We consider the problem of using simulation to efficiently estimate the win probabilities for participants in a general random knockout tournament. Both of our proposed estimators, one based on the notion of “observed survivals” and the other based on conditional expectation and post-stratification, are highly effective in terms of variance reduction when compared to the raw simulation estimato...

Positron emission tomography (PET) image reconstruction is challenging for low count frame. The reconstruction is important method to retrieve information that has been lost in the images. To improve image quality, prior information are used. Based on kernel method, PET image intensity in each pixel is obtained from prior information and the coefficients can be estimated by the maximum likeliho...

Simulation is widely used to estimate losses due to default and other credit events in financial portfolios. The accurate measurement of credit risk can be modeled as a rare event simulation problem. While Monte Carlo simulation is time-consuming for rare events, importance sampling techniques can effectively reduce the simulation time, thus improving simulation efficiency. This chapter propose...

We consider the problem of improving the Gaussian approximate posterior marginals computed by expectation propagation and the Laplace method in latent Gaussian models and propose methods that are similar in spirit to the Laplace approximation of Tierney and Kadane (1986). We show that in the case of sparse Gaussian models, the computational complexity of expectation propagation can be made comp...

An old math puzzle goes: Suppose there are six people in a room; some of them shake hands. Prove that there are at least three people who all shook each others’ hands or three people such that no pair of them shook hands. Generalized a bit, this is the classic Ramsey problem. The diagonal Ramsey numbers R(k) are de ned as follows. R(k) is the smallest integer n such that in every two-coloring o...