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Bayesian nonparametric smoothers for regular processes
Author(s) -
Weerahandi S.,
Zidek J. V.
Publication year - 1988
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315064
Subject(s) - mathematics , taylor series , a priori and a posteriori , series (stratigraphy) , nonparametric statistics , bayesian probability , joint probability distribution , smoothing , multivariate statistics , statistics , interval (graph theory) , distribution (mathematics) , noise (video) , econometrics , computer science , mathematical analysis , artificial intelligence , paleontology , philosophy , epistemology , combinatorics , image (mathematics) , biology
This report is about the analysis of stochastic processes of the form R = S + N , where S is a “smooth” functional and N is noise. The proposed methods derive from the assumption that the observed R ‐values and unobserved values of R , the assumed inferential objectives of the analysis, are linearly related through Taylor series expansions of observed about unobserved values. The expansion errors and all other priori unspecified quantities have a joint multivariate normal distribution which expresses the prior uncertainty about their values. The results include interpolators, predictors, and derivative estimates, with credibility‐interval estimates automatically generated in each case. An analysis of an acid‐rain wet‐deposition time series is included to indicate the efficacy of the proposed method. It was this problem which led to the methodological developments reported in this paper.