Bayesian Markov Research Articles

Semi-parametric Bayesian tail risk forecasting incorporating realized measures of volatility

Realized measures employing intra-day sources of data have proven effective for dynamic volatility and tail-risk estimation and forecasting. Expected shortfall (ES) is a tail risk measure, now recommended by the Basel Committee, involving a conditional expectation that can be semi-parametrically estimated via an asymmetric sum of squares function. The conditional autoregressive expectile class of model, used to implicitly model ES, has been extended to allow the intra-day range, not just the daily return, as an input. This model class is here further extended to incorporate information on realized measures of volatility, including realized variance and realized range (RR), as well as scaled and smoothed versions of these. An asymmetric Gaussian density error formulation allows a likelihood that leads to direct estimation and one-step-ahead forecasts of quantiles and expectiles, and subsequently of ES. A Bayesian adaptive Markov chain Monte Carlo method is developed and employed for estimation and forecasting. In an empirical study forecasting daily tail risk measures in six financial market return series, over a seven-year period, models employing the RR generate the most accurate tail risk forecasts, compared to models employing other realized measures as well as to a range of well-known competitors.

Learning word meanings and grammar for verbalization of daily life activities using multilayered multimodal latent Dirichlet allocation and Bayesian hidden Markov models

Intelligent systems need to understand and respond to human words to enable them to interact with humans in a natural way. Several studies attempted to realize these abilities by investigating the symbol grounding problem. For example, we proposed multilayered multimodal latent Dirichlet allocation (mMLDA) to enable the formation of various concepts and inference using grounded concepts. We previously reported on the issue of connecting words to various hierarchical concepts and also proposed a simple preliminary algorithm for generating sentences. This paper proposes a novel method that enables a sensing system to verbalize an everyday scene it observes. The method uses mMLDA and Bayesian hidden Markov models (BHMM) and the proposed algorithm improves the word inference of our previous work. The advantage of our approach is that grammar learning based on BHMM not only boosts concept selection results but enables our method to process functional words. The proposed verbalization algorithm produces results that are far superior to those of previous methods. Finally, we developed a system to obtain multimodal data from human everyday activities. We evaluate language learning and sentence generation as a complete process under this realistic setting. The results demonstrate the effectiveness of our method.

Hidden Markov model for discrete circular–linear wind data time series

ABSTRACTIn this work, we deal with a bivariate time series of wind speed and direction. Our observed data have peculiar features, such as informative missing values, non-reliable measures under a specific condition and interval-censored data, that we take into account in the model specification. We analyse the time series with a non-parametric Bayesian hidden Markov model, introducing a new emission distribution, suitable to model our data, based on the invariant wrapped Poisson, the Poisson and the hurdle density. The model is estimated on simulated datasets and on the real data example that motivated this work.

A Bayesian Analysis of Copy Number Variations in Array Comparative Genomic Hybridization Data

Array Comparative Genomic Hybridization (CGH) has been widely used for detecting genomic copy number variations (CNVs). The central goal of array CGH data analysis is to accurately detect homogeneous regions of log intensity ratios which represent relative changes in DNA copy number. Various methods have been proposed in recent years. Most methods, however, do not consider correlations of neighboring probe measurements, and are usually designed for analysis at single sample level rather than detecting common or recurrent CNVs among multiple samples. We propose a Bayesian segment-based approach for efficient analysis of array CGH data. The proposed method is based on simple assumptions but is general enough to accommodate various spatial correlations among probe measurements. It also allows for multiple samples with recurrent CNVs, therefore is able to borrow strength across samples. In contrast to another probe-based approach developed in the same Bayesian framework, the segment-based approach parameterizes the mean log intensity ratios in a more appropriate way, which leads to a posterior sampling scheme based on reversible-jump Markov chain Monte Carlo. We perform a simulation study to compare these two approaches and the commonly-used circular binary segmentation method and Bayesian hidden Markov model method. The segment-based approach achieves better estimation accuracy and higher computational efficiency compared to the probe-based approach, and also provides improved results compared to the other two methods, especially for data with relatively low signal to noise ratio and high correlation. The segment-based approach is further applied to the Corriel cell lines data and Pancreatic Adenocarcinoma data.

Bayesian Estimation of the Three Key Parameters in CT for the National Lung Screening Trial Data

In this study cancer screening likelihood method was used to analyze the CT scan group in the National Lung Screening Trial (NLST) data. Three key parameters: screening sensitivity, transition probability density from disease free to preclinical state, and sojourn time in the preclinical state, were estimated using Bayesian approach and Markov Chain Monte Carlo simulations. The sensitivity for lung cancer screening using CT scan is high; it does not depend on a patient’s age, and is slightly higher in females than in males. The transition probability from the disease-free to the preclinical state has a peak around age 70 for both genders, which agrees with the fact that the highest lung cancer incidence rate appears between age 65 and 74. The posterior mean sojourn time is around 1.5 years for all groups, and that explains why screening only have a short time interval to catch lung cancer. Accurate estimation of the three key parameters is critical for other estimations such as lead time and over-diagnosis, because these quantities are functions of the three key parameters.

