For a spatial pattern of points interacting with a repulsive potential in a given finite region of the plane, Bayesian estimation of parametric interaction potential functions between individuals (the Soft-Core models) is proposed. The computations are performed by the use of MCMC (Markov Chain Monte Carlo) methods. We consider two prior distributions with the jumping distributions within Markov chain simulations. Simulated marginal posterior densities of model parameters are fitted to the generalized gamma distribution. We compare marginal posterior modes with the maximum likelihood estimates of the model parameters. The validity of our procedure is graphically demonstrated by the L-statistics. As illustrations, the application to several real data is presented.
The paper presents a feasible numerical procedure for evaluating the maximum Whittle likelihood estimates and the likelihood-ratio statistics, where to obtain the maximum Whittle likelihood estimates under specific cointegration ranks, we introduce an iterative method in which the set of the ARMA coefficient estimates is adjusted so as to guarantee that in each step they satisfy the root conditions imposed by respective cointegration rank hypotheses. The method is incorporated in the Whittle likelihood maximization.
Stochastic volatility (SV) models provide useful tools to describe the evolution of asset returns, which exhibit time-varying volatility. This paper extends a basic SV model to capture a leverage effect, a fat-tailed distribution of asset returns and a nonlinear relationship between the current volatility and the previous volatility process. The Bayesian approach with the Markov chain Monte Carlo method is employed to estimate model parameters. To assess the goodness of the estimated model, we calculated several Bayesian model selection criteria that include the Bayes factor, the Bayesian predictive information criterion and the deviance information criterion. The proposed method is tested on simulated data and then applied to daily returns on the Nikkei 225 index where several SV models are formally compared.
This paper reviews several MCMC methods for estimating the class of ARCH models, and compare performances of them. With respect to the mixing, efficiency and computational requirement of the MCMC, this paper found the best method is the tailored approach based on the acceptance-rejection Metropolis-Hastings algorithm.
In this paper we discuss various definitions of bivariate reversed hazard rate and their properties. An exponential representation of bivariate distribution using reversed hazard rates is given and we also develop a new family of bivariate distributions using bivariate reversed hazard rate. Finally we give a local dependence measure using bivariate reversed hazard rates and study its properties. Various applications of the models are pointed out.
It is well known that X + Y has the F distribution when X and Y follow the inverted Dirichlet distribution. In this paper, we derive the exact distribution of the general form αX + βY (involving the Gauss hypergeometric function) and the corresponding moment properties. We also propose approximations and discuss evidence of their robustness based on the powerful Kolmogorov-Smirnov test. The work is motivated by real-life examples in quality and reliability engineering.
Under the assumption that the three-factor and higher-order interactions are negligible, we consider two kinds of partially balanced fractional 2m1+m2 factorial designs derived from simple partially balanced arrays, where 2 ≤ mk for k = 1, 2. One is a design such that the general mean, the m1 + m2 main effects, the (m12) two-factor interactions, the (m22) two-factor ones and some linear combinations of the m1m2 two-factor ones are estimable, and the other is a design such that the general mean, the m1 + m2 main effects, the (m12) two-factor interactions, the m1m2 two-factor ones and some linear combinations of the (m22) two-factor ones are estimable. In each kind of designs, we present optimal designs with respect to the generalized A-optimality criterion when the number of assemblies is less than the number of non-negligible factorial effects, where ≤ m1, m2 ≤ 4.