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xi • Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise Log-Sum-Exp Inequalities by Frank Nielsen and Ke Sun • A Sequence of Escort Distributions and Generalizations of Expectations on q-Exponential Family by Hiroshi Matsuzoe • The Information Geometry of Sparse Goodness-of-Fit Testing by Paul Marriott, Radka Sabolová, Germain Van Bever and Frank Critchley Chapter IV : Density of Probability on manifold and metric space The fourth Chapter proposes new approaches to estimate parametric and non-parametric probabilities densities for structured covariance matrices (Toeplitz and Block-Toeplitz Hermitian Positive Definite Matrix, Symmetric Positive Definite Matrix). • Kernel Density Estimation on the Siegel Space with an Application to Radar Processing by Emmanuel Chevallier, Thibault Forget, Frédéric Barbaresco and Jesus Angulo • Riemannian Laplace Distribution on the Space of Symmetric Positive Definite Matrices by Hatem Hajri, Ioana Ilea, Salem Said, Lionel Bombrun and Yannick Berthoumieu Chapter V: Statistics on Paths and on Riemannian Manifolds The fifth chapter describes new methods to introduce statistical tools for paths and for data on Riemannian manifolds, with the following three contributions: • Entropy Minimizing Curves with Application to Flight Path Design and Clustering by Stéphane Puechmorel and Florence Nicol • Anisotropically Weighted and Nonholonomically Constrained Evolutions on Manifolds by Stefan Sommer • Non-Asymptotic Confidence Sets for Circular Means by Thomas Hotz, Florian Kelma and Johannes Wieditz Chapter VI: Entropy and Complexity in Linguistic The sixth chapter concludes this edited book with new perspectives for defining topological structures, entropy and complexity in linguistics with the following contribution: • Syntactic Parameters and a Coding Theory Perspective on Entropy and Complexity of Language Families by Matilde Marcolli Frédéric Barbaresco and Frank Nielsen Guest Editors References 1. BARBARESCO, F. & DJAFARI, A., ”Information, Entropy and Their Geometric Structures”, MDPI Entropy, September 2015; http://www.mdpi.com/books/pdfview/book/127 2. BAYES, Th., «An essay towards solving a problem in the doctrine of chance», Philosophical Transactions of the Royal Society of London, 53 (1763), trad. J.-P. Cléro, Cahiers d'histoire et de philosophie des sciences, n° 18, 1988. 3. BERNOULLI, J., Ars conjectandi (1713), die Werke von Jakob Bernoulli, 3 vols., Basel, 1969-1975. 4. BYRNE, E., Probability and Opinion: A Study in the Medieval Pre-suppositions of Post-Medieval Theories of probability, La Haye, Martinus Nijhoff, 1968. 5. CARDANO, De ludo aleae (ca. 1520), Opera Omnia, 10 vols., Stuttgart, 1966.