James C. West

Inference in hybrid Bayesian networks using mixtures of polynomials

The main goal of this paper is to describe inference in hybrid Bayesian networks (BNs) using mixture of polynomials (MOP) approximations of probability density functions (PDFs). Hybrid BNs contain a mix of discrete, continuous, and conditionally deterministic random variables. The conditionals for continuous variables are typically described by conditional PDFs. A major hurdle in making inference in hybrid BNs is marginalization of continuous variables, which involves integrating combinations of conditional PDFs. In this paper, we suggest the use of MOP approximations of PDFs, which are similar in spirit to using mixtures of truncated exponentials (MTEs) approximations. MOP functions can be easily integrated, and are closed under combination and marginalization. This enables us to propagate MOP potentials in the extended Shenoy-Shafer architecture for inference in hybrid BNs that can include deterministic variables. MOP approximations have several advantages over MTE approximations of PDFs. They are easier to find, even for multi-dimensional conditional PDFs, and are applicable for a larger class of deterministic functions in hybrid BNs.

The slightly-rough facet model in radar imaging of the ocean surface

Abstract The slightly-rough facet model of the ocean surface, an extension of the two-scale radar scattering model, is well suited for investigating synthetic aperture radar (SAR) imaging of the surface. We derive several statistical properties of the facets that are important in an imaging model. The two-scale scattering model is extended to include both first-order and second-order large-scale effects (tilt and curvature) using physical optics, showing that a spectrum of small-scale ripples, rather than a single ripple given by the Bragg resonance condition, contributes to the backscatter from a facet. The bandwidth of the resonant ripple spectrum depends on the radar wavelength, large-scale curvature and illumination widths. The properties of the facets are deduced from this dependence. The large-scale curvature of the surface determines the size of the facets. The expected facet size depends directly on the radar wavelength and is much smaller than the resolution of realistic radars. The resonant ripp...

Extended Shenoy--Shafer architecture for inference in hybrid bayesian networks with deterministic conditionals

The main goal of this paper is to describe an architecture for solving large general hybrid Bayesian networks (BNs) with deterministic conditionals for continuous variables using local computation. In the presence of deterministic conditionals for continuous variables, we have to deal with the non-existence of the joint density function for the continuous variables. We represent deterministic conditional distributions for continuous variables using Dirac delta functions. Using the properties of Dirac delta functions, we can deal with a large class of deterministic functions. The architecture we develop is an extension of the Shenoy-Shafer architecture for discrete BNs. We extend the definitions of potentials to include conditional probability density functions and deterministic conditionals for continuous variables. We keep track of the units of continuous potentials. Inference in hybrid BNs is then done in the same way as in discrete BNs but by using discrete and continuous potentials and the extended definitions of combination and marginalization. We describe several small examples to illustrate our architecture. In addition, we solve exactly an extended version of the crop problem that includes non-conditional linear Gaussian distributions and non-linear deterministic functions.

Inference in Hybrid Bayesian Networks with Deterministic Variables

The main goal of this paper is to describe an architecture for solving large general hybrid Bayesian networks (BNs) with deterministic variables. In the presence of deterministic variables, we have to deal with non-existence of joint densities. We represent deterministic conditional distributions using Dirac delta functions. Using the properties of Dirac delta functions, we can deal with a large class of deterministic functions. The architecture we develop is an extension of the Shenoy-Shafer architecture for discrete BNs. We illustrate the architecture with some small illustrative examples.

Synthetic-aperture-radar imaging of the ocean surface using the slightly-rough facet model and a full surface-wave spectrum

Abstract A new technique to model synthetic-aperture-radar (SAR) imaging of ocean waves is developed using the slightly-rough-facet model of the surface. The facets are mapped into the image plane individually and their responses are added coherently to give the composite image. A windowing technique allows the orbital motions of all electromagnetically large-scale waves to be included in the mapping function deterministically; no scene coherence time is used. Simulated images show that the image cut-off of azimuthally propagating waves is due to smearing by wind-generated intermediate waves. The focus adjustment that gives the greatest image contrast when imaging azimuthally propagating waves is half the phase velocity of the dominant long wave. However, spatially offsetting the multiple looks in the image domain to compensate the propagation of the long waves during the integration time of the SAR appears to be the optimal processing technique. The imaging process is highly non-linear under most realist...