We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childjparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is intractable, we show how to compute upper and lower bounds on many probabilities of interest. In particular, using methods from large deviation theory, we derive rigor...

Properties of a specification test for the parametric form of the variance function in diffusion processes dXt = b (t,Xt) dt + σ (t,Xt) dWt are discussed. The test is based on the estimation of certain integrals of the volatility function. If the volatility function does not depend on the variable x it is known that the corresponding statistics have an asymptotic normal distribution. However, m...

In this report, we discuss how to compute exactly and efficiently the optical transfer function (OTF) of various computational cameras, under the assumptions of far-field wave optics and ideal thin lens. Approximations of the magnitudes of the OTFs have been previously given in [8], with derivations for cubic phase plates given in [12]. For ease and simplicity of derivation, let us stipulate th...