On asymptotic validity of naive inference with an approximate likelihood

Many statistical models have likelihoods which are intractable: it is impossible or too expensive to compute the likelihood exactly. In such settings, a common approach is to replace the likelihood with an approximation, and proceed with inference as if the approximate likelihood were the exact likelihood. In this paper, we describe conditions on the approximate likelihood which guarantee that this naive inference with an approximate likelihood has the same first-order asymptotic properties as inference with the exact likelihood. We investigate the implications of these results for inference using a Laplace approximation to the likelihood in a simple two-level latent variable model, and using reduced dependence approximations to the likelihood in an Ising model on a lattice.Comment: Updated to add an additional example (inference for an Ising model on a lattice using reduced dependence approximations to the likelihood

The storage of art on paper : a basic guide for institutions

Includes bibliographical references (p. 27-30)

On non-uniqueness in the traction boundary- value problem for a compressible elastic solid

For a compressible isotropic elastic solid local and global non-uniqueness of the homogeneous deformation resulting from prescribed dead-load boundary tractions is examined. In particular, for the plane-strain problem with equibiaxial in-plane tension, equations governing the paths of deformation branching from the bifurcation point on a deformation path corresponding to in-plane pure dilatation are derived. Explicit calculations are given for a specific strain-energy function and the stability of the branches is discussed. Some general results are then given for an arbitrary form of strain-energy function

Memorandum on The Use of Struksnes Polls to Test Majority Status, 1979

Memo to all consultants, presenting the ways an employer is able to determine a union\u27s majority status. May 21, 197

Memorandum on Unilateral Implementation Of Wage And Benefit Changes, 1979

Memo to all consultants regarding the employers\u27 negotiations with the union, with an example case. June 18, 1979

Memorandum on Bargaining-From-Scratch Statements, 1979

Memo to all consultants regarding bargaining from scratch and techniques to prevent employers from violating the Labor Management Relations Act (LMRA), with relevant documentation. April 10, 1979

Memorandum on Preventing Needless Strikes, 1978

A memo sent to all consultants about how to prevent strikes, September 15, 197