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Distributions, spatial statistics and a Bayesian perspective - IMAGe

**Distributions**, **spatial** **statistics** **and** a **Bayesian** **perspective** Doug Nychka National Center for Atmospheric Research • **Distributions** **and** densities • Conditional distributions **and** Bayes Thm • Bivariate normal • Spatial **statistics** **and** the ”data product” Supported by the National Science Foundation DMS NCAR/**IMAGe** July 2007

- Page 2 and 3: Overview As a specific example we w
- Page 4 and 5: Densities A probability density fun
- Page 6 and 7: ‘You can see alot just by looking
- Page 8 and 9: o ooo o oo o oo o o oo o o o ooo o
- Page 10 and 11: Statisticians have their moments! A
- Page 12 and 13: Sampling variability Same thing sev
- Page 14 and 15: If X 1 , X 2 , ..., X n is a random
- Page 16 and 17: Multivariate distributions f(x, y)
- Page 18 and 19: Conditional distributions A key ste
- Page 20 and 21: A more formal definition of Conditi
- Page 22 and 23: Conditional densities f(x, y) the j
- Page 24 and 25: Bayes Theorem Bayes Theorem gives a
- Page 26 and 27: Conditional densities for the Bould
- Page 28 and 29: Infilled Fraser means based on Boul
- Page 30 and 31: Some comments All infills have the
- Page 32 and 33: The data {Y 1 , ..., Y n } are the
- Page 34 and 35: Temperature fields for the Front Ra
- Page 36 and 37: Dependence of correlation on distan
- Page 38 and 39: Ensemble of fields for July 1993 Me
- Page 40: Summary • pdf can be approximated