David R. Wolf

Base compositional structure of genomes.

We model the base compositional structure of the human and Escherichia coli genomes. Three particular properties are first quantified: (1) There is a significant tendency for any region of either genome to have a strand-symmetric base composition. (2) The variation in base composition from region to region, within each genome, is very much larger than expected from common homogeneous stochastic models. (3) A given local base composition tends to persist over a scale of at least kilobases (E. coli) or tens of kilobases (human). Multidomain stochastic models from the literature are reviewed and sharpened. In particular, quantitative measurements of the third property lead us to suggest a significant shift in the style of domain models, in which the variation of A+T content with position is modeled by a random walk with frequent small steps rather than with large quantum jumps. As an application, we suggest a way to reduce the amount of computation in the assembly of large sequences from sequences of randomly chosen fragments.

Tomographic reconstruction based on flexible geometric models

When dealing with ill-posed inverse problems in data analysis, the Bayesian approach allows one to use prior information to guide the result toward reasonable solutions. In this work the model consists of an object whose amplitude is constant inside a flexible boundary. The flexibility of the boundary is controlled by through a distortion energy. We present an example of reconstruction of the cross section of a blood vessel from just two projections.<<ETX>>

Object-oriented implementation of a graphical-programming system

Object-oriented (OO) analysis, design, and programming is a powerful paradigm for creating software that is easily understood, modified, and maintained. In this paper we demonstrate how the OO concepts of abstraction, inheritance, encapsulation, polymorphism, and dynamic binding have aided in the design of a graphical-programming tool. The tool that we have developed allows a user to build radiographic system models for computing simulated radiographic data. It will eventually be used to perform Bayesion reconstructions of objects given radiographic data. The models are built by connecting icons that represent physical transformations, such as line integrals, exponentiation, and convolution, on a canvas. We will also briefly discuss ParcPlaces application development environment, VisualWorks, which we have found to be as helpful as the OO paradigm.

Alpha, Evidence, and the Entropic Prior

First, the correct entropic prior is computed by marginalization of alpha. This is followed by a discussion of improvements to the “evidence” approximation. Surprisingly, it appears that the approximations used to restore the famous “Susie” image may have questionable aspects.

An object-oriented optimization system

We have described the implementation of a graphical programming tool in the object-oriented language, Smalltalk-80, that allows a user to construct a radiographic measurement model. The measurement model can be used to generate the measurements predicted by a given parameterized model of an experimental object. In this paper, we describe extensions to the graphical programming tool that allow it to be used to perform Bayesian inference on very large sets of object parameters, given real experimental data, by optimizing the likelihood or posterior probability of the parameters, given the real data.<<ETX>>

AN INTERACTIVE TOOL FOR BAYESIAN INFERENCE

The Bayes Inference Engine (BIE) is a flexible software tool that allows one to interactively define models of radiographic measurement systems and geometric models of experimental objects so that the geometric properties of the objects being radiographed can be inferred from a limited amount of data. The BIE also allows a user to investigate confidence intervals on the estimated object geometry and compare the likelihoods of competing hypotheses.

A Bayesian Reflection on Surfaces

The topic of this paper is a novel continuous-basis field representation and inference framework applied to the inference of continuous surfaces from measurements (for example camera image data). Traditional approaches to surface representation and inference are briefly reviewed. The new field representation and inference paradigm is then introduced within a maximally informative (MI) (see [1]) inference framework. The knowledge representation is introduced and discussed in the context of MI inference. Then, using the MI inference approach, the here-named Generalized Kaiman Filter (GKF) equations are derived. The GKF equations allow the update of field knowledge from previous knowledge at any scale, and new data, to new knowledge at any other scale. The GKF equations motivate a location-dependent scale or multigrid approach to the MI inference of continuous-basis fields.

Estimators for the Cauchy Distribution

We discuss the properties of various estimators of the central position of the Cauchy distribution. The performance of these estimators is evaluated for a set of simulated experiments. Estimators based on the maximum and mean of the posterior probability density function are empirically found to be well behaved when more than two measurements are available. On the contrary, because of the infinite variance of the Cauchy distribution, the average of the measured positions is an extremely poor estimator of the central position. However, the median of the measured positions is well behaved. The rms errors for the various estimators are compared to the Fisher-Cramer-Rao lower bound. We find that the square root of the variance of the posterior density function is predictive of the rms error in the mean posterior estimator.

Posterior Moments of the Cauchy Distribution

The posterior moments of parameters specifying distributions are minimum mean square Bayesian estimators for the corresponding moments of those parameters, and as such are ubiquitous in the Bayesian approach to statistical inference of distributions. The Cauchy distribution is most notable for its wide tails, decided absence of high-order moments, and non-existence of less-than-data dimension sufficient statistics. Thus it vastly differs qualitatively from the Gaussian distribution, where tails are small, moments of all orders exist, and dimension-two sufficient statistics always exist. In this paper the posterior moments of the position parameter of the Cauchy distribution are found in closed form. (Estimating the other parameter, the width or distance parameter of the Cauchy is done using the same mathematics.) The interplay between the amount of data acquired for the estimation of the position parameter and the existence of higher order moments of the inferred posterior distribution for the postition parameter is made explicit.