Bayesian quantile regression for hierarchical linear models

The paper proposes a Bayesian quantile regression method for hierarchical linear models. Existing approaches of hierarchical linear quantile regression models are scarce and most of them were not from the perspective of Bayesian thoughts, which is important for hierarchical models. In this paper, based on Bayesian theories and Markov Chain Monte Carlo methods, we introduce Asymmetric Laplace distributed errors to simulate joint posterior distributions of population parameters and across-unit parameters and then derive their posterior quantile inferences. We run a simulation as the proposed method to examine the effects on parameters induced by units and quantile levels; the method is also applied to study the relationship between Chinese rural residents' family annual income and their cultivated areas. Both the simulation and real data analysis indicate that the method is effective and accurate.

Estimation of SV Model with Leverage Effect Based on MCMC Technique

This paper is to study the estimation of stochastic volatility model with leverage effect using Bayesian approach and Markov Chain Monte Carlo (MCMC) simulation technique. The data used is China's Shenzheng stock index. Estimations of model parameters are achieved by using MCMC technique in Openbugs Software, results show that there is leverage effect in Shenzheng stock series, convergence diagnostics suggest that parameters of the model are convergent.

A sensor-driven structural health prognosis procedure considering sensor performance degradation

This article presents a general framework for sensor-driven structural health prognosis and its application to probabilistic maintenance scheduling. Continuously collected sensor data is used to update the parameters of the stochastic structural degradation model. Uncertainty in sensor data (i.e. measurement error) is explicitly modelled as an evolving stochastic process. The proposed framework utilises Bayesian theorem and Markov Chain Monte Carlo (MCMC) sampling to calculate the posterior distributions of stochastic parameters of the structural degradation model. Bayesian updating allows the use of dynamic diagnostic information with prior knowledge for improved prognosis including risk analysis and remaining useful life (RUL) estimation. Although the proposed sensor-driven structural health prognosis procedure is illustrated with a fatigue-related example, it is applicable to more general applications such as corrosion and pavement cracking. A case study of the fatigue details found in a prototype steelgirder bridge has been conducted to demonstrate the proposed prognosis and maintenance scheduling procedure.

Rapid quantification of uncertainty in permeability and porosity of oil reservoirs for enabling predictive simulation

One of the most difficult tasks in subsurface flow simulations is the reliable characterization of properties of the subsurface. A typical situation employs dynamic data integration such as sparse (in space and time) measurements to be matched with simulated responses associated with a set of permeability and porosity fields. Among the challenges found in practice are proper mathematical modeling of the flow, persisting heterogeneity in the porosity and permeability, and the uncertainties inherent in them. In this paper we propose a Bayesian framework Monte Carlo Markov Chain (MCMC) simulation to sample a set of characteristics of the subsurface from the posterior distribution that are conditioned to the production data. This process requires obtaining the simulated responses over many realizations. In reality, this can be a prohibitively expensive endeavor with possibly many proposals rejection, and thus wasting the computational resources. To alleviate it, we employ a two-stage MCMC that includes a screening step of a proposal whose simulated response is obtained via an inexpensive coarse-scale model. A set of numerical examples using a two-phase flow problem in an oil reservoir as a benchmark application is given to illustrate the procedure and its use in predictive simulation.

Evaluating the system reliability of corroding pipelines based on inspection data

This paper presents a methodology for evaluating the time-dependent system reliability of a pressurised gas pipeline segment containing multiple active metal-loss corrosion defects. The methodology incorporates three distinctive failure modes of the pipe segment due to corrosion, namely small leak, large leak and rupture. The growth of the depth of individual corrosion defect is assumed to follow a power-law function of time. The Bayesian updating and Markov Chain Monte Carlo (MCMC) simulation techniques are used to quantify the parameters of the power-law growth model based on data obtained from multiple inspections carried out at different times. The simple Monte Carlo and MCMC techniques are combined to evaluate the system reliability. A numerical example involving an in-service gas pipeline located in Alberta, Canada, is used to illustrate the proposed methodology. Results of the sensitivity analysis suggest that the use of a defect-specific or segment-specific growth model for the defect depth has a marked impact on the evaluated system reliability. The proposed methodology can be incorporated in reliability-based pipeline corrosion management programmes to assist integrity engineers in making informed decisions about defect repair and mitigation.

