16
G. Pistone
5. Cena, A., Pistone, G.: Exponential statistical manifold. Ann. Inst. Statist. Math. 59(1), 27–56
(2007)
6. Chirco, G., Malagò, L., Pistone, G.: Lagrangian and Hamiltonian mechanics for probabilities
on the statistical manifold, arXiv:2009.09431
7. Gibilisco, P., Pistone, G.: Connections on non-parametric statistical manifolds by Orlicz space
geometry. IDAQP 1(2), 325–347 (1998)
8. Hyvärinen, A.: Estimation of non-normalized statistical models by score matching. J. Mach.
Learn. Res. 6, 695–709 (2005)
9. Karatzas, I., Shreve, S.E.: Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol. 113. Springer-Verlag, New York, second edn. (1991). https://doi.org/10.1007/9781-4612-0949-2
10. Kriegl, A., Michor, P.W.: The convenient setting of global analysis, Mathematical Surveys and
Monographs, vol. 53. American Mathematical Society, Providence, RI (1997). https://doi.org/
10.1090/surv/053
11. Lang, S.: Differential and Riemannian manifolds, Graduate Texts in Mathematics, vol. 160,
3rd edn. Springer-Verlag (1995)
12. Li, W., Montúfar, G.: Natural gradient via optimal transport. Inf. Geom. 1(2), 181–214 (2018).
https://doi.org/10.1007/s41884-018-0015-3
13. Lods, B., Pistone, G.: Information geometry formalism for the spatially homogeneous Boltzmann equation. Entropy 17(6), 4323–4363 (2015)
14. Lott, J.: Some geometric calculations on Wasserstein space. Comm. Math. Phys. 277(2), 423–
437 (2008). https://doi.org/10.1007/s00220-007-0367-3
15. Malliavin, P.: Integration and probability, Graduate Texts in Mathematics, vol. 157. SpringerVerlag (1995), with the collaboration of Héléne Airault, Leslie Kay and Gérard Letac, Edited
and translated from the French by Kay, With a foreword by Mark Pinsky
16. Malliavin, P.: Stochastic analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 313. Springer-Verlag (1997)
17. Musielak, J.: Orlicz spaces and modular spaces. Lecture Notes in Mathematics, vol. 1034.
Springer-Verlag (1983)
18. Naudts, J.: Generalised thermostatistics. Springer-Verlag London Ltd. (2011). https://doi.org/
10.1007/978-0-85729-355-8
19. Newton, N.J.: A class of non-parametric statistical manifolds modelled on Sobolev space. Inf.
Geom. 2(2), 283–312 (2019). https://doi.org/10.1007/s41884-019-00024-z
20. Newton, N.J.: Sobolev statistical manifolds and exponential models. In: Geometric science of
information, Lecture Notes in Comput. Sci., vol. 11712, pp. 443–452. Springer, Cham (2019)
21. Nourdin, I., Peccati, G.: Normal approximations with Malliavin calculus, Cambridge Tracts
in Mathematics, vol. 192. Cambridge University Press, Cambridge (2012). https://doi.org/10.
1017/CBO9781139084659, from Stein’s method to universality
22. Otto, F.: The geometry of dissipative evolution equations: the porous medium equation. Comm.
Partial Differ. Equa. 26(1-2), 101–174 (2001)
23. Parry, M., Dawid, A.P., Lauritzen, S.: Proper local scoring rules. Ann. Statist. 40(1), 561–592
(2012). https://doi.org/10.1214/12-AOS971
24. Pistone, G.: Examples of the application of nonparametric information geometry to statistical
physics. Entropy 15(10), 4042–4065 (2013). https://doi.org/10.3390/e15104042
25. Pistone, G.: Nonparametric information geometry. In: Nielsen, F., Barbaresco, F. (eds.) Geometric science of information, Lecture Notes in Comput. Sci., vol. 8085, pp. 5–36. Springer,
Heidelberg (2013), first International Conference, GSI 2013 Paris, France, August 28-30, 2013
Proceedings
26. Pistone, G.: Translations in the exponential Orlicz space with Gaussian weight. In: Nielsen,
F., Barbaresco, F. (eds.) Geometric Science of Information. pp. 569–576. No. 10589 in LNCS,
Springer (2017), third International Conference, GSI 2017, Paris, France, November 7-9, 2017,
Proceedings
27. Pistone, G.: Information geometry of the Gaussian space. In: Information geometry and its
applications, Springer Proc. Math. Stat., vol. 252, pp. 119–155. Springer, Cham (2018)
G. Pistone
5. Cena, A., Pistone, G.: Exponential statistical manifold. Ann. Inst. Statist. Math. 59(1), 27–56
(2007)
6. Chirco, G., Malagò, L., Pistone, G.: Lagrangian and Hamiltonian mechanics for probabilities
on the statistical manifold, arXiv:2009.09431
7. Gibilisco, P., Pistone, G.: Connections on non-parametric statistical manifolds by Orlicz space
geometry. IDAQP 1(2), 325–347 (1998)
