Exploiting Causal Independence in Bayesian Network Inference

A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional probabilities. We present a notion of causal independence that enables one to further factorize the conditional probabilities into a combination of even smaller factors and consequently obtain a finer-grain factorization of the joint probability. The new formulation of causal independence lets us specify the conditional probability of a variable given its parents in terms of an associative and commutative operator, such as ``or'', ``sum'' or ``max'', on the contribution of each parent. We start with a simple algorithm VE for Bayesian network inference that, given evidence and a query variable, uses the factorization to find the posterior distribution of the query. We show how this algorithm can be extended to exploit causal independence. Empirical studies, based on the CPCS networks for medical diagnosis, show that this method is more efficient than previous methods and allows for inference in larger networks than previous algorithms.Comment: See http://www.jair.org/ for any accompanying file

Homogeneous and heterogeneous chemistry along air parcel trajectories

The study of coupled heterogeneous and homogeneous chemistry due to polar stratospheric clouds (PSC's) using Lagrangian parcel trajectories for interpretation of the Airborne Arctic Stratosphere Experiment (AASE) is discussed. This approach represents an attempt to quantitatively model the physical and chemical perturbation to stratospheric composition due to formation of PSC's using the fullest possible representation of the relevant processes. Further, the meteorological fields from the United Kingdom Meteorological office global model were used to deduce potential vorticity and inferred regions of PSC's as an input to flight planning during AASE

Wave spectra of a shoaling wave field: A comparison of experimental and simulated results

Wave profile measurements made from an aircraft crossing the North Carolina continental shelf after passage of Tropical Storm Amy in 1975 are used to compute a series of wave energy spectra for comparison with simulated spectra. Results indicate that the observed wave field experiences refraction and shoaling effects causing statistically significant changes in the spectral density levels. A modeling technique is used to simulate the spectral density levels. Total energy levels of the simulated spectra are within 20 percent of those of the observed wave field. The results represent a successful attempt to theoretically simulate, at oceanic scales, the decay of a wave field which contains significant wave energies from deepwater through shoaling conditions

Minimal-resource computer program for automatic generation of ocean wave ray or crest diagrams in shoaling waters

A computer program for studying linear ocean wave refraction is described. The program features random-access modular bathymetry data storage. Three bottom topography approximation techniques are available in the program which provide varying degrees of bathymetry data smoothing. Refraction diagrams are generated automatically and can be displayed graphically in three forms: Ray patterns with specified uniform deepwater ray density, ray patterns with controlled nearshore ray density, or crest patterns constructed by using a cubic polynomial to approximate crest segments between adjacent rays

Exploiting Contextual Independence In Probabilistic Inference

Bayesian belief networks have grown to prominence because they provide compact representations for many problems for which probabilistic inference is appropriate, and there are algorithms to exploit this compactness. The next step is to allow compact representations of the conditional probabilities of a variable given its parents. In this paper we present such a representation that exploits contextual independence in terms of parent contexts; which variables act as parents may depend on the value of other variables. The internal representation is in terms of contextual factors (confactors) that is simply a pair of a context and a table. The algorithm, contextual variable elimination, is based on the standard variable elimination algorithm that eliminates the non-query variables in turn, but when eliminating a variable, the tables that need to be multiplied can depend on the context. This algorithm reduces to standard variable elimination when there is no contextual independence structure to exploit. We show how this can be much more efficient than variable elimination when there is structure to exploit. We explain why this new method can exploit more structure than previous methods for structured belief network inference and an analogous algorithm that uses trees

Reducing Polarization Mode Dispersion With Controlled Polarization Rotations

One of the fundamental limitations to high bit rate, long distance, telecommunication in optical fibers is Polarization Mode Dispersion (PMD). Here we introduce a conceptually new method to reduce PMD in optical fibers by carrying out controlled rotations of polarization at predetermined locations along the fiber. The distance between these controlled polarization rotations must be less than both the beat length and the mode coupling length of the fiber. This method can also be combined with the method in which the fiber is spun while it drawn. The incidence of imperfections on the efficiency of the method is analysed.Comment: 4 page

Ince's limits for confluent and double-confluent Heun equations

We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable $z$, while the other is given by a series of modified Bessel functions and converges for $|z|>|z_{0}|$, where $z_{0}$ denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when $z_{0}$ tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schr\"odinger equation for inverse fourth and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.Comment: Submitted to Journal of Mathmatical Physic