An iterative method of restoring degraded images was developed by treating images, point spread functions, and degraded images as probability-frequency functions and by applying Bayes’s theorem. The method functions effectively in the presence of noise and is adaptable to computer operation.

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Recent Developments in Information and Decision Processes

Bayesian-Based Iterative Method of Image Restoration

The Bayesian approach to probability theory is presented as an alternative to the currently used long-run relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions to well-posed statistical problems, and is historically the original approach to statistics. The reasons for earlier rejection of Bayesian methods are discussed, and it is noted that the work of Cox, Jaynes, and others answers earlier objections, giving Bayesian inference a firm logical and mathematical foundation as the correct mathematical language for quantifying uncertainty. The Bayesian approaches to parameter estimation and model comparison are outlined and illustrated by application to a simple problem based on the gaussian distribution. As further illustrations of the Bayesian paradigm, Bayesian solutions to two interesting astrophysical problems are outlined: the measurement of weak signals in a strong background, and the analysis of the neutrinos detected from supernova SN 1987A. A brief bibliography of astrophysically interesting applications of Bayesian inference is provided.

From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics

Data mining techniques are provided which are effective and efficient for discovering useful information from an amorphous collection or data set of records. For example, the present invention provides for the mining of data, e.g., of several or many records, to discover interesting associations between entries of qualitative text, and covariances between data of quantitative numerical types, in records. Although not limited thereto, the invention has particular application and advantage when the data is of a type such as clinical, pharmacogenomic, forensic, police and financial records, which are characterized by many varied entries, since the problem is then said to be one of “high dimensionality” which has posed mathematical and technical difficulties for researchers. This is especially true when considering strong negative associations and negative covariance, i.e., between items of data which may so rarely come together that their concurrence is never seen in any record, yet the fact that this is not expected is of potential great interest.

Method and apparatus for data mining to discover associations and covariances associated with data

The claim that information theory provides a foundation for statistical thermodynamics which is independent of the use of ensembles can be sustained only if probabilities can be determined numerically without treating them as frequencies. The use of Shannon's measure of information to assign probabilities is correct only in the same conditions as justify Gibbs's use of ensembles.

Probability, Information and Entropy

I will discuss the usefulness of approaching an understanding of evolution through a conceptual analysis of the random and nonrandom processes which occur at the molecular level of proteins and nucleic acids, rather than volunteer an exposition of mathematical methodology available elsewhere in the literature. A qualitatively incorrect concept, however mathematically transformed and quantified, remains biologically uninformative. A correct concept, even though imperfectly quantified, is at least useful; the quantitation can be improved as additional data and insight permit. With cautious optimism, Vogel et al. (this volume) state: “the prospects may not be so poor, provided that we do not expect to develop a final and altogether perfect concept. Our model should be refined step by step. After the first few steps, the picture admittedly may still be oversimplified, but at least the most obvious flaws of the old one are corrected.” On the other hand, the known facts are not likely to be accounted for by an arbitrary choice of model. The evolutionary model presented here embodies both selective (i. e., deterministic) and probabilistic evolutionary mechanisms; it reasonably accounts, both qualitatively and quantitatively, for both the observed random and nonrandom and the Darwinian and selectively neutral patterns of protein and nucleic acid variation. The values for evolutionary divergence between species which were calculated from this model when it was first published in 1972 (Holmquist et al., 1972; Jukes and Holmquist, 1972a) were at that time 2–4 times higher than the values then considered correct.

Recent Developments in Information and Decision Processes

Citations

Bayesian-Based Iterative Method of Image Restoration

From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics

Method and apparatus for data mining to discover associations and covariances associated with data

Probability, Information and Entropy

Random and Nonrandom Processes in the Molecular Evolution of Higher Organisms

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