LAN property for an ergodic diffusion with jumps

In this paper, we consider a multidimensional ergodic diffusion with jumps driven by a Brownian motion and a Poisson random measure associated with a compound Poisson process, whose drift coefficient depends on an unknown parameter. Considering the process discretely observed at high frequency, we derive the local asymptotic normality (LAN) property.     

A new Bayesian wavelet thresholding estimator of nonparametric regression

The methods of estimation of nonparametric regression function are quite common in statistical application. In this paper, the new Bayesian wavelet thresholding estimation is considered. The new mixture prior distributions for the estimation of nonparametric regression function by applying wavelet transformation are investigated. The reversible jump algorithm to obtain the appropriate prior distributions and value of thresholding is used. The performance of the proposed estimator is assessed with simulated data from well-known test functions by comparing the convergence rate of the proposed estimator with respect to another by evaluating the average mean square error and standard deviations. Finally by applying the developed method, density function of galaxy data is estimated.     

A Bayesian model for multiple change point to extremes,with application to environmental and financial data

Abrupt changes often occur for environmental and financial time series. Most often, these changes are due to human intervention. Change point analysis is a statistical tool used to analyze sudden changes in observations along the time series. In this paper, we propose a Bayesian model for extreme values for environmental and economic datasets that present a typical change point behavior. The model proposed in this paper addresses the situation in which more than one change point can occur in a time series. By analyzing maxima, the distribution of each regime is a generalized extreme value distribution. In this model, the change points are unknown and considered parameters to be estimated. Simulations of extremes with two change points showed that the proposed algorithm can recover the true values of the parameters, in addition to detecting the true change points in different configurations. Also, the number of change points was a problem to be considered, and the Bayesian estimation can correctly identify the correct number of change points for each application. Environmental and financial data were analyzed and results showed the importance of considering the change point in the data and revealed that this change of regime brought about an increase in the return levels, increasing the number of floods in cities around the rivers. Stock market levels showed the necessity of a model with three different regimes.     

A probabilistic clustering method for data elements with normal distributed attributes

By considering uncertainty in the attributes common methods cannot be applicable in data clustering. In the recent years, many researches have been done by considering fuzzy concepts to interpolate the uncertainty. But when data elements attributes have probabilistic distributions, the uncertainty cannot be interpreted by fuzzy theory. In this article, a new concept for clustering of elements with predefined probabilistic distributions for their attributes has been proposed, so each observation will be as a member of a cluster with special probability. Two metaheuristic algorithms have been applied to deal with the problem. Squared Euclidean distance type has been considered to calculate the similarity of data elements to cluster centers. The sensitivity analysis shows that the proposed approach will converge to the classic approaches results when the variance of each point tends to be zero. Moreover, numerical analysis confirms that the proposed approach is efficient in clustering of probabilistic data.     

Bayesian parameter inference for stochastic SIR epidemic model with hyperbolic diffusion

This paper is concerned with the Bayesian estimation parameters of the stochastic SIR (Susceptible-Infective-Removed) epidemic model from the trajectory data. Specifically, the data from the count of both infectives and susceptibles is assumed to be available on some time grid as the epidemic progresses. The diffusion approximation of the appropriate jump process is then used to estimate missing data between every pair of observation times. If the time step of imputations is small enough, we derive the posterior distributions of the infection and recovery rates using the Milstein scheme. The paper also presents Markov-chain Monte Carlo (MCMC) simulation that demonstrates that the method provides accurate estimates, as illustrated by the synthetic data from SIR epidemic model and the real data.     

An evaluation of the reconstructed coefficient of determination and potential adjustments

Previously, a method was proposed for calculating a reconstructed coefficient of determination in the case of right-censored regression using the expectation–maximization (EM) algorithm. This measure is assessed via simulation study for the purpose of evaluating the utility of model fit. Further, several reconstructed adjusted coefficients of determination are proposed and compared via simulation study for the purpose of model selection. The application of these proposed measures is illustrated on a real dataset.     

Parameter estimation of a composite production function model based on improved artificial fish swarm algorithm and model application

The traditional Cobb–Douglas production function uses the compact mathematical form to describe the relationship between the production results and production factors in the production technology process. However, in macro-economic production, multi-structured production exists universally. In order to better demonstrate such input–output relation, a composite production function model is proposed in this article. In aspect of model parameter estimation, artificial fish swarm algorithm is applied. The algorithm has satisfactory performance in overcoming local extreme value and acquiring global extreme value. Moreover, realization of the algorithm does not need the gradient value of the objective function. For this reason, it is adaptive to searching space. Through the improved artificial fish swarm algorithm, convergence rate and precision are both considerably improved. In aspect of model application, the composite production function model is mainly used to calculate economic growth factor contribution rate. In this article, a relatively more accurate calculating method is proposed. In the end, empirical analysis on economic growth contribution rate of China is implemented.     

A new family of multivariate slash distributions

In this article, a new form of multivariate slash distribution is introduced and some statistical properties are derived. In order to illustrate the advantage of this distribution over the existing generalized multivariate slash distribution in the literature, it is applied to a real data set.     

基于蚁群算法参数的最优选择问题研究

蚁群算法是受现实蚂蚁群体行为启发而得出的一类仿生算法。通过对蚁群算法中影响算法性能的参数进行分析和研究,并对蚁群算法中参数的最优选择问题进行实验分析,从而给出算法参数的最佳取值范围,以利于算法在实际问题中的应用和推广.     

MAP segmentation in Bayesian hidden Markov models: a case study

We consider the problem of estimating the maximum posterior probability (MAP) state sequence for a finite state and finite emission alphabet hidden Markov model (HMM) in the Bayesian setup, where both emission and transition matrices have Dirichlet priors. We study a training set consisting of thousands of protein alignment pairs. The training data is used to set the prior hyperparameters for Bayesian MAP segmentation. Since the Viterbi algorithm is not applicable any more, there is no simple procedure to find the MAP path, and several iterative algorithms are considered and compared. The main goal of the paper is to test the Bayesian setup against the frequentist one, where the parameters of HMM are estimated using the training data.