Narrow Results

The constant elasticity of variance (CEV) model is widely studied and applied for volatility forecasting and optimal decision making in both areas of financial engineering and operational management, especially in option pricing, due to its good fitting effect for the volatility process of various assets such as stocks and commodities. However, it is extremely difficult to conduct parameter estimation for the CEV model in practice since the precise likelihood function cannot be derived. Motivated by the gap between theory and practice, this paper initiatively applies the Markov Chain-Monte Carlo (MCMC) method into parameter estimation for the CEV model. We first construct a theoretical structure on how to implement the MCMC method into the CEV model, and then execute an empirical analysis with big data of CSI 300 index collected from the Chinese stock market. The final empirical results reveal insights on two aspects: On one aspect, the simulated results of the convergence test are convergent, which demonstrates that the MCMC estimation method for the CEV model is effective; On the other aspect, by a comparison with other two most frequently used estimation methods, the maximum likelihood estimation (MLE) and the generalized moment estimation (GMM), our method is proved to be of high accuracy and has a simpler implementation and wider application.

In this paper, the holographic dark energy in Brans–Dicke theory is confronted by cosmic observations from SN Ia, BAO, OHD and CMB via Markov-Chain Monte-Carlo (MCMC) method. The best fit parameters are found in 1σ region: and (equivalently ω = 2415.653 which is less than the solar system bound and consistent with other constraint results). With these best fit values of the parameters, it is found that the universe is undergoing accelerated expansion, and the current value of equation of state of holographic dark energy which is phantom like in Brans–Dicke theory. The effective Newton's constant decreases with the expansion of our universe for the negative value of model parameter α.

A self-consistent global fitting method based on the Markov Chain Monte Carlo technique to study the dark matter (DM) property associated with the cosmic ray electron/positron excesses was developed in our previous work. In this work we further improve the previous study to include the hadronic branching ratio of DM annihilation/decay. The PAMELA data are employed to constrain the hadronic branching ratio. We find that the 95% (2σ) upper limits of the quark branching ratio allowed by the PAMELA data is ~0.032 for DM annihilation and ~0.044 for DM decay, respectively. This result shows that the DM coupling to pure leptons is indeed favored by the current data. Based on the global fitting results, we further study the neutrino emission from DM in the galactic center. Our predicted neutrino flux is some smaller than previous works since the constraint from γ-rays is involved. However, it is still capable to be detected by the forthcoming neutrino detector such as IceCube. The improved points of the present study compared with previous works include: (1) the DM parameters, both the particle physical ones and astrophysical ones, are derived in a global fitting way, (2) constraints from various species of data sets, including γ-rays and antiprotons are included, and (3) the expectation of neutrino emission is fully self-consistent.

Numerically estimating the integral of functions in high dimensional spaces is a nontrivial task. A oft-encountered example is the calculation of the marginal likelihood in Bayesian inference, in a context where a sampling algorithm such as a Markov Chain Monte Carlo provides samples of the function. We present an Adaptive Harmonic Mean Integration (AHMI) algorithm. Given samples drawn according to a probability distribution proportional to the function, the algorithm will estimate the integral of the function and the uncertainty of the estimate by applying a harmonic mean estimator to adaptively chosen regions of the parameter space. We describe the algorithm and its mathematical properties, and report the results using it on multiple test cases.

In this paper, an attempt has been made to estimate the augmented strength reliability of a system for the generalized case of Augmentation Strategy Plan (ASP) by assuming that the strength $(X)$ and common stress $(Y)$ are independently but not identically distributed as gamma distribution with parameters $({\alpha }_1,{\lambda }_1)$ and $({\alpha }_2,{\lambda }_2)$, respectively. ASP deals with two important challenges (i) early failures in a newly manufactured system while first and subsequent use and (ii) frequent failures of used system. ASP has a significant role in enhancing the strength of a weaker (or poor) system for failure-free journey to achieve its mission life. The maximum likelihood (ML) and Bayes estimation of augmented strength reliability are considered. In Bayesian context, the informative types of priors (Gamma and Inverted gamma) are chosen under symmetric and asymmetric loss functions for better comprehension purpose. A comparison between the ML and Bayes estimators of the augmented strength reliability is carried out on the basis of their mean square errors (mse’s) and absolute biases by simulating Monte-Carlo samples from posterior distribution through Metropolis–Hasting approximation. Real life data sets are also considered for illustration purpose.

