Reliability Criteria in Information Theory and in Statistical Hypothesis Testing

A Neyman-Pearson Proper Way to Universal Testing of Multiple Hypotheses Formed by Groups of Distributions

“…Construction of LAO tests sequence is realized applying "Kullback-Leibler balls" around the hypothetic distributions in the space of distributions as sets for detection of corresponding hypotheses. This concept, introduced in [16]- [17] and applied in [20]- [31] and in the present paper, conforms to the idea of "r-divergent sequences" defined in [17] and used in other works.…”

“…As was noted in introduction, our study applies the method of types, developed in information theory [7,11,13,31]. The basic notion in this method is the notion of the type Q x of the vector x ∈ X N , which is equivalent to the statistical notion of the empirical distribution of the sample x:…”

“…Our study is based on information theoretic methods including the method of types. Applications of methods of information theory in mathematical statistics, in particular in hypotheses testing, are exposed in the monographs by Csiszár and Körner [11], Blahut [5], Cover and Thomas [7], Csiszár and Shields [13], Poor [37], Kullback [33] Haroutunian and all [31] , in paper of Blahut [4].…”

Discussion on Steganographic Methods from the Perspective of E-Voting Implementation

“…We have to send the data through a channel that might be prone to outside attacks, the data may be corrupted or the attacker may try to imitate the data and send fake votes to the counting server. A model that addresses the attacks by an active adversary is described in [5]. Using two stage hypothesis testing, we first decide if the data is valid and has a candidate index in it, and then we decide if it is an outside attacker trying to imitate valid votes.…”

“…The implementation of the statistical method algorithm, depending on the choice of hypothesis testing technique, has been studied in a number of works. Two-stage optimal hypothesis testing for extraction and authentication was studied in [5]. Statistical techniques were suggested using syndrome trellis codes with additive distortion function in steganography and matrix embedding with wet paper codes in [16], [17] respectively.…”