The use of Bayes factors to compare interest rate term structure models

Studies of the term structure of interest rates try to explain the relationship between the yield to maturity on zero-coupon bonds and their time to maturity. Over the years, many theoretical models have been developed to explain the stylized facts of U.S. Treasury yields; however, model comparison, parameter estimation and hypothesis testing remain thorny issues. The purpose of this paper is to show that Bayesian methods and Markov Chain Monte Carlo (MCMC) methods, in particular, may help resolve a number of these problems, especially those related to model comparison. We use MCMC to compare the seminal models of Vasicek and Cox, Ingersoll and Ross (CIR). The most surprising result of our analysis is that one of these two models is almost 50 000 times more likely than the other. In contrast, results in the previous literature have been much more ambiguous because they are based on a variety of goodness-of-fit measures. A Monte Carlo study shows that these results are not spurious: the MCMC method is able to select the correct data generation model, whereas goodness-of-fit measures are virtually indistinguishable regardless of whether the data were generated from Vasicek or CIR.

Bayesian coalescent analysis of pandemic H1N1 influenza A virus circulating in the South American region

The first influenza pandemic of this century was declared in April of 2009, with the emergence of a novel H1N1 influenza A virus strain (H1N1pdm). Understanding the evolution of H1N1pdm populations within the South American region is essential for studying global diversification, emergence, resistance and vaccine efficacy. In order to gain insight into these matters, we have performed a Bayesian coalescent Markov Chain Monte Carlo analysis of hemagglutinin (HA) and neuraminidase (NA) gene sequences of all available and comparable HA and NA sequences obtained from H1N1pdm IAV circulating in the South American region. High evolutionary rates and fast population growths characterize the population dynamics of H1N1pdm strains in this region of the world. A significant contribution of first codon position to the mean evolutionary rate was found for both genes studied, revealing a high contribution of non-synonymous substitutions to the mean substitution rate. In the 178days period covered by these studies, substitutions in all HA epitope regions can be observed. HA substitutions D239G/N and Q310H have been observed only in Brazilian patients. While substitution D239G/N is not particularly associated to a specific genetic lineage, all strains bearing substitution Q310H were assigned to clade 6, suggesting a founder effect. None of the substitutions found in the NA proteins of H1N1pdm strains isolated in South America appears sufficiently close to affect the drug binding pocket for the three NA inhibitor antivirals tested. A more detailed analysis of NA proteins revealed epitope differences among 2010 vaccine and H1N1pdm IAV strains circulating in the South American region.

Application of Bayesian Statistics and Markov Model in Medical Decision

Bayesian statistics is another scientific method for statistics besides classical statistics which makes use of the prior information mixed with the sample information to draw some inferences about the posterior distributions of parameters based on the Bayesian formula. The Markov process is a random one transiting from one state to another. The models based on Markov process match well to the medical clinical practice. The medical intervention measures need to be evaluated not only the clinical effect and safety, but also their cost-utility. We study the application of evaluating the cost-utility of medical intervention measures based on analysis of Bayesian statistics and Markov model hoping for providing medical decision-making reference.

MRI Tissue Classification Using High-Resolution Bayesian Hidden Markov Normal Mixture Models

Magnetic resonance imaging (MRI) is used to identify the major tissues within a subject's brain. Classification is usually based on a single image providing one measurement for each volume element, or voxel, in a discretization of the brain. A simple model views each voxel as homogeneous, belonging entirely to one of the three major tissue types: gray matter, white matter, or cerebrospinal fluid. The measurements are normally distributed, with means and variances depending on the tissue types of their voxels. Because nearby voxels tend to be of the same tissue type, a Markov random field model can be used to capture the spatial similarity of voxels. A more realistic model takes into account the fact that some voxels are not homogeneous and contain tissues of more than one type. Our approach to this problem is to construct a higher-resolution image in which each voxel is divided into subvoxels and subvoxels are in turn assumed to be homogeneous and to follow a Markov random field model. In the present work we used a Bayesian hierarchical model to perform MRI tissue classification. Conditional independence was exploited to improve the speed of sampling. The subvoxel approach provides more accurate tissue classification and also allows more effective estimation of the proportion of major tissue types present in each voxel for both simulated and real datasets.

Demand Forecast of Petroleum Product Consumption in the Chinese Transportation Industry

In this paper, petroleum product (mainly petrol and diesel) consumption in the transportation sector of China is analyzed. This was based on the Bayesian linear regression theory and Markov Chain Monte Carlo method (MCMC), establishing a demand-forecast model of petrol and diesel consumption introduced into the analytical framework with explanatory variables of urbanization level, per capita GDP, turnover of passengers (freight) in aggregate (TPA, TFA), and civilian vehicle number (CVN) and explained variables of petrol and diesel consumption. Furthermore, we forecast the future consumer demand for oil products during “The 12th Five Year Plan” (2011–2015) based on the historical data covering from 1985 to 2009, finding that urbanization is the most sensitive factor, with a strong marginal effect on petrol and diesel consumption in this sector. From the viewpoint of prediction interval value, urbanization expresses the lower limit of the predicted results, and CVN the upper limit of the predicted results. Predicted value from other independent variables is in the range of predicted values which display a validation range and reference standard being much more credible for policy makers. Finally, a comparison between the predicted results from autoregressive integrated moving average models (ARIMA) and others is made to assess our task.

