Properties of the Bayesian parameter estimation of a~regression based on Gaussian processes
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 53-65.

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We consider the regression approach based on Gaussian processes and outline our theoretical results about the properties of the posterior distribution of the corresponding covariance function's parameter vector. We perform statistical experiments confirming that the obtained theoretical propositions are valid for a wide class of covariance functions commonly used in applied problems.
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A. A. Zaytsev; E. V. Burnaev; V. G. Spokoiny. Properties of the Bayesian parameter estimation of a~regression based on Gaussian processes. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 53-65. http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a3/

[1] Burnaev E. V., Zaitsev A. A., Spokoinyi V. G., “Svoistva aposteriornogo raspredeleniya modeli zavisimosti na osnove gaussovskikh sluchainykh polei”, Avtomatika i telemekhanika, 2013, no. 10, 55–67

[2] Burnaev E. V., Zaitsev A. A., Spokoinyi V. G., “Teorema Bernshteina–fon Mizesa dlya regressii na osnove gaussovskikh protsessov”, Uspekhi mat. nauk, 68:5 (2013), 179–180 | DOI | Zbl

[3] Ibragimov I. A., Khasminskii R. Z., Asimptoticheskaya teoriya otsenivaniya, Nauka, M., 1979 | MR

[4] Chervonenkis A. Ya., Chernova S. S., Zykova T. V., “Primenenie yadernoi grebnevoi otsenki k zadache raschëta aerodinamicheskikh kharakteristik passazhirskogo samoleta (sravnenie s rezultatami, poluchennymi s ispolzovaniem iskusstvennykh neironnykh setei)”, Avtomatika i telemekhanika, 2011, no. 5, 175–182 | Zbl

[5] Shiryaev A. N., Veroyatnost, v. 1, 2, MTsNMO, M., 2011

[6] Eidsvik J., Finley A. O., Banerjee S., Rue H., “Approximate Bayesian inference for large spatial datasets using predictive process models”, Comput. Statist. Data Analysis, 56:6 (2011), 1362–1380 | DOI | MR

[7] Forrester A., Sobester A., Keane A., Engineering Design via Surrogate Modelling, A Practical Guide, Wiley, 2008

[8] Kaufman C. G., Schervish M. J., Nychka D. W., “Covariance tapering for likelihood-based estimation in large spatial data sets”, J. Am. Statist. Assoc., 103:484 (2008), 1545–1555 | DOI | MR | Zbl

[9] Kok S., “The asymptotic behaviour of the maximum likelihood function of Kriging approximations using the Gaussian correlation function”, EngOpt 2012, Internat. Conf. on Engineering Optimization (Rio de Janeiro, Brazil, 1–5 July 2012)

[10] Mardia K. V., Marshall R. J., “Maximum likelihood estimation of models for residual covariance in spatial regression”, Biometrika, 71:1 (1984), 135–146 | DOI | MR | Zbl

[11] Rasmussen C. E., Williams C. K. I., Gaussian Processes for Machine Learning, v. 1, MIT Press, Cambridge, MA, 2006 | MR | Zbl

[12] Shaby B., Ruppert D., “Tapered covariance: Bayesian estimation and asymptotics”, Journal Comput. Graph. Statist., 21:2 (2012), 433–452 | DOI | MR

[13] Spokoiny V., “Parametric estimation. Finite sample theory”, Ann. Statist., 6 (2012), 2877–2909 | DOI | MR

[14] Spokoiny V., Bernstein–von Mises theorem for growing parameter dimension, 2013, arXiv: 1302.3430[math.ST]

[15] Wasserman L., All of Statistics. A Concise Course in Statistical Inference, Springer, Berlin, 2004 | MR | Zbl