Exact bounds on failure probability in the “strength-load” model with incomplete information

The infimum and supremum of failure probability (i. e., the probability that the load exceeds the strength) are obtained under the following assumptions: (a) one of the variables is Erlang distributed and the other has known mean and variance; (b) the distribution functions of both random variables are unknown and only the means and the upper bound of one of the distributions are known.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 56–63, September–October, 1992.     

A note on the choice of a weighting function to give an efficient method for estimating the probability of misclassification

The problem of estimating the performance of a given classifier on a given data set is considered. In an attempt to provide a nonparametric estimator which not only uses the data efficiently but is also essentially an unbiased estimator of the probability of misclassification, Toussaint evaluated empirically an estimator formed by weighting the resubstitution and rotation estimators. In this study theoretical consideration is given to the choice of a suitable weighting function for this estimator.     

An interpretation of probability in the law of evidence based on pro-et-contra argumentation

The purpose of this paper is to improve on the logical and measure-theoretic foundations for the notion of probability in the law of evidence, which were given in my contributions Åqvist [ (1990) Logical analysis of epistemic modality: an explication of the Bolding–Ekelöf degrees of evidential strength. In: Klami HT (ed) Rätt och Sanning (Law and Truth. A symposium on legal proof-theory in Uppsala May 1989). Iustus Förlag, Uppsala, pp 43–54; (1992) Towards a logical theory of legal evidence: semantic analysis of the Bolding–Ekelöf degrees of evidential strength. In: Martino AA (ed) Expert systems in law. Elsevier Science Publishers BV, Amsterdam, North-Holland, pp 67–86]. The present approach agrees with the one adopted in those contributions in taking its main task to be that of providing a semantic analysis, or explication, of the so called Bolding–Ekelöf degrees of evidential strength (“proof-strength”) as applied to the establishment of matters of fact in law-courts. However, it differs from the one advocated in our earlier work on the subject in explicitly appealing to what is known as “Pro-et-Contra Argumentation”, after the famous Norwegian philosopher Arne Naess. It tries to bring out the logical form of that interesting kind of reasoning, at least in the context of the law of evidence. The formal techniques used here will be seen to be largely inspired by the important work done by Patrick Suppes, notably Suppes [(1957) Introduction to logic. van Nostrand, Princeton and (1972) Finite equal-interval measurement structures. Theoria 38:45–63].     

Search for the upper bound of Bayesian estimates of the parameter in an exponential failure model with two known quantiles of an a priori distribution function

A fast exact algorithm of searching for the upper bound of Bayesian estimates for the parameter of the exponential distribution under the condition that an a priori distribution belongs to the class of all distribution functions with two equal quantiles. This problem arises in analyzing the sensitivity of Bayesian estimates to the choice of an a priori distribution in an exponential failure model. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 90–102, January–February 2007.