UNCERTML - DESCRIBING
AND COMMUNICATING
UNCERTAINTY
Matthew Williams
williamw@aston.ac.uk
OVERVIEW
 Introduction.
 Motivation
Webs.
 UncertML
 Use
– the Semantic and Sensor
overview.
case – The INTAMAP project.
 Conclusions.
MOTIVATION
The semantic and sensor webs
THE SENSOR WEB
SENSOR WEB ENABLEMENT
(SWE)

Open Geospatial Consortium (OGC) initiative
Interoperability interfaces and metadata encodings.
<Quantity
id="elevationAngle" fixed="false"
 Real time integration of heterogeneous sensor webs
definition="urn:ogc:def:scanElevationAngle">
into the information infrastructure.
<uom xlink:href="urn:ogc:unit:degree"/>

<quality>
<Tolerance definition="urn:ogc:def:tolerance2std">
 Current
SWE
standards
<value>
-0.02
0.02 </value>
</Tolerance> & Measurements
 Observations
</quality>
 SensorML
<value> 25.3 </value>
</Quantity>
 SWE Common

No formal standard for quantifying uncertainty
HOW UNCERTAINTY IS USED
WITHIN THE SEMANTIC WEB

PR-OWL: a Bayesian Ontology Language for the
Semantic Web:
Extends OWL to allow probabilistic knowledge to be
represented in an ontology.
 Used for reasoning with Bayesian inference.
 Random variables are described by either a PR-OWL
table (discrete probability) or using a proprietary
format.


Other standards looking at similar concepts:


BayesOWL.
FuzzyOWL.
What