Convolutional stochastic processes


Stochastic processes generated by convolution of white noise with smoothing kernels, which is not unlike kernel density estimation where the “data” is random.

For now, I am mostly interested in certain special cases Gaussian process convolutionss and subordinator convolutions.

References

Bolin, David. 2014. “Spatial Matérn Fields Driven by Non-Gaussian Noise.” Scandinavian Journal of Statistics 41 (3): 557–79. https://doi.org/10.1111/sjos.12046.
Higdon, Dave. 2002. “Space and Space-Time Modeling Using Process Convolutions.” In Quantitative Methods for Current Environmental Issues, edited by Clive W. Anderson, Vic Barnett, Philip C. Chatwin, and Abdel H. El-Shaarawi, 37–56. London: Springer. https://doi.org/10.1007/978-1-4471-0657-9_2.
Higdon, David. 1998. “A Process-Convolution Approach to Modelling Temperatures in the North Atlantic Ocean.” Environmental and Ecological Statistics 5 (2): 173–90. https://doi.org/10.1023/A:1009666805688.
Lee, Herbert K. H., Dave M. Higdon, Zhuoxin Bi, Marco A. R. Ferreira, and Mike West. 2002. “Markov Random Field Models for High-Dimensional Parameters in Simulations of Fluid Flow in Porous Media.” Technometrics 44 (3): 230–41. https://doi.org/10.1198/004017002188618419.
Lee, Herbert KH, Dave M Higdon, Catherine A Calder, and Christopher H Holloman. 2005. “Efficient Models for Correlated Data via Convolutions of Intrinsic Processes.” Statistical Modelling 5 (1): 53–74. https://doi.org/10.1191/1471082X05st085oa.
Scharf, Henry R., Mevin B. Hooten, Devin S. Johnson, and John W. Durban. 2017. “Process Convolution Approaches for Modeling Interacting Trajectories.” November 21, 2017. http://arxiv.org/abs/1703.02112.
Thiebaux, HJ, and MA Pedder. 1987. “Spatial Objective Analysis with Applications in Atmospheric Science.” London and Orlando, FL, Academic Press, 1987, 308.
Wolpert, R. 1998. “Poisson/Gamma Random Field Models for Spatial Statistics.” Biometrika 85 (2): 251–67. https://doi.org/10.1093/biomet/85.2.251.
Wolpert, Robert L. 2006. “Stationary Gamma Processes,” 13.

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