8. Hyvärinen, A.: Estimation of non-normalized statistical models by score matching. J. Mach.
Learn. Res. 6, 695–709 (2005)
9. Karatzas, I., Shreve, S.E.: Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol. 113. Springer-Verlag, New York, second edn. (1991). https://doi.org/10.1007/9781-4612-0949-2
10. Kriegl, A., Michor, P.W.: The convenient setting of global analysis, Mathematical Surveys and
Monographs, vol. 53. American Mathematical Society, Providence, RI (1997). https://doi.org/
10.1090/surv/053
11. Lang, S.: Differential and Riemannian manifolds, Graduate Texts in Mathematics, vol. 160,
3rd edn. Springer-Verlag (1995)
12. Li, W., Montúfar, G.: Natural gradient via optimal transport. Inf. Geom. 1(2), 181–214 (2018).
https://doi.org/10.1007/s41884-018-0015-3
13. Lods, B., Pistone, G.: Information geometry formalism for the spatially homogeneous Boltzmann equation. Entropy 17(6), 4323–4363 (2015)
14. Lott, J.: Some geometric calculations on Wasserstein space. Comm. Math. Phys. 277(2), 423–
437 (2008). https://doi.org/10.1007/s00220-007-0367-3
15. Malliavin, P.: Integration and probability, Graduate Texts in Mathematics, vol. 157. SpringerVerlag (1995), with the collaboration of Héléne Airault, Leslie Kay and Gérard Letac, Edited
and translated from the French by Kay, With a foreword by Mark Pinsky
16. Malliavin, P.: Stochastic analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 313. Springer-Verlag (1997)
17. Musielak, J.: Orlicz spaces and modular spaces. Lecture Notes in Mathematics, vol. 1034.
Springer-Verlag (1983)
18. Naudts, J.: Generalised thermostatistics. Springer-Verlag London Ltd. (2011). https://doi.org/
10.1007/978-0-85729-355-8
19. Newton, N.J.: A class of non-parametric statistical manifolds modelled on Sobolev space. Inf.
Geom. 2(2), 283–312 (2019). https://doi.org/10.1007/s41884-019-00024-z
20. Newton, N.J.: Sobolev statistical manifolds and exponential models. In: Geometric science of
information, Lecture Notes in Comput. Sci., vol. 11712, pp. 443–452. Springer, Cham (2019)
21. Nourdin, I., Peccati, G.: Normal approximations with Malliavin calculus, Cambridge Tracts
in Mathematics, vol. 192. Cambridge University Press, Cambridge (2012). https://doi.org/10.
1017/CBO9781139084659, from Stein’s method to universality
22. Otto, F.: The geometry of dissipative evolution equations: the porous medium equation. Comm.
Partial Differ. Equa. 26(1-2), 101–174 (2001)
23. Parry, M., Dawid, A.P., Lauritzen, S.: Proper local scoring rules. Ann. Statist. 40(1), 561–592
(2012). https://doi.org/10.1214/12-AOS971
24. Pistone, G.: Examples of the application of nonparametric information geometry to statistical
physics. Entropy 15(10), 4042–4065 (2013). https://doi.org/10.3390/e15104042
25. Pistone, G.: Nonparametric information geometry. In: Nielsen, F., Barbaresco, F. (eds.) Geometric science of information, Lecture Notes in Comput. Sci., vol. 8085, pp. 5–36. Springer,
Heidelberg (2013), first International Conference, GSI 2013 Paris, France, August 28-30, 2013
Proceedings
26. Pistone, G.: Translations in the exponential Orlicz space with Gaussian weight. In: Nielsen,
F., Barbaresco, F. (eds.) Geometric Science of Information. pp. 569–576. No. 10589 in LNCS,
Springer (2017), third International Conference, GSI 2017, Paris, France, November 7-9, 2017,
Proceedings
27. Pistone, G.: Information geometry of the Gaussian space. In: Information geometry and its
applications, Springer Proc. Math. Stat., vol. 252, pp. 119–155. Springer, Cham (2018)