Libre Courseware For Bayesian Decision Making

This paper describes the ideas and problems of the Edukalibre e-learning project, in which the author takes part. The basic objective of the project shares the development and exploitation of software components for web-based information systems applied to education as well as organizing of teaching material for them. The paper concerns a problem of the mathematical-oriented courseware and describes the experience in developing LaTeX-supporting online converting tool.

Detection and Tracking of Traffic Signs Using a Recursive Bayesian Decision Framework

In this paper we propose a new method for the automatic detection and tracking of road traffic signs using an on-board single camera. This method aims to increase the reliability of the detections such that it can boost the performance of any traffic sign recognition scheme. The proposed approach exploits a combination of different features, such as color, appearance, and tracking information. This information is introduced into a recursive Bayesian decision framework, in which prior probabilities are dynamically adapted to tracking results. This decision scheme obtains a number of candidate regions in the image, according to their HS (Hue-Saturation). Finally, a Kalman filter with an adaptive noise tuning provides the required time and spatial coherence to the estimates. Results have shown that the proposed method achieves high detection rates in challenging scenarios, including illumination changes, rapid motion and significant perspective distortion

Application of Decision Theory methods for a Community of Madrid Soil classification case

A land classification method was designed for the Community of Madrid (CM), which has lands suitable for either agriculture use or natural spaces. The process started from an extensive previous CM study that contains sets of land attributes with data for 122 types and a minimum-requirements method providing a land quality classification (SQ) for each land. Borrowing some tools from Operations Research (OR) and from Decision Science, that SQ has been complemented by an additive valuation method that involves a more restricted set of 13 representative attributes analysed using Attribute Valuation Functions to obtain a quality index, QI, and by an original composite method that uses a fuzzy set procedure to obtain a combined quality index, CQI, that contains relevant information from both the SQ and the QI methods.

Notes on decision theory.

"These notes were prepared at Cornell University from lectures given in Mathematics 742 in 1953 ... and were recorded by J. Sacks. The notes are intended only for the convenience of the student and are not intended to be considered as a text on the subject matter. These notes were mimeographed under a contract with the Office of Naval Research."

Bayesian invariant measurements of generalisation

The problem of evaluating different learning rules and other statistical estimators is analysed. A new general theory of statistical inference is developed by combining Bayesian decision theory with information geometry. It is coherent and invariant. For each sample a unique ideal estimate exists and is given by an average over the posterior. An optimal estimate within a model is given by a projection of the ideal estimate. The ideal estimate is a sufficient statistic of the posterior, so practical learning rules are functions of the ideal estimator. If the sole purpose of learning is to extract information from the data, the learning rule must also approximate the ideal estimator. This framework is applicable to both Bayesian and non-Bayesian methods, with arbitrary statistical models, and to supervised, unsupervised and reinforcement learning schemes.

Dynamic decision networks for decision-making in self-adaptive systems:a case study

Bayesian decision theory is increasingly applied to support decision-making processes under environmental variability and uncertainty. Researchers from application areas like psychology and biomedicine have applied these techniques successfully. However, in the area of software engineering and speci?cally in the area of self-adaptive systems (SASs), little progress has been made in the application of Bayesian decision theory. We believe that techniques based on Bayesian Networks (BNs) are useful for systems that dynamically adapt themselves at runtime to a changing environment, which is usually uncertain. In this paper, we discuss the case for the use of BNs, speci?cally Dynamic Decision Networks (DDNs), to support the decision-making of self-adaptive systems. We present how such a probabilistic model can be used to support the decision making in SASs and justify its applicability. We have applied our DDN-based approach to the case of an adaptive remote data mirroring system. We discuss results, implications and potential bene?ts of the DDN to enhance the development and operation of self-adaptive systems, by providing mechanisms to cope with uncertainty and automatically make the best decision.

Developing Collective Teaching Computer Software for the Course “Decision Theory”

Improvement of training students using modern information technologies, like collective developing teaching computer software, is discussed. Organizational, technical, technological advices are given. Experience of using information technologies in educational course “Decision Theory” is described.

Evaluation of the evidential value of the elemental composition of glass, ink and paper by laser-based microspectrochemical methods

Elemental analysis can become an important piece of evidence to assist the solution of a case. The work presented in this dissertation aims to evaluate the evidential value of the elemental composition of three particular matrices: ink, paper and glass. In the first part of this study, the analytical performance of LIBS and LA-ICP-MS methods was evaluated for paper, writing inks and printing inks. A total of 350 ink specimens were examined including black and blue gel inks, ballpoint inks, inkjets and toners originating from several manufacturing sources and/or batches. The paper collection set consisted of over 200 paper specimens originating from 20 different paper sources produced by 10 different plants. Micro-homogeneity studies show smaller variation of elemental compositions within a single source (i.e., sheet, pen or cartridge) than the observed variation between different sources (i.e., brands, types, batches). Significant and detectable differences in the elemental profile of the inks and paper were observed between samples originating from different sources (discrimination of 87–100% of samples, depending on the sample set under investigation and the method applied). These results support the use of elemental analysis, using LA-ICP-MS and LIBS, for the examination of documents and provide additional discrimination to the currently used techniques in document examination. In the second part of this study, a direct comparison between four analytical methods (µ-XRF, solution-ICP-MS, LA-ICP-MS and LIBS) was conducted for glass analyses using interlaboratory studies. The data provided by 21 participants were used to assess the performance of the analytical methods in associating glass samples from the same source and differentiating different sources, as well as the use of different match criteria (confidence interval (±6s, ±5s, ±4s, ±3s, ±2s), modified confidence interval, t-test (sequential univariate, p=0.05 and p=0.01), t-test with Bonferroni correction (for multivariate comparisons), range overlap, and Hotelling's T2 tests. Error rates (Type 1 and Type 2) are reported for the use of each of these match criteria and depend on the heterogeneity of the glass sources, the repeatability between analytical measurements, and the number of elements that were measured. The study provided recommendations for analytical performance-based parameters for µ-XRF and LA-ICP-MS as well as the best performing match criteria for both analytical techniques, which can be applied now by forensic glass examiners.

