We explain how to apply statistical techniques to solve several language-recognition problems that arise in cryptanalysis and other domains. Language recognition is important in cryptanalysis because, among other applications, an exhaustive key search of any cryptosystem from ciphertext alone requires a test that recognizes valid plaintext. Written for cryptanalysts, this guide should also be helpful to others as an introduction to statistical inference on Markov chains. Modeling language as a finite stationary Markov process, we adapt a statistical model of pattern recognition to language recognition. Within this framework we consider four welldefined language-recognition problems: 1) recognizing a known language, 2) distinguishing a known language from uniform noise, 3) distinguishing unknown 0th-order noise from unknown 1st-order language, and 4) detecting non-uniform unknown language. For the second problem we give a most powerful test based on the Neyman-Pearson Lemma. For the oth...

errors or omissions remain my responsibility. 1 Space-time analysis of GDP disparities among European regions: A Markov chains approach The purpose of this paper is to study the evolution of the disparities between 138 European regions over the 1980-1995 period. We characterize the regional per capita GDP cross-sectional distribution by means of nonparametric estimations of density functions and we model the growth process as a first-order stationary Markov chain. Spatial effects are then introduced within the Markov chain framework using regional conditioning and spatial Markov chains. The results of the analysis indicate the persistence of regional disparities, a progressive bias toward a poverty trap and the importance of geography to explain growth and convergence processes.

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Between rrenarche and nenopause, \\OITeIl ' S reproductive histories consist of periods of pregnancy, pregnancy outcomes--births, fetal deaths, induced abortions, etc.--and inter-conoeptional non-pregnant intervals of varying length, depending upcn sexual activity, COI1traceptive practioe, and fectmdity. Eeproductive histories may thus be COIlpletely described within a finite set of states which includes all pregnant and non-pregnant periods as well as pregnancy outcares. To consider individual or group rrovenent fran state to state as a stochastic process, we observe that at any given t.ine a wanan will be found in one of the defined states, and her novemen.ts to other states are governed by a probabilistic law. When the probability of a transition fran state (i) to a state (j) at sooe ti.ne (n) depends en n, the process is said to be t.ine-dependent.

The general linear model approach for the analysis of categorical data is extended to the case of supplemental data. In the usual case, each individual i ~ classified according to each of the d dimensions of the corresponding contingency table. With supplementation, there is additional information on d ' < d dimensions for a random sample selected from the same homogeneous population. This situation might arise if there was special interest in only certain of the responses and/or possibly for reasons of economy and is distinctly different from the empty cell problem. Starting with the simplest case, maximum likelihood and iterated weighted least squares estimates are obtained for the basic parameters for 2 x 2 tables with one margin supplemented. The maximum likelihood estimates are unbiased and have the same asymptotic covariance matrix

The responsibility for the contents of the working papers rests with the author, not the Institute. Since working papers are of a preliminary nature, it may be useful to contact the author of a particular working paper about results or caveats before referring to, or quoting, a paper. Any comments on working papers should be sent directly to the author. Markov or Not Markov – This Should Be a Question Although it is well known that Markov process theory, frequently applied in the literature on income convergence, imposes some very restrictive assumptions upon the data generating process, these assumptions have generally been taken for granted so far. The present paper proposes, resp. recalls chi-square tests of the Markov property, of spatial independence, and of homogeneity across time and space to assess the reliability of estimated Markov transition matrices. As an illustration we show that the evolution of the income distribution across the 48