Amari, S. (2005). Integration of stochastic evidences in population coding – theory of α-mixture. In *Proceedings of the Second International Symposium on Information Geometry and its Applications*, (pp. 15–21). University of Tokyo, 12–16 December 2005.

Amari, S., Nagaoka, H. (1982). Differential geometry of smooth families of probability distributions. Technical Report METR 82-7, Department of Mathematical Engineering and Instrumentation Physics, University of Tokyo.

Amari, S., Nagaoka, H. (2000). *Methods of Information Geometry*. Translations of Mathematical Monographs, Vol. 191. Providence, Rhode Island: American Mathematical Society and Oxford University Press.

Bernardo J.M. (1979). Expected information as expected utility. Annals of Statistics 7, 686–690

MATHMathSciNetGoogle ScholarBregman L.M. (1967). The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics 7, 200–217

CrossRefGoogle ScholarCover T., Thomas J.A. (1991). Elements of Information Theory. New York, Wiley Interscience.

MATHGoogle ScholarCsiszár I. (1991). Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems. Annals of Statistics 19, 2032–2066

MATHMathSciNetGoogle ScholarDawid A.P. (1975). Discussion of Efron (1975). *Annals of Statistics* 3, 1231–1234

Dawid, A.P. (1998). Coherent measures of discrepancy, uncertainty and dependence, with applications to Bayesian predictive experimental design. Technical Report 139, Department of Statistical Science, University College London. http://www.ucl.ac.uk/Stats/research/abs94.html#139.

Dawid, A. P., Lauritzen, S.L. (2006). The geometry of decision theory. In *Proceedings of the Second International Symposium on Information Geometry and its Applications*, (pp.22–28). University of Tokyo, 12–16 December 2005.

Dawid A.P., Sebastiani P. (1999). Coherent dispersion criteria for optimal experimental design. Annals of Statistics 27, 65–81

MATHCrossRefMathSciNetGoogle ScholarEaton M.L. (1982). A method for evaluating improper prior distributions. In: Gupta S., Berger J.O. (eds) Statistical Decision Theory and Related Topics III. New York, Academic Press, pp. 320–352

Google ScholarEaton M.L., Giovagnoli A., Sebastiani P. (1996). A predictive approach to the Bayesian design problem with application to normal regression models. Biometrika 83, 11–25

CrossRefMathSciNetGoogle ScholarEfron B.(1975). Defining the curvature of a statistical problem (with applications to second-order efficiency) (with Discussion). Annals of Statistics 3, 1189–1242

MATHMathSciNetGoogle ScholarEguchi, S. (2005). Information geometry and statistical pattern recognition. *Sugaku Exposition*, American Mathematical Society(to appear).

Epstein E.S. (1969). A scoring system for probability forecasts of ranked categories. Journal of Applied Meteorology 8, 985–987

CrossRefGoogle ScholarGneiting, T., Raftery, A. E. (2005). Strictly proper scoring rules, prediction, and estimation. Technical Report 463R, Department of Statistics, University of Washington.

Good, I.J. (1971). Comment on “Measuring information and uncertainty” by Robert J. Buehler. In V.P. Godambe, D.A. Sprott(Eds.) *Foundations of Statistical Inference*, (pp. 337–339)Toronto: Holt, Rinehart and Winston.

Grünwald P.D., Dawid A.P. (2004). Game theory, maximum entropy, minimum discrepancy, and robust Bayesian decision theory. Annals of Statistics 32, 1367–1433

MATHCrossRefMathSciNetGoogle ScholarLauritzen, S. L. (1987a). Conjugate connections in statistical theory. In C. T. J. Dobson(Ed.) *Geometrization of Statistical Theory: Proceedings of the GST Workshop*, (pp. 33–51) Lancaster: ULDM Publications, Department of Mathematics, University of Lancaster.

Lauritzen, S. L. (1987b). Statistical manifolds. In *Differential Geometry in Statistical Inference*, IMS Monographs(Vol. X, pp. 165–216) Hayward, California: Institute of Mathematical Statistics.

Murata N., Takenouchi T., Kanamori T., Eguchi S. (2004). Information geometry of

*U*-boost and Bregman divergence. Neural Computing 16, 1437–1481

MATHCrossRefGoogle ScholarTsallis C. (1988). Possible generalization of Boltzmann–Gibbs statistics. Journal of Statistical 52, 479–487

MATHCrossRefMathSciNetGoogle Scholar