16/20 example (1). ⢠input A E -â-â> sampling to fit TfIo for o1= P o2=Pr. ⢠output P Pr -â-â> Fo so one gets. Tf modelled as. Extracºon. Availability. A. E. A. E. A. E.
Didier G. Leibovici & Mike Jackson No6ngham Geospa;al Ins;tute University of No6ngham, UK
A bit of la;n
Metadata
Known but la;n as well …
2/20
SDI and geoprocessing: the logic! • GISiences geocomputa5on mashups, scien;fic models, spa;al analysis
• Geoworklfow management Web Services Open Source Open Standard, metadata • Quality management data & geoprocess (& workflow) visualisa;on, error propaga5on, decision making
metadata about quality • Quality management data & process (& workflow) uncertainty es;ma;on, error propaga;on, visualisa;on,
data ISO19157 WFS, WCS quality elements > sub-‐elements > measures • Processing / geo-‐processing WPS no standard metadata for geoprocess quality uncertainty analysis (sensi;vity) error propaga;on
4/20
metadata for processes / basic measures
5
5/20
see Leibovici et al. 2013 Journal of Spa8al Science
meta-‐propaga;on principle
ISO19157 19139
Scope
DQ_ PQ_
•
6/20
SIEL / LEIS example 10 years ago …
GIS see also Arc
+ SIEL / LEIS example now
r
+
n o i t a g a p o w meta-pr o l f k r o w le o h w e h t r ove
flow edito
any work
+
ModelBuilde
r
7
7/20
but then … • full pdf
• mul;variate pdf
• and other mul8variate … spa8al dependence, mul8ple quality elements …!!!
cumula8ve distribu8on func8on
pdf probability density func8on
cdf
8/20
copula • C is a mul;variate distribu;on on the unit hypercube
• C is modelling the dependence … separately to the univariate margins 9/20
Copula “input” metadata est • during an uncertainty analysis is fibed • reusing the atomic workflow • then either mul8variate meta-‐propaga8on or reused in sampling to fit a Tf 10/20
Copula “output” metadata est • during an uncertainty analysis is fibed and • then reusing the atomic workflow recovering univariate ouput margins or from another error propaga;on method
• then easier mul8variate meta-‐propaga8on Or beFer decision making 11/20
Copula “geoprocess” metadata est • during an uncertainty analysis is fibed (or ) keeping also ini;al • then reusing the atomic workflow one input to one output Tf fi6ng? alterna;ng algorithm:
12/20
Copulae “altogether now” metadata sunt • during an uncertainty analysis and each are fibed keeping also each ini;al • then reusing the atomic workflow all input to all output Tf fi6ng alterna;ng algorithm: (n) (n+1) (end) 13/20
a real example!
Niger − − − −
Dantiandou Tondikendia Keita Torodi
Un observatoire est défini par : 14/20
biomass Availability Extrac5on
A
a real example! E A
Absolute pressure Agr local ra;o For P = E/A Pas Pr=(E/A)/ (Eu/Aa)
E A
E
rela;ve pressure homogeneity Eu: average of E for the same unit type Aa: average of A for all
15/20
biomass Availability Extrac5on
A
example (1) E A
Absolute pressure Agr local ra;o For P = E/A Pas Pr=(E/A)/ (Eu/Aa)
E A
E
rela;ve pressure homogeneity Eu: average of E for the same unit type Aa: average of A for all
• input A E -‐-‐> sampling to fit TfIo for o1= P o2=Pr • output P Pr -‐-‐> Fo so one gets Tf modelled as
16/20
biomass Availability Extrac5on
A
Absolute pressure Agr local ra;o For P = E/A Pas
example (2) E A
Pr=(E/A)/ (Eu/Aa)
E A
rela;ve pressure homogeneity
E
Eu: average of E for the same unit type Aa: average of A for all
• “geoprocess” metadata and ini;al A on Pr -‐-‐> fi6ng “Tf” • Idem on P -‐-‐> 17/20
implementa;on within R
• Tes;ng the independence is important (no need of C) • copula R Package (tes;ng and modelling) other R packages on copula: CDVine, copBasic, coclust, fCopulae, sbgcop … • numerical results …exemple (1) more difficult than (2)!
18/20
Conclusion: copula as metadata for? • meta-‐propaga;on
-‐basic e.g. variance, parametric families , -‐more comprehensive, with pdf, mul$variate -‐theore;cal solu;on? … appropriate uncertainty
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Dec 9, 2004 - sensitivity analysis for CDOs in Gaussian ... Model risk: choice of copula ... B(t) discount factor, T maturity of CDO ..... correlation levels.
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