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Slide 1 Trans-dimensional models for nonparametric Bayesian function estimation a Juha Heikkinen Finnish Forest Research Institute Univ. Helsinki, Dept. Mathematics and Statistics juha.heikkinen@metla.fi Joint Statistical Seminars @ Ume? University Department of Statistics Department of Mathematics and Mathematical Statistics February 15, 2005 a Slides available at http://www.metla.fi/pp/JuHe/pub 1 J. Heikkinen:Transdimensional Bayesian functions. Joint Statistical Seminars @ Ume? University. Feb 15, 2005. METS?NTUTKIMUSLAITOS SKOGSFORSKNINGINSTITUT FINNISH FOREST RESEARCH INSTITUTE www.metla.fi Slide 2 Aims of the talk Review closely related methods (Green 1995, Heikkinen 1998, Nicholls 1998, M?ller Skare 2001, Hansen Kooperberg 2002, Denison et al. 2002) for nonparametric Bayesian surface estimation. Tell something about more recent own applications for curve estimation on one hand and for higher (than 2) dimensional functions on the other. Mention a couple of more recent interesting developments. 2 J. Heikkinen:Transdimensional Bayesian functions. Joint Statistical Seminars @ Ume? University. Feb 15, 2005. METS?NTUTKIMUSLAITOS SKOGSFORSKNINGINSTITUT FINNISH FOREST RESEARCH INSTITUTE www.metla.fi Slide 3 Basic idea (pictures from Arjas Heikkinen 1997) 0.0 0.2 0.4 0.6 0.8 1.0 0 5 0 0 1 0 0 0 2 0 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0 5 0 0 1 0 0 0 2 0 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0 5 0 0 1 0 0 0 2 0 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0 5 0 0 1 0 0 0 2 0 0 0 in te n s it y 0.0 0.2 0.4 0.6 0.8 1.0 0 200 400 600 800 1000 1200 1400 ··· · ··· ·· ·· · · · · ·· ·· · · ··· · · ·· ·· ·· · · · · · ··· · · ·· ··· · · · · ·· · ·· ·· · · ·· ··· ·· · ·· · · · · · · · · · · ·· · ··· · ··· ·· ·· ·· · · ·· · ·· · ·· ··· · · ·· ·· · ·· · ···· ·· ·· ·· · ·· · · ·· · · · ·· ·· ·· ·· · · · ·· · ·· ·· · ·· ···· · · · · · · · · · · · · ·· · · ·· · ·· · ·· · · · · · ····· ···· · · · ··· ·· ·· ··· · · · · · ··· ·· · · ·· · ··· · ·· ·· · ·· · · · · Think of many histograms of same data with variable num

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