Due to the unavailability of complete data in various circumstances in biological, epidemiological, and medical studies, the analysis of censored data is very common among practitioners. But the analysis of bivariate censored data is not a regular mechanism because it is not necessary to always have independent data. Observed and unobserved covariates affect the variables under study. So, heterogeneity is present in the data. Ignoring observed and unobserved covariates may have objectionable consequences. But it is not easy to find that whether there is any effect of the unobserved covariate or not. Shared frailty models are the viable choice to counter such scenarios. However, due to certain restrictions such as the identifiability condition and the requirement that their Laplace transform exists, finding a frailty distribution can be difficult. As a result, in this paper, we introduce a new frailty distribution generalized Lindley (GL) for reversed hazard rate (RHR) setup that outperforms the gamma frailty distribution. So, our main motive is to establish a new frailty distribution under the RHR setup. By assuming exponential Gumbel (EG) and generalized inverted exponential (GIE) baseline distributions, we propose a new class of shared frailty models based on RHR. We estimate the parameters in these frailty models and use the Bayesian paradigm of the Markov Chain Monte Carlo (MCMC) technique. Model selection criteria have been performed for the comparison of models. We analyze Australian twin data and suggest a better model.

We present and study a Langevin MCMC approach for sampling nonlinear diffusion bridges. The method is based on recent theory concerning stochastic partial differential equations (SPDEs) reversible with respect to the target bridge, derived by applying the Langevin idea on the bridge pathspace. In the process, a Random-Walk Metropolis algorithm and an Independence Sampler are also obtained. The novel algorithmic idea of the paper is that proposed moves for the MCMC algorithm are determined by discretising the SPDEs in the time direction using an implicit scheme, parametrised by θ ∈ [0,1]. We show that the resulting infinite-dimensional MCMC sampler is well-defined only if θ = 1/2, when the MCMC proposals have the correct quadratic variation. Previous Langevin-based MCMC methods used explicit schemes, corresponding to θ = 0. The significance of the choice θ = 1/2 is inherited by the finite-dimensional approximation of the algorithm used in practice. We present numerical results illustrating the phenomenon and the theory that explains it. Diffusion bridges (with additive noise) are representative of the family of laws defined as a change of measure from Gaussian distributions on arbitrary separable Hilbert spaces; the analysis in this paper can be readily extended to target laws from this family and an example from signal processing illustrates this fact.

This study proposes a safety evaluation process for a prevention structure against tsunamis, in which the most updated guideline (i.e. FEMA P-646) is used as the deterministic analysis and a probabilistic approach is adopted to consider uncertainties involved. To overcome the incomplete data on Tsunamis, a Markov chain Monte Carlo (MCMC) simulation is developed to increase the quantity of historical data from Taiwan followed by the use of the least squares support vector machine (LS-SVM) to estimate the probability density function (PDF) of random variables. Based on the fragility analyses of the superstructure, substructure and entire system, if the wall thickness is below 4.45m, the wall thickness is more likely to be the governing factor compared with the pile diameter. Conversely, the pile diameter would more likely be the dominating factor. When the pile size decreases from 75cm to 65cm, the threshold value will shift from 4.45m to 3.85m. In addition, when the wall thickness and height are greater, there is a greater likelihood of the failure probability being governed by the substructure. Based on historical records only, the probability of failure of the seawall is extremely low. Nevertheless, results shown here are in line with the engineering judgement and the computation procedure established in the present study can be used as a reference for performing safety analysis on tsunami structures with insufficient data.

Studying different theoretical properties of epidemiological models has been widely addressed, while numerical studies and especially the calibration of models, which are often complicated and loaded with a high number of unknown parameters, against measured data have received less attention. In this paper, we describe how a combination of simulated data and Markov Chain Monte Carlo (MCMC) methods can be used to study the identifiability of model parameters with different type of measurements. Three known models are used as case studies to illustrate the importance of parameter identifiability: a basic SIR model, an influenza model with vaccination and treatment and a HIV–Malaria co-infection model. The analysis reveals that calibration of complex models commonly studied in mathematical epidemiology, such as the HIV–Malaria co-dynamics model, can be difficult or impossible, even if the system would be fully observed. The presented approach provides a tool for design and optimization of real-life field campaigns of collecting data, as well as for model selection.

