A general method for assessing local influence of minor perturbations of prior in Bayesian analysis is developed in this paper. Using some elementary ideas from differential geometry, we provide a unified approach for handling a variety of problems of local prior influence. As applications, we discuss the local influence of small perturbations of normal-gamma prior density in linear model and investigate local prior influence from the predictive view.

The bearings of a certain type have their lives following a Weibull distribution. In a life test with 20 sets of bearings, only one set failed within the specified time, and none of the remainder failed even after the time of test has been extended. With a set of testing data like that in Table 1, it is required to estimate the reliability at the mission time. In this paper, we first use hierarchical Bayesian method to determine the prior distribution and the Bayesian estimates of various probabilities of failures, p_i’s, then use the method of least squares to estimate the parameters of the Weibull distribution and the reliability. Actual computation shows that the estimates so obtained are rather robust. And the results have been adopted for practical use.

This paper concerns with the core of nonatomic games of form f(μ), whereμ is a nonatomic nonnegative measure and f is a continuous convex function on the domain ofμ. The main result of this paper is that the core of the game is not compact under the norm topology unless the game itself is a measure. This shows the largeness of the core in a sense other than that defined by Sharky for finite cases.

Letn,s₁,s₂,...,s_n be non-negative integers andM(s₁,s₂,...,s_n)=a₁,a₂,...,a_n)|a_iis an integer and 0≤a_i≤s_i for eachi∼. In this paper, the cardinality of maximum trees of finite sequences inM(s₁,s₂,...,s_n) is obtained, which generalizes some of Frankl’s results on families of finite sets with prescribed cardinalities for pairwise intersections.

Spontaneous potential well-logging is one of the important techniques in petroleum exploitation. A spontaneous potential satisfies and elliptic equivalued surface boundary value problem with discontinuous interface conditions. In practice, the measuring electrode is so small that we can simplify the corresponding equalued surface to a point. In this paper, we give a positive answer to this approximation process: when the equivalued surface shrinks to a point, the solution of the original equivalued surface boundary value problem converges to the solution of the corresponding limit boundary value problem.

We consider a nonlinear parabolic system describing compressible miscible displacement in a porous medium [5]. Continuous time and discrete time Galerkin methods are introduced to approximate the solution and optimalH¹ error estimates are obtained. One contribution of this paper is a demonstration of how molecular dispersion can be handled.

In this paper, the normative matrices and their doubleLR transformation with origin shifts are defined, and the essential relationship between the doubleLR transformation of a normative matrix and theQR transformation of the related symmetric tridiagonal matrix is proved. We obtain a stable doubleLR algorithm for doubleLR transformation of normative matrices and give the error analysis of our algorithm. The operation number of the stable doubleLR algorithm for normative matrices is only four sevenths of the rationalQR algorithm for real symmetric tridiagonal matrices.