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The aim of this research is to create a medical expert system based on Bayes theorem to diagnose level of disc hernia based on real foot force measurement signals obtained using sensors and implement the whole system on field programable gate array (FPGA). We have created a database of attributes based on recorded foot force values of 33 patients pre-diagnosed with herniated disc on levels L4/L5 or L5/S1 on the left or right side. The results obtained by software (Matlab) and hardware (FPGA simulation) are matching well, achieving high accuracy, which shows that VHDL implementation of Naïve Bayes theorem for disc hernia diagnostics is adequate. The output on FPGA is easy to understand for any user, as it is implemented as four-bit output where the position of bit value 1 indicates the level of disc herniation. The system is able to distinguish between the healthy subjects and subjects with disc herniation and is able to detect if improvement in stability is present after surgery or physical therapy. Our proposed measurement platform can be coupled with FPGA to create a portable and not expensive tool for real time signal acquisition, processing and decision support system in disc hernia diagnosis and post-surgical recovery.

A structural model for the estimation of software failure rates is proposed which is based on a partition of the code into components. Systematic failure is assumed to be induced by the interaction of these components. A Bayesian inference scheme is used to perform failure rate estimation on the basis of N failure free test runs. The approach splits the problem of constructing a system prior up into the smaller, conceivably simpler problems of constructing subtask priors. Thereby a wider range of prior information is used in the process of assessing system safety. The work in this paper constitutes a first step towards a formal statistical understanding of the relationship between system complexity and system testing for reliability. Long-term implications are the achievement of more informative reliability estimates and guidelines on cost-effective testing.

Classification is an important task in data mining because it helps to address a variety of problems. Statistical techniques can provide the means to solve these problems in a simple way. Specifically, the Bayesian approach provides a natural and flexible way to approach classification problems and other probability-related questions. The Bayes Theorem is the basis of this methodology, and it can also be used as a building block and starting point for more complex methodologies such as the popular Bayesian networks.

In a previous paper (Uncertainty and the Role of the Observer, co-authored with G. Minati and A. Trotta, Proceedings of the 2004 Conference of the Italian Systems Society in publication by Springer), we focused on the deep epistemological contribution of the Italian mathematician Bruno de Finetti (1906 - 1985), from a systemic point of view. He considered the probability of an event nothing but the degree of believe of the observer in its occurrence, relating this degree of believe to the information available, in that moment, to the observer. He pointed out how, when considering probability, we need to focus on the role of the observer expressing the degree of believe and how S/He can construct a system of coherent probabilities. The purpose of this paper is to show how this subjective conception of probability is based on assuming a systemic framework, even in cases of conditional events. Regarding this, we underline how the fundamental conceptual and methodological tool is the well-known Bayes Theorem. With reference to this theorem, we will be introducing examples to show how its usage is not only crucial in generating probabilities suitable for the emergence of a system of coherent evaluations, but even able to explain some paradoxical aspects.