We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey-Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of non-monotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994), (Gärdenfors, 1993). ‘Expectation’ ...

Many economic environments are modeled as games under incomplete information. A fundamental concept in these models is the hypothesis of a Bayesian Nash equilibrium. However, in spite of the common use of this hypothesis in economic theory and econometric estimation models, no statistical methods have been suggested how to use real life data to test its validity. There are many doubts whether e...

The correlation and interactions among different biological entities comprise the biological system. Although already revealed interactions contribute to the understanding of different existing systems, researchers face many questions everyday regarding inter-relationships among entities. Their queries have potential role in exploring new relations which may open up a new area of investigation....

We extend the mathematical theory of quantum hypothesis testing to the general W ∗-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.

Referential utterances are by their nature ambiguous to novice language learners. Each utterance consists of multiple layers of information that must be decoded: 1) the linguistic structure (how the sounds and words should be packaged into meaningful units), 2) the world structure (how people, objects and actions in the world relate to one another and which is the current focus of attention) an...

It is argued that a Gibbsian formula for the space-time distribution of microscopic trajectories of a nonequilibrium system provides a unifying framework for recent results on the fluctuations of the entropy production. The variable entropy production is naturally expressed as the time-reversal symmetry breaking part of the space-time action functional. Its mean is always positive. This is both...

The paper presents a new defense against adversarial attacks for deep neural networks. We demonstrate the effectiveness of our approach against the popular adversarial image generation method DeepFool. Our approach uses Wald’s Sequential Probability Ratio Test to sufficiently sample a carefully chosen neighborhood around an input image to determine the correct label of the image. On a benchmark...

This paper introduces a novel approach for region segmentation. In order to represent the regions, we devise and test new features based on low and high frequency wavelet coefficients which allow to capture and judge regions using changes in brightness and texture. A fusion process through statistical hypothesis testing among regions is established in order to obtain the final segmentation. The...

This survey is devoted to one of the central problems of Information Theory — the problem of determination of interdependence between coding rate and error probability exponent for different information transmission systems. The overview deals with memoryless systems of finite alphabet setting. It presents material complementary to the contents of the series of the most remarkable in Informatio...

Discussion on the converse theorem in statistical hypothesis testing. Hypothesis testing for two Markov chains is considered. Under the constraint that the first-kind error probability is less than or equal to exp( T R ), the second-kind error probability is minimized. The geodesic that connects the two Markov chains is defined. By analyzing the geodesic, the power exponents are calculated and ...