Functional and dynamic magnetic resonance imaging using vector adaptive weights smoothing

We consider the problem of statistical inference for functional and dynamic magnetic resonance imaging (MRI). A new approach is proposed which extends the adaptive weights smoothing procedure of Polzehl and Spokoiny that was originally designed for image denoising. We demonstrate how the adaptive weights smoothing method can be applied to time series of images, which typically occur in functional and dynamic MRI. It is shown how signal detection in functional MRI and the analysis of dynamic MRI can benefit from spatially adaptive smoothing. The performance of the procedure is illustrated by using real and simulated data.     

Dynamic mixing probability measures of mixtures

ABSTRACT

Lifetime of heterogeneous population can be modeled as mixture of a family of lifetime distributions according to a mixing probability measure. With the help of dynamic mixing measure, the hazard rate of the mixture can also be expressed as the mixture of the hazard rates of the lifetime distributions. Various local stochastic orderings are defined in this article. Applying these local stochastic orderings, we can explore the behavior of the dynamic mixing measures locally and then compare the hazard rates of two heterogeneous populations in both the local and global ways.     

Fast computing for dynamic screening systems when analyzing correlated data

In practice, we often need to identify individuals whose longitudinal behaviour is different from the behaviour of those well-functioning individuals, so that some unpleasant consequences (e.g. stroke) can be avoided or early detected. To handle such applications, a new statistical method, called dynamic screening system, has been developed in the literature. A recent version of this method can analyze correlated data. However, the computation involved is intensive. In this paper, we suggest a fast computing algorithm for the dynamic screening system. The algorithm can improve the effectiveness of the conventional dynamic screening system in certain cases. Numerical results show that the new algorithm works well in different cases.     

股票组合VaR估计：基于动态Copula方法

已有的使用动态时变Copula估计VaR的研究都仅限于考虑两个资产,对两个资产以上,Copula函数的参数过多,逐一设定参数的动态过程,将使模型复杂化,在计算上也不可行。为解决这一问题,文中使用条件Copula的概念,结合Engle的DCC方法,将椭球Copula的相关系数矩阵动态化,并将t-Copula的自由度设定为一动态过程的Logistic变换,由此得到的动态正态Copula和t-Copula可用于刻画两个以上资产相关结构的动态关系,进而可估计两个以上资产组合的VaR。最后,文章给出了一个经验应用。     

Treatment-competing events in dynamic regimes

A dynamic treatment regime is a sequence of decision rules for assigning treatment based on a patient’s current need for treatment. Dynamic regimes are viewed, by many, as a natural way of treating patients with chronic diseases; that is, treating patients with adaptive, complex, longitudinal treatment regimens. In developing dynamic treatment strategies, treatment-competing events may play an important role in the overall treatment strategy, and their effects on subsequent treatment decisions and eventual outcome should be considered. Treatment-competing events may be defined generally as patient-specific, random events which interrupt the ongoing treatment decision process in a dynamic regime. Treatment-competing events censor later treatment decisions that would otherwise be made on a particular dynamic treatment regime had the competing events not occurred. For example, in therapeutic studies of HIV, physicians may assign treatment based on a patient’s current level HIV1-RNA; this defines a treatment assignment rule. However, the presence of opportunistic infections or severe adverse events may preclude a strict adherence of the treatment assignment rule. In other contexts, the “censoring”-by-death phenomenon may be viewed as an example of a treatment-competing event for a particular dynamic treatment regime. Treatment-competing events can be built into the dynamic treatment regime framework and counting processes are a natural mechanism to facilitate this development. In this paper, we develop treatment-competing events in a dynamic infusion policy, a random dynamic treatment regime where multiple infusion treatments are initiated simultaneously and given continuously over time subject to the presence/absence of a treatment-competing event. We illustrate how our methodology may be used to suggest an estimator for a particular causal estimand of recent interest. Finally, we exemplify our methods in a recent study of patients undergoing coronary stent implantation.     

