On simulated EM algorithms

The EM algorithm is a popular and useful algorithm for finding the maximum likelihood estimator in incomplete data problems. Each iteration of the algorithm consists of two simple steps: An E-step, in which a conditional expectation is calculated, and an M-step, where the expectation is maximized. In some problems, however, the EM algorithm cannot be applied since the conditional expectation required in the E-step cannot be calculated. Instead one may try to estimate the expectation by simulation. We call this a simulated EM algorithm. The simulations can --at least in principle-- be done in two ways. Either new independent random variables are drawn in each iteration, or the same uniforms are reused in each iteration. In this paper the properties of these two versions of the simulated EM algorithm are discussed and compared. Keywords: Simulation, EM algorithm 2 S.F. Nielsen 1 Simulated EM algorithms The EM algorithm (cf Dempster, Laird, and Rubin (1978)) has two steps, an E-step an..

Virtual Prototyping - An Open System Environment to Support the Integrated Product Development Process

The ability to rapidly prototype a proposed design is becoming a key contributor towards fulfilling the business requirements embodied in a short time-to-market, in cost-effective and high quality manufacturing, and in easy support and maintenance. Reorganizing the design and development process along the lines implied by the concept, Concurrent Engineering, means that advanced information technologies must be taken advantage of. However, most of today's generic, commercial, off-the-shelf technlogies have to be extended and adapted to the needs of the product development process. The integration of existing technologies in CAD modelling, design, analysis, simulation, networked cooperation, and virtual reality leads to a distributed desktop-environment which provides the basis to take the greatest advantage of the Virtual Prototyping technique