Investigation of the chemical origin and evidential value of differences in the SERS spectra of blue gel inks

Highly swellable polymer films doped with Ag nanoparticle aggregates (poly-SERS films) have been used to record very high signal:noise ratio, reproducible surface-enhanced (resonance) Raman (SER(R)S) spectra of in situ dried ink lines and their constituent dyes using both 633 and 785 nm excitation. These allowed the chemical origins of differences in the SERRS spectra of different inks to be determined. Initial investigation of pure samples of the 10 most common blue dyes showed that the dyes which had very similar chemical structures such as Patent Blue V and Patent Blue VF (which differ only by a single OH group) gave SERRS spectra in which the only indications that the dye structure had been changed were small differences in peak positions or relative intensities of the bands. SERRS studies of 13 gel pen inks were consistent with this observation. In some cases inks from different types of pens could be distinguished even though they were dominated by a single dye such as Victoria Blue B (Zebra Surari) or Victoria Blue BO (Pilot Acroball) because their predominant dye did not appear in other inks. Conversely, identical spectra were also recorded from different types of pens (Pilot G7, Zebra Z-grip) because they all had the same dominant Brilliant Blue G dye. Finally, some of the inks contained mixtures of dyes which could be separated by TLC and removed from the plate before being analysed with the same poly-SERS films. For example, the Pentel EnerGel ink pen was found to give TLC spots corresponding to Erioglaucine and Brilliant Blue G. Overall, this study has shown that the spectral differences between different inks which are based on chemically similar, but nonetheless distinct dyes, are extremely small, so very close matches between SERRS spectra are required for confident identification. Poly-SERS substrates can routinely provide the very stringent reproducibility and sensitivity levels required. This, coupled with the awareness of the reasons underlying the observed differences between similarly coloured inks allows a more confident assessment of the evidential value of inks SERS and should underpin adoption of this approach as a routine method for the forensic examination of inks.

Evaluation of the Evidential Value of the Elemental Composition of Glass, Ink and Paper by Laser-Based Micro-Spectrochemical Methods

Elemental analysis can become an important piece of evidence to assist the solution of a case. The work presented in this dissertation aims to evaluate the evidential value of the elemental composition of three particular matrices: ink, paper and glass. In the first part of this study, the analytical performance of LIBS and LA-ICP-MS methods was evaluated for paper, writing inks and printing inks. A total of 350 ink specimens were examined including black and blue gel inks, ballpoint inks, inkjets and toners originating from several manufacturing sources and/or batches. The paper collection set consisted of over 200 paper specimens originating from 20 different paper sources produced by 10 different plants. Micro-homogeneity studies show smaller variation of elemental compositions within a single source (i.e., sheet, pen or cartridge) than the observed variation between different sources (i.e., brands, types, batches). Significant and detectable differences in the elemental profile of the inks and paper were observed between samples originating from different sources (discrimination of 87 – 100% of samples, depending on the sample set under investigation and the method applied). These results support the use of elemental analysis, using LA-ICP-MS and LIBS, for the examination of documents and provide additional discrimination to the currently used techniques in document examination. In the second part of this study, a direct comparison between four analytical methods (µ-XRF, solution-ICP-MS, LA-ICP-MS and LIBS) was conducted for glass analyses using interlaboratory studies. The data provided by 21 participants were used to assess the performance of the analytical methods in associating glass samples from the same source and differentiating different sources, as well as the use of different match criteria (confidence interval (±6s, ±5s, ±4s, ±3s, ±2s), modified confidence interval, t-test (sequential univariate, p=0.05 and p=0.01), t-test with Bonferroni correction (for multivariate comparisons), range overlap, and Hotelling’s T2 tests. Error rates (Type 1 and Type 2) are reported for the use of each of these match criteria and depend on the heterogeneity of the glass sources, the repeatability between analytical measurements, and the number of elements that were measured. The study provided recommendations for analytical performance-based parameters for µ-XRF and LA-ICP-MS as well as the best performing match criteria for both analytical techniques, which can be applied now by forensic glass examiners.

Apply response adaptive randomization to group sequential with early stopping

Group sequential methods and response adaptive randomization (RAR) procedures have been applied in clinical trials due to economical and ethical considerations. Group sequential methods are able to reduce the average sample size by inducing early stopping, but patients are equally allocated with half of chance to inferior arm. RAR procedures incline to allocate more patients to better arm; however it requires more sample size to obtain a certain power. This study intended to combine these two procedures. We applied the Bayesian decision theory approach to define our group sequential stopping rules and evaluated the operating characteristics under RAR setting. The results showed that Bayesian decision theory method was able to preserve the type I error rate as well as achieve a favorable power; further by comparing with the error spending function method, we concluded that Bayesian decision theory approach was more effective on reducing average sample size.^

Measurements of generalisation based on information geometry

Neural networks are statistical models and learning rules are estimators. In this paper a theory for measuring generalisation is developed by combining Bayesian decision theory with information geometry. The performance of an estimator is measured by the information divergence between the true distribution and the estimate, averaged over the Bayesian posterior. This unifies the majority of error measures currently in use. The optimal estimators also reveal some intricate interrelationships among information geometry, Banach spaces and sufficient statistics.