投资组合动态VaR风险度量

投资组合的VaR风险度量依赖于投资组合中金融资产间联合分布函数的确定，随着投资组合规模的扩大，其VaR的计算难度也不断加大。利用ICA可以将多元联合概率分布函数转化为一元概率分布函数乘积实现简化计算的特点，基于ICA的投资组合动态VaR风险度量方法和计算步骤，克服了多元非正态条件下VaR测算上的困难。实证研究表明，与EWMA模型法、MGARCH模型法相比，ICA法能够准确地度量投资组合动态VaR。     

Investigate Data Dependency for Dynamic Gene Regulatory Network Identification through High-dimensional Differential Equation Approach

Gene regulation plays a fundamental role in biological activities. The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. We proposed a comprehensive statistical procedure for ODE model to identify the dynamic GRN. In this article, we applied this model to different segments of time course gene expression data from a simulation experiment and a yeast cell cycle study. We found that the two cell cycle and one cell cycle data provided consistent results, but half cell cycle data produced biased estimation. Therefore, we may conclude that the proposed model can quantify both two cell cycle and one cell cycle gene expression dynamics, but not for half cycle dynamics. The findings suggest that the model can identify the dynamic GRN correctly if the time course gene expression data are sufficient enough to capture the overall dynamics of underlying biological mechanism.     

The misspecification of dynamic regression models

This paper investigates some of the hazards of estimating dynamic regression relationships with misspecified models. It is argued that, whenever the dynamic specification is in doubt, we should do well to adopt models which attribute separate sets of parameters to the systematic and disturbance parts of the regression relationship. Some of the models which are commonly adopted in applied econometrics attempt to capture the basic dynamic properties of the two parts of the relationship with the same set of parameters. If the properties of these two parts differ radically, then they are bound to be misrepresented by such models which can give rise to very misleading estimates.     

Dynamic Bayesian analysis of generalized odds ratios assuming multivariate skew-normal distribution for the error terms in the system equation

In this paper, we develop a methodology for the dynamic Bayesian analysis of generalized odds ratios in contingency tables. It is a standard practice to assume a normal distribution for the random effects in the dynamic system equations. Nevertheless, the normality assumption may be unrealistic in some applications and hence the validity of inferences can be dubious. Therefore, we assume a multivariate skew-normal distribution for the error terms in the system equation at each step. Moreover, we introduce a moving average approach to elicit the hyperparameters. Both simulated data and real data are analyzed to illustrate the application of this methodology.     

An integrated dominance analysis and dynamic programing approach for measuring predictor importance for customer satisfaction

Abstract

Dominance analysis is a procedure for measuring the importance of predictors in multiple regression analysis. We show that dominance analysis can be enhanced using a dynamic programing approach for the rank-ordering of predictors. Using customer satisfaction data from a call center operation, we demonstrate how the integration of dominance analysis with dynamic programing can provide a better understanding of predictor importance. As a cautionary note, we recommend careful reflection on the relationship between predictor importance and variable subset selection. We observed that slight changes in the selected predictor subset can have an impact on the importance rankings produced by a dominance analysis.     

A Modified Empirical Martingale Simulation for Financial Derivative Pricing

This article extends the empirical martingale simulation (EMS) method from using a risk-neutral measure to using a dynamic measure for financial derivative pricing. Although the EMS is shown to be capable of obtaining consistent estimate of financial derivative prices in a more efficient way than the standard Monte Carlo simulation procedure, it can proceed only under a risk-neutral framework. In practice, however, it is cumbersome to obtain the explicit expression of a risk-neutral model when dealing with a complex model. To alleviate this difficulty, we compute the financial derivative prices under the dynamic model and impose the martingale property on the simulated sample paths of both the change of measure process and the underlying asset prices under the dynamic P measure. Hence, we call this modification the empirical P-martingale simulation (EPMS). The strong consistency of the EPMS is established and its efficiency is performed by simulation in the GARCH framework. Simulation results shows that EPMS has the similar variance reduction as the EMS method in option pricing if the risk-neutral model can be obtained, and is more efficient than the standard Monte Carlo simulation in most cases.     

Testing the stability of a linear dynamic model

In this paper we present a Wald or distance test for testing the stability of a linear dynamic model. Stability requires that all latent roots of the system simultaneously satisfy inequality restrictions. Unlike previous tests proposed in the literature our procedure is capable of testing the restrictions simultaneously. Therefore, the test asymptotically has the correct size. The procedure can be applied in practice if stability is not a requirement for identification of the dynamic model.     

An alternative approach for analysis of performance of one-sided cusum charts with variable sampling intervals

An alternative approach for analyzing performance of one-sided Cusum charts with variable sampling intervals (VSI) is proposed. In this approach, a Markov chain with some dummy states is used. By this approach some dynamic performance measures of the VSI Cusum charts, such as the distribution of time to signal and the average time to signal against a change-point, can be determined. Some numerical results are shown, and from these results the dynamic performance of VSI Cusum charts is discussed.     