In this paper, we formulate and analyze a mathematical model to investigate the transmission dynamics of tomato bacterial wilt disease (TBWD) in Mukono district, Uganda. We derive the basic reproduction number $R_0$ and prove the existence of a disease-free equilibrium point which is globally stable if $R_0<1$ and an endemic equilibrium which exists if $R_0>1$. Model parameters are estimated using the Markov Chain Monte Carlo (MCMC) methods and robustness tested. The model parameters were observed to be identifiable. Numerical simulations show that soil solarization and sensitization of farmers can help to eliminate the disease in Uganda. A modified tomato bacterial wilt model with control terms is formulated.

Engineering vehicles are widely used under various harsh working conditions. For many components in them, service loadings they suffered are usually random and nonstationary due to their remarkable characteristic called cyclic operation. To deal with that, section method can be applied. However, this method will neglect those transition cycles caused by switching load section, which can contribute a lot to fatigue. In order to consider those transition cycles, this paper applied the model called “Switching Markov Chain of Turning Points” (SMCTP). Then the expected rain-flow matrix is compared with the overall rain-flow matrix conducted by section method. The comparison result shows that SMCTP can perform well in processing nonstationary loadings. As a result, the Switching Markov Chain method (SMC) was proved to be effective in stochastically characterizing the nonstationary switching loadings of engineering vehicles.

The field of computational statistics refers to statistical methods or tools that are computationally intensive. Due to the recent advances in computing power, some of these methods have become prominent and central to modern data analysis. In this paper, we focus on several of the main methods including density estimation, kernel smoothing, smoothing splines, and additive models. While the field of computational statistics includes many more methods, this paper serves as a brief introduction to selected popular topics.

Empirical convergence analyses have helped provide insight as to whether economies are converging. Previous works on convergence have tended to focus on a particular economic indicator exclusively, even though the convergence process has multiple components. Improved estimates of convergence are likely to result from an integrated approach wherein several indicators are considered simultaneously. The proposed model integrates convergence analyses for three convergence variables to estimate the overall rate of economic convergence in the EU during 1960 to 1990. The research indicates that convergence is occurring overall, but that employment convergence is happening at a considerably slower pace than are the other types of convergence.

There have been substantial interests in investigating HIV dynamics for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. However, it is difficult to establish a relationship between pharmacokinetics (PK) and antiviral response due to too many confounding factors related to antiviral response during the treatment process. In this article, a mechanism-based dynamic model for HIV infection with intervention by antiretroviral therapies is proposed. In this model, we directly incorporate drug concentration, adherence and drug susceptibility into a function of treatment efficacy defined as an inhibition rate of virus replication. In order to focus our attention on estimating dynamic parameters for all subjects, we investigate a Bayesian approach under a framework of the hierarchical Bayesian (mixed-effects) model. The proposed methods and models not only can help to alleviate the difficulty in identifiability, but also can flexibly deal with sparse and unbalanced longitudinal data. The viral dynamic parameters estimated from the proposed method are, thus, more accurate since the variations in PK, adherence and drug resistance have been considered in the model.

Insurance companies have to build a reserve for their future payments which is usually done by deterministic methods giving only a point estimate. In this paper two semi-stochastic methods are presented along with a more sophisticated hierarchical Bayesian model containing MCMC technique. These models allow us to determine quantiles and confidence intervals of the reserve which can be more reliable as just a point estimate. A sort of cross-validation technique is also used to test the models.

Latent, that is Incurred But Not Reported (IBNR) claims influence heavily the calculation of the reserves of an insurer, necessitating an accurate estimation of such claims. The highly diverse estimations of the latent claim amount produced by the traditional estimation methods (chain-ladder, etc.) underline the need for more sophisticated modelling. We are aimed at predicting the number of latent claims, not yet reported. This means the continuation the so called run-off triangle by filling in the lower triangle of the delayed claims matrix. In order to do this the dynamics of claims occurrence and reporting tendency is specified in a hierarchical Bayesian model. The complexity of the model building requires an algorithmic estimation method, that we carry out along the lines of the Bayesian paradigm using the MCMC technique. The predictive strength of the model against the future disclosed claims is analysed by cross validation. Simulations serve to check model stability. Bootstrap methods are also available as we have full record of the individual claims at our disposal. Those methods are used for assessing the variability of the estimated structural parameters.

