Two related methods exist for sampling from posterior distributions of the MLE with a known prior Newton & Raftery (1994) [8], Efron (2011) [4]. We compare them by examining asymptotic Edgeworth expansions of their pivotal distributions. The result is that Newton & Raftery (1994) is 2nd order consistent to the posterior distribution with prior proportional to the Fisher Information, under some ...

We consider the fast solution of large, piecewise smooth minimization problems as typically arising from the nite element discretization of porous media ow. For lack of smoothness, usual Newton multigrid methods cannot be applied. We propose a new approach based on a combination of convex minization with constrained Newton linearization. No regularization is involved. We show global convergence...

Australotarsius Solodovnikov & Newton, gen. nov., a new genus of rove beetles of the tribe Staphylinini, endemic to Australia, is described and compared to other Staphylinini. It includes two new species, A. grandis Solodovnikov & Newton, sp. n. from Queensland and New South Wales, and A. tasmanicus Solodovnikov & Newton, sp. n. from Tasmania. The systematic position of Australotarsius within S...

We derive an indefinite quadrature formula, based on a theorem of Ganelius, for Hp functions, for p > 1, over the interval (−1, 1). The main factor in the error of our indefinite quadrature formula is O(e−π √ ), with 2N nodes and 1 p + 1 q = 1. The convergence rate of our formula is better than that of the Stenger-type formulas by a factor of √ 2 in the constant of the exponential. We conjectur...

We consider a positive measure on [0,∞) and a sequence of nested spaces L0 ⊂ L1 ⊂ L2 · · · of rational functions with prescribed poles in [−∞, 0]. Let {φk}k=0, with φ0 ∈ L0 and φk ∈ Lk \ Lk−1, k = 1, 2, . . . be the associated sequence of orthogonal rational functions. The zeros of φn can be used as the nodes of a rational Gauss quadrature formula that is exact for all functions in Ln · Ln−1, a...

Let {Q„)denote a sequenceof quadrature formulas, Q„(j) m Yfj-iW^fix^), such that ß„(/) -> P0 j(x) dx for all / G CTO, 1], Let 0 < e < \ and a sequence (aX_j.be given, where a, ä si ^ a, 5 • • • , and where a„ —> 0 as n —* c°. Then there exists a function / G CTO, l]and a sequence |nt-)"=i suchthat |/(x)| g 2(7,71(1 4e)|, and such that n,Kx)dx Q„k(1) = ak,k = 1,2, 3, ••• .

In this paper a new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function f(t) is continuous with (known) compact support. An adaptive iterative method and an adaptive stopping rule, which yield the convergence of the approximate solution to f(t), are proposed in this paper. MSC: 15A12; 47A5...

In this paper we establish Gauss-type quadrature formulas for weakly singular integrals. An application of the quadrature scheme is given to obtain numerical solutions of the weakly singular Fredholm integral equation of the second kind. We call this method a discrete product-integration method since the weights involved in the standard product-integration method are computed numerically.

We show, for each n > 1, that the (2ra + l)-point Kronrod extension of the n-point Gaussian quadrature formula for the measure do-^t) = (1 + 7)2(1 t2)^2dt/((l + -y)2 47t2), -K -y < 1, has the properties that its n + 1 Kronrod nodes interlace with the n Gauss nodes and all its 2ra + 1 weights are positive. We also produce explicit formulae for the weights.

It is shown that the zeros of the Faber polynomials generated by a regular m-star are located on the m-star. This proves a recent conjecture of J. Bartolomeo and M. He. The proof uses the connection between zeros of Faber polynomials and Chebyshev quadrature formulas.