias caused by differences in the distributions of covariates. In order to estimate the average treatment effects when the treatment variable is binary, Rosenbaum and Rubin [1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41-55] proposed an adjustment method for pre-treatment variables using propensity scores. Imbens [2000. The role of the propensity score in estimating dose-response functions. Biometrika 87, 706-710] extended the propensity score methodology for estimation of average treatment effects with multivalued treatments.However, these studies focused only on estimating the marginal mean structure. In many substantive sciences such as the biological and social sciences, a general estimation method is required to deal with more complex analyses other than regression, such as testing group differences on latent variables. For latent variable models, the EM algorithm or the traditional Monte Carlo methods are necessary. However, in propensity score adjustment, these methods cannot be used because the full distribution is not specified.In this paper, we propose a quasi-Bayesian estimation method for general parametric models that integrate out the distributions of covariates using propensity scores. Although the proposed Bayes estimates are shown to be consistent, they can be calculated by existing Markov chain Monte Carlo methods such as Gibbs sampler. The proposed method is useful to estimate parameters in latent variable models, while the previous methods were unable to provide valid estimates for complex models such as latent variable models.We also illustrated the procedure using the data obtained from the US National Longitudinal Survey of Children and Youth (NLSY1979-2002) for estimating the effect of maternal smoking during pregnancy on the development of the child's cognitive functioning.     

Using neural network for forecasting TXO price under different volatility models

This study applies backpropagation neural network for forecasting TXO price under different volatility models, including historical volatility, implied volatility, deterministic volatility function, GARCH and GM-GARCH models. The sample period runs from 2008 to 2009, and thus contains the global financial crisis stating in October 2008. Besides RMSE, MAE and MAPE, this study introduces the best forecasting performance ratio (BFPR) as a new performance measure for use in option pricing. The analytical result reveals that forecasting performances are related to the moneynesses, volatility models and number of neurons in the hidden layer, but are not significantly related to activation functions. Implied and deterministic volatility function models have the largest and second largest BFPR regardless of moneyness. Particularly, the forecasting performance in 2008 was significantly inferior to that in 2009, demonstrating that the global financial crisis during October 2008 may have strongly influenced option pricing performance.     

基于贝叶斯推理的HCM延误模型修正

针对以1个周期时长为分析单位、使用HCM2000延误模型推导信号控制交叉口延误的问题,提出推导模型中参数修正的方法,用t检验验证参数提取的精度。对延误提取模型中的饱和度、启动损失时间及交叉口几何修正系数等参数进行分析,采用贝叶斯定理和马尔科夫链蒙特卡罗模拟方法对参数进行修正。结果证明该方法可以提高按照周期提取延误参数的精度。     

A Structure Learning Algorithm for Bayesian Network Using Prior Knowledge

Learning structure from data is one of the most important fundamental tasks of Bayesian network research. Particularly, learning optional structure of Bayesian network is a non-deterministic polynomial...