(i) The procedure introduced here for the clustering of frequency vectors takes into account the uncertainty arising from dealing with small observed frequencies. The smaller observed absolute frequencies, the more uncertainty about the “true” probability vector. The object is not represented by a single point in the multidimensional space but rather by the fuzzy set spread around this point. Consequently, the distance between two such objects is a fuzzy value, too. The expected mean distance between two objects generally differs from the simple distance: for instance, two objects with the same frequency vectors have a positive mean distance. The exact formula for estimation of the mean distance is given; this makes the algorithmization of the proposed procedure possible. The approach corresponds to that of the Bayesian estimation. The matrix of expected mean distances is an input to the hierarchical cluster analysis. (ii) The conventional hierarchical cluster analysis investigates similarities between objects from a given class. A modified general procedure is proposed seeking analogies between two classes of objects. The “two-class cluster analysis” is applicable to any kind of objects to be clustcred; it is not confined to the herein discussed special case of frequency vectors. (iii) The development of the procedure was developed initially for the field of the psychotherapy research - investigation of relationship patterns found within verbatirn protocols of sessions using the “guided imagery”, a psychotherapy technique dealing with evoked daydrearns. This constitutes an application example.
Probabilistic mixtures provide flexible "universal'' approximation of probability density functions. Their wide use is enabled by the availability of a range of efficient estimation algorithms. Among them, quasi-Bayesian estimation plays a prominent role as it runs "naturally'' in one-pass mode. This is important in on-line applications and/or extensive databases. It even copes with dynamic nature of components forming the mixture. However, the quasi-Bayesian estimation relies on mixing via constant component weights. Thus, mixtures with dynamic components and dynamic transitions between them are not supported. The present paper fills this gap. For the sake of simplicity and to give a better insight into the task, the paper considers mixtures with known components. A general case with unknown components will be presented soon.
This text describes a method of estimating the hazard rate of survival data following monotone Aalen regression model. The proposed approach is based on techniques which were introduced by Arjas and Gasbarra \cite{gasbarra}. The unknown functional parameters are assumed to be a priori piecewise constant on intervals of varying count and size. The estimates are obtained with the aid of the Gibbs sampler and its variants. The performance of the method is explored by simulations. The results indicate that the method is applicable on small sample size datasets.
The paper presents the stopping rule for random search for Bayesian model-structure estimation by maximising the likelihood function. The inspected maximisation uses random restarts to cope with local maxima in discrete space. The stopping rule, suitable for any maximisation of this type, exploits the probability of finding global maximum implied by the number of local maxima already found. It stops the search when this probability crosses a given threshold. The inspected case represents an important example of the search in a huge space of hypotheses so common in artificial intelligence, machine learning and computer science.