A Bayesian autoregressive three-state hidden Markov model for identifying switching monotonic regimes in Microarray time course data

When modeling time course microarray data special interest may reside in identifying time frames in which gene expression levels follow a monotonic (increasing or decreasing) trend. A trajectory may change its regime because of the reaction to treatment or of a natural developmental phase, as in our motivating example about identification of genes involved in embryo development of mice with the 22q11 deletion. To this aim we propose a new flexible Bayesian autoregressive hidden Markov model based on three latent states, corresponding to stationarity, to an increasing and to a decreasing trend. In order to select a list of genes, we propose decision criteria based on the posterior distribution of the parameters of interest, taking into account the uncertainty in parameter estimates. We also compare the proposed model with two simpler models based on constrained formulations of the probability transition matrix.

BaRMS: A Bayesian Reputation Management Approach for P2P Systems

Current distributed Peer-to-Peer (P2P) applications offer a variety of flexible and convenient services through the Internet to users from different geographic locations and also support enhanced communications and interactions among them. However, security and trust are the key concerns in such applications as users in such an environment are typically unknown to each other. Trust management systems aim to decrease the risks in such applications and protect benign users from malicious users. In this paper, we introduce six attack models and propose a novel Bayesian Reputation Management System (BaRMS) for P2P environments using Bayesian probability and Markov Chain theories. BaRMS handles both positive and negative feedback. Through a case study, we show that this approach is better than the existing EigenTrust framework for P2P systems. Moreover, our simulation results of a P2P file sharing system also show that the proposed algorithm can greatly improve the performance over a system that does not include a trust management service under various attack models. We show that our proposed Bayesian Reputation Computation Algorithm (BaRCA) performs better than the EigenTrust algorithm under various models.

Bayesian identification of stochastic linear systems with observations at multiple scales

A Bayesian system identification approach to modelling stochastic linear dynamical systems involving multiple scales is proposed, where multiscale means that the output of the system is observed at one (coarse) resolution whilst the input of the system can only be observed at another (fine) resolution. The proposed method identifies linear models at different levels of resolution, where the link between the two resolutions is realised via a non-overlapping averaging process. The averaged data at the coarse level of resolution is assumed to be a set of observations from an implied process so that the implied process and the output of the system result in an errors-in-variables model at the coarse level of resolution. By using a Bayesian inference and Markov chain Monte Carlo method, such a modelling framework results in different dynamical models at different levels of resolution at the same time. The new method is also shown to have the ability to combine information across different levels of resolution. Simulation examples are provided to show the efficiency of the new method. Furthermore, an application to the analysis of the relativistic electron intensity at the geosynchronous orbit is also included.

Component-Oriented Reliability Analysis Based on Hierarchical Bayesian Model for an Open Source Software

The successful experience of adopting distributed development models in such open source projects includes GNU/Linux operating system, Apache HTTP server, Android, BusyBox, and so on. The open source project contains special features so-called software composition by which several geographically-dispersed compo-nents are developed in all parts of the world. We propose a method of component-oriented reliability as-sessment based on hierarchical Bayesian model and Markov chain Monte Carlo methods. Especially, we fo-cus on the fault-detection rate for each component reported to the bug tracking system. We can assess the reliability for the whole open source software system by using the confidence interval for each component. Also, we analyze actual software fault-count data to show numerical examples of reliability assessment for OSS.

Model Reduction Techniques for Characterization of Fractured Subsurfaces

Abstract One of the most diffcult tasks in reservoir simulations is reliable characterization of fractured subsurfaces. A typical situation in petroleum engineering employs dynamic data integrations such as the oil production history to be matched with simulated responses associated with a set of porosity and/or permeability fields. Among the challenges found in practice are proper mathematical modelings of the flow in the presence of fractured systems, persisting heterogeneity in the porosity and permeability, and the uncertainties inherent in them. In this paper we propose a Bayesian framework Monte Carlo Markov Chain simulation (MCMC) to sample a set of subsurface's characteristics from the posterior distribution that are conditioned to the production data. This process requires obtaining the simulated responses over many realizations. The flow for this simulated response is governed by a dual porosity, dual permeability model. As this can be a prohibitively expensive endeavor, we address the possibility of using the Multiscale Finite Volume Element (MsFVEM) combined with a sparse stochastic collocation technique to provide a venue for an effcient computation. A set numerical examples illustrating the procedure will be presented.