Martin Adamčík

Independent Researcher

Meta–analysis is a powerful tool for combining related studies but such an aggregation would be flawed if studies investigated different populations or applied different methods in this investigation. While studies with differences that are statistically detected but not explained can be analysed by techniques of random–effects meta–analysis, it is...

The aim of this paper is to explore the applicability of the ‘number of possible states’ argument in inferential problems in multi–expert reasoning. The argument is Bayesian and it is similar in spirit to the one used to derive the maximum entropy inference process. Under certain conditions a particular way of applying it surprisingly suggests that...

The aim of this paper is to develop a comprehensive study of the geometry involved in combining Bregman divergences with pooling operators over closed convex sets in a discrete probabilistic space. A particular connection we develop leads to an iterative procedure, which is similar to the alternating projection procedure by Csiszár and Tusnády. Alt...

In this paper we present a result that relates merging of closed convex sets of discrete probability functions respectively by the squared Euclidean distance and the Kullback-Leibler divergence, using an inspiration from the Rényi entropy. While selecting the probability function with the highest Shannon entropy appears to be a convincingly justifi...

Corrections on Adamčík, M. The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning, Entropy 2014, 16; pp. 6338-6381

The present work presents a general theoretical framework for the study of operators which merge partial probabilistic knowledge from different sources which are individually consistent, but may be collectively inconsistent. We consider a number of principles for such an operator to satisfy including a set of principles derived from those of Koniec...

Within the framework of discrete probabilistic uncertain reasoning a large literature exists justifying the maximum entropy inference process, ME, as being optimal in the context of a single agent whose subjective probabilistic knowledge base is consistent. In [9] Paris and Vencovská, extending the work of Johnson and Shore [6], completely characte...

Iterating the triple construction applied consecutively to n Boolean algebras, we introduce two finitely axiomatizable subclasses \({{\bf SA}^{\rm i}_n}\) and \({{\bf SA}^{\rm s}_n}\) of the class SA n of all Stone algebras of degree n with all the structure homomorphisms in their P-product representation injective or surjective, respectively. Then...