Bayesian analysis of multivariate threshold autoregressive models with missing data

In some fields, we are forced to work with missing data in multivariate time series. Unfortunately, the data analysis in this context cannot be carried out in the same way as in the case of complete data. To deal with this problem, a Bayesian analysis of multivariate threshold autoregressive models with exogenous inputs and missing data is carried out. In this paper, Markov chain Monte Carlo methods are used to obtain samples from the involved posterior distributions, including threshold values and missing data. In order to identify autoregressive orders, we adapt the Bayesian variable selection method in this class of multivariate process. The number of regimes is estimated using marginal likelihood or product parameter-space strategies.     

Asymptotic equipartition property for second-order circular Markov chains indexed by a two-rooted Cayley tree

In this paper, we introduce a model of a second-order circular Markov chain indexed by a two-rooted Cayley tree and establish two strong law of large numbers and the asymptotic equipartition property (AEP) for circular second-order finite Markov chains indexed by this homogeneous tree. In the proof, we apply a limit property for a sequence of multi-variable functions of a non homogeneous Markov chain indexed by such tree. As a corollary, we obtain the strong law of large numbers and AEP about the second-order finite homogeneous Markov chain indexed by the two-rooted homogeneous tree.     

Modeling Australian twin data using shared positive stable frailty models based on reversed hazard rate

Unobserved heterogeneity, also called frailty, is a major concern in the application of survival analysis. The shared frailty models allow for the statistical dependence between the observed survival data. In this paper, we consider shared positive stable frailty model with the reversed hazard rate (RHR) with three different baseline distributions, namely the exponentiated Gumbel, the generalized Rayleigh, and the generalized inverse Rayleigh distributions. With these three baseline distributions we propose three different shared frailty models. We develop the Bayesian estimation procedure using Markov Chain Monte Carlo technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. A search of the literature suggests that currently no work has been done for these three baseline distributions with a shared positive stable frailty with the RHR so far. We also apply these three models by using a real-life bivariate survival data set of Australian twin data given by Duffy et a1. (1990 Duffy, D.L., Martin, N.G., Mathews, J.D. (1990). Appendectomy in Australian twins. Aust. J. Hum. Genet. 47(3):590–592.[PubMed], [Web of Science ®] , [Google Scholar]) and a better model is suggested for the data.     

The strong laws of large numbers for countable non homogeneous hidden Markov models

In this article, we are going to study the strong laws of large numbers for countable non homogeneous hidden Markov models. First, we introduce the notion of countable non homogeneous hidden Markov models. Then, we obtain some properties for those Markov models. Finally, we establish two strong laws of large numbers for countable non homogeneous hidden Markov models. As corollaries, we obtain some known results of strong laws of large numbers for finite non homogeneous Markov chains.     

Not every Gibbs sampler is a special case of the Metropolis–Hastings algorithm

It is commonly asserted that the Gibbs sampler is a special case of the Metropolis–Hastings (MH) algorithm. While this statement is true for certain Gibbs samplers, it is not true in general for the version that is taught and used most often, namely, the deterministic scan Gibbs sampler. In this note, I prove that that there exist deterministic scan Gibbs samplers that do not exhibit detailed balance and hence cannot be considered MH samplers. The nuances of various Gibbs sampling schemes are discussed.     

基于前景理论的跨市场状态转移多阶段资产配置研究

在行为金融前景理论框架下研究跨市场间的状态转移资产配置问题,构建隐Markov——混合正态分布模型描述股票、债券和商品混合市场间的状态特征,用Baum-Welch算法估计模型参数,并利用状态转移思想进行情景生成建立多阶段随机优化模型。进一步,以我国股票、债券和商品混合市场的实际数据为背景,利用滚动窗口方法实证分析基于状态转移的多阶段随机模型的表现,并与忽略状态转移特征的基准模型、等权重组合、沪深300指数的结果进行对比。结果表明,与其他组合相比,基于状态转移的投资组合有助于规避风险,且混合市场间的状态转移信息能够对前景理论投资者的最优投资决策产生影响。     

The Impact of Estimation: A New Method for Clustering and Trajectory Estimation in Patient Flow Modeling

The ability to accurately forecast and control inpatient census, and thereby workloads, is a critical and long‐standing problem in hospital management. The majority of current literature focuses on optimal scheduling of inpatients, but largely ignores the process of accurate estimation of the trajectory of patients throughout the treatment and recovery process. The result is that current scheduling models are optimizing based on inaccurate input data. We developed a Clustering and Scheduling Integrated (CSI) approach to capture patient flows through a network of hospital services. CSI functions by clustering patients into groups based on similarity of trajectory using a novel semi‐Markov model (SMM)‐based clustering scheme, as opposed to clustering by patient attributes as in previous literature. Our methodology is validated by simulation and then applied to real patient data from a partner hospital where we demonstrate that it outperforms a suite of well‐established clustering methods. Furthermore, we demonstrate that extant optimization methods achieve significantly better results on key hospital performance measures under CSI, compared with traditional estimation approaches, increasing elective admissions by 97% and utilization by 22% compared to 30% and 8% using traditional estimation techniques. From a theoretical standpoint, the SMM‐clustering is a novel approach applicable to any temporal‐spatial stochastic data that is prevalent in many industries and application areas.     

Routing in a queueing system with two heterogeneous servers in speed and in quality of resolution

Heterogeneous servers, in manufacturing and service systems, may have different speeds and different quality levels for the provided service or good For a two-server queueing model, we formulate the job routing problem for minimizing the stationary weighted sum of the expected time spent in the system and the number of unsatisfied customers per time unit. Using a Markov decision process approach, we prove that the optimal routing policy of jobs to service is a threshold policy that depends on the queue length. When the number of waiting jobs in the queue is below a certain threshold, only one server should work and the other one remains idle. At or above this threshold, both servers should serve jobs. This is an extension of the known result where only the heterogeneity in speed is considered.