The paper surveys almost two decades of progress by me and colleagues in three psychometric research areas involving the probability modeling and statistical analysis of standardized ability test data: nonparametric multidimensional latent ability structure modeling and assessment, test fairness modeling and assessment, and modeling and assessment of skills diagnosis via educational testing. In the process, it is suggested that the unidimensional scoring testing paradigm that has driven standardized ability testing research for over half a century is giving way to a new multidimensional latent ability modeling and multiple scoring paradigm that in particular explains and allows the effective detection of test bias and embraces skills-level formative assessment, opening up a plethora of challenging, exciting, and societally important research problems for psychometricians. It is hoped that this light-stepping history will interest probabilists and statisticians in exploring the field of psychometrics.

Informally, test bias occurs when an examinee is under or over evaluated by his test score in terms of the purpose of the test. Also informally, skills diagnosis refers to evaluating examinee levels of mastery (usually done dichotomously as master versus nonmaster of each skill) on a moderate number of carefully selected skills for which having student skills profiles can greatly help individual student learning and classroom level.

My strategy, strongly influenced by his probabilistic background, for producing interesting and effective psychometric research is to choose psychometric research questions from practical challenges facing educational testing. Then, I and colleagues bring to bear sophisticated probability modeling and modern statistical thought to solve these questions, making effectiveness of the resulting research in meeting the educational testing challenges the ultimate criterion for judging its worth.

It is somebody's ancient proverb that the acorn sometimes falls far from the oak tree. Y. S. Chow taught me the tools of probability limit theorem research, taught me to approach research with enthusiasm and tenacity, and provided a very supportive environment for me and his other graduate students. Although psychometrics/educational measurement is far from the probabilistic oak tree, whatever success I've had as a psychometrician has been strongly influenced by the supportive, demanding, and creative environment Y. S. creates for his students. By now I have had many Ph.D. students in psychometrics: it was the just described model of Y. S.'s for mentoring Ph.D. students that I followed with all of them.

The field of computational statistics refers to statistical methods or tools that are computationally intensive. Due to the recent advances in computing power, some of these methods have become prominent and central to modern data analysis. In this paper, we focus on several of the main methods including density estimation, kernel smoothing, smoothing splines, and additive models. While the field of computational statistics includes many more methods, this paper serves as a brief introduction to selected popular topics.

The proliferation of sequencing technologies in biomedical research has raised many new privacy concerns. These include concerns over the publication of aggregate data at a genomic scale (e.g. minor allele frequencies, regression coefficients). Methods such as differential privacy can overcome these concerns by providing strong privacy guarantees, but come at the cost of greatly perturbing the results of the analysis of interest. Here we investigate an alternative approach for achieving privacy-preserving aggregate genomic data sharing without the high cost to accuracy of differentially private methods. In particular, we demonstrate how other ideas from the statistical disclosure control literature (in particular, the idea of disclosure risk) can be applied to aggregate data to help ensure privacy. This is achieved by combining minimal amounts of perturbation with Bayesian statistics and Markov Chain Monte Carlo techniques. We test our technique on a GWAS dataset to demonstrate its utility in practice. An implementation is available at https://github.com/seanken/PrivMCMC.

The methodology of Markov basis initiated by Diaconis and Sturmfels¹ stimulated active research on Markov bases for more than ten years. It also motivated improvements of algorithms for Gröbner basis computation for toric ideals, such as those implemented in 4ti2.² However at present explicit forms of Markov bases are known only for some relatively simple models, such as the decomposable models of contingency tables. Furthermore general algorithms for Markov bases computation often fail to produce Markov bases even for moderate-sized models in a practical amount of time. Hence so far we could not perform exact tests based on Markov basis methodology for many important practical problems.

In this article we propose to use lattice bases for performing exact tests, in the case where Markov bases are not known. Computation of lattice bases is much easier than that of Markov bases. With many examples we show that the approach with lattice bases is practical. We also check that its performance is comparable to Markov bases for the problems where Markov bases are known.