References

[1]

Jean-Paul Chilès and Pierre Delfiner. Geostatistics: Modeling Spatial Uncertainty. Wiley, 1999.

[2]

Pierre Del Moral, Arnaud Doucet, and Ajay Jasra. Sequential monte carlo samplers. Journal of the Royal Statistical Society: Series B, 68(3):411–436, 2006. doi:10.1111/j.1467-9868.2006.00553.x.

[3]

Amparo Gil, Javier Segura, and Nico M. Temme. Numerical Methods for Special Functions. Society for Industrial and Applied Mathematics, 2007. doi:10.1137/1.9780898717822.

[4]

Heikki Haario, Eero Saksman, and Johanna Tamminen. An adaptive metropolis algorithm. Bernoulli, 7(2):223–242, 2001. doi:10.2307/3318737.

[5]

W. K. Hastings. Monte carlo sampling methods using markov chains and their applications. Biometrika, 57(1):97–109, 1970. doi:10.1093/biomet/57.1.97.

[6]

Matthew D. Hoffman and Andrew Gelman. The no-u-turn sampler: adaptively setting path lengths in hamiltonian monte carlo. Journal of Machine Learning Research, 15(47):1593–1623, 2014. URL: https://jmlr.org/papers/v15/hoffman14a.html.

[7]

Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller. Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6):1087–1092, 1953. doi:10.1063/1.1699114.

[8]

Radford M. Neal. Mcmc using hamiltonian dynamics. In Steve Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng, editors, Handbook of Markov Chain Monte Carlo, pages 113–162. Chapman and Hall/CRC, 2011.

[9]

Sébastien J. Petit, Julien Bect, Paul Feliot, and Emmanuel Vazquez. Parameter selection in gaussian process interpolation: an empirical study of selection criteria. SIAM/ASA Journal on Uncertainty Quantification, 11(4):1308–1328, 2023. URL: https://arxiv.org/abs/2107.06006, doi:10.1137/21M1444710.

[10]

Carl Edward Rasmussen and Christopher K. I. Williams. Gaussian Processes for Machine Learning. MIT Press, 2006. URL: https://gaussianprocess.org/gpml/.

[11]

Herbert Robbins and Sutton Monro. A stochastic approximation method. The Annals of Mathematical Statistics, 22(3):400–407, 1951. doi:10.1214/aoms/1177729586.

[12]

Gareth O. Roberts, Andrew Gelman, and Walter R. Gilks. Weak convergence and optimal scaling of random walk metropolis algorithms. The Annals of Applied Probability, 7(1):110–120, 1997. doi:10.1214/aoap/1034625254.

[13]

Michael L. Stein. Interpolation of Spatial Data: Some Theory for Kriging. Springer, 1999. doi:10.1007/978-1-4612-1494-6.

[14]

NIST Digital Library of Mathematical Functions. NIST Digital Library of Mathematical Functions. Edited by F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain. URL: https://dlmf.nist.gov/.

[15]

SLATEC Common Mathematical Library. DASYIK: uniform asymptotic expansion for modified bessel functions. URL: https://netlib.org/slatec/src/dasyik.f.