基于RiskMetrics模型的单个期货合约保证金比例设计

为了规避价格波动风险,期货交易所应该采取动态保证金设置方式。本文对单个期货合约的日收益序列建立了基于RiskMetrics的VaR模型,用滚动样本预测下一交易日的VaR值,而LR检验表明所建立的VaR模型能较好地测度价格波动风险。因此,下一交易日保证金比例可以设置为预测的VaR值和所规定的涨跌停板率的最小值,这样就能以相应的概率抵御该交易日价格波动带来的风险。     

Mixture Kalman filters

In treating dynamic systems, sequential Monte Carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling, importance sampling and weighted resampling to complete the on-line 'filtering' task. We propose a special sequential Monte Carlo method, the mixture Kalman filter, which uses a random mixture of the Gaussian distributions to approximate a target distribution. It is designed for on-line estimation and prediction of conditional and partial conditional dynamic linear models, which are themselves a class of widely used non-linear systems and also serve to approximate many others. Compared with a few available filtering methods including Monte Carlo methods, the gain in efficiency that is provided by the mixture Kalman filter can be very substantial. Another contribution of the paper is the formulation of many non-linear systems into conditional or partial conditional linear form, to which the mixture Kalman filter can be applied. Examples in target tracking and digital communications are given to demonstrate the procedures proposed.     

基于Factor-GARCH模型的动态VaR与CVaR度量及实证研究

动态CVaR作为投资组合的风险度量工具较动态VaR有很多优点,但同动态VaR的计算一样,随着投资组合资产数量的增加,计算难度迅速增大。通过改良Factor-GARCH模型,将其用于多种资产时变方差-协方差矩阵的估计,实现了降维的目的,克服了计算多元动态CVaR时的困难。实证研究表明,与动态VaR相比,动态CVaR作为一种更保守的风险度量工具,能准确反映投资组合的可能损失。     

Temperature schedules for simulated annealing

It is well known that the behaviour of the simulated annealing approach to optimization is crucially dependent on the choice of temperature schedule. In this paper, a dynamic programming approach is used to find the temperature schedule which is optimal for a simple minimization problem. The optimal schedule is compared with certain standard non-optimal choices. These generally perform well provided the first and last temperatures are suitably selected. Indeed, these temperatures can be chosen in such a way as to make the performance of the logarithmic schedule almost optimal. This optimal performance is fairly robust to the choice of the first temperature.The dynamic programming approach cannot be applied directly to problems of more realistic size, such as those arising in statistical image reconstruction. Nevertheless, some simulation experiments suggest that the general conclusions from the simple minimization problem do carry over to larger problems. Various families of schedules can be made to perform well with suitable choice of the first and last temperatures, and the logarithmic schedule combines good performance with reasonable robustness to the choice of the first temperature.     

Multiple change points detection and clustering in dynamic networks

The increasing amount of data stored in the form of dynamic interactions between actors necessitates the use of methodologies to automatically extract relevant information. The interactions can be represented by dynamic networks in which most existing methods look for clusters of vertices to summarize the data. In this paper, a new framework is proposed in order to cluster the vertices while detecting change points in the intensities of the interactions. These change points are key in the understanding of the temporal interactions. The model used involves non-homogeneous Poisson point processes with cluster-dependent piecewise constant intensity functions and common discontinuity points. A variational expectation maximization algorithm is derived for inference. We show that the pruned exact linear time method, originally developed for change points detection in univariate time series, can be considered for the maximization step. This allows the detection of both the number of change points and their location. Experiments on artificial and real datasets are carried out, and the proposed approach is compared with related methods.     

ELICITING A DIRECTED ACYCLIC GRAPH FOR A MULTIVARIATE TIME SERIES OF VEHICLE COUNTS IN A TRAFFIC NETWORK

The problem of modelling multivariate time series of vehicle counts in traffic networks is considered. It is proposed to use a model called the linear multiregression dynamic model (LMDM). The LMDM is a multivariate Bayesian dynamic model which uses any conditional independence and causal structure across the time series to break down the complex multivariate model into simpler univariate dynamic linear models. The conditional independence and causal structure in the time series can be represented by a directed acyclic graph (DAG). The DAG not only gives a useful pictorial representation of the multivariate structure, but it is also used to build the LMDM. Therefore, eliciting a DAG which gives a realistic representation of the series is a crucial part of the modelling process. A DAG is elicited for the multivariate time series of hourly vehicle counts at the junction of three major roads in the UK. A flow diagram is introduced to give a pictorial representation of the possible vehicle routes through the network. It is shown how this flow diagram, together with a map of the network, can suggest a DAG for the time series suitable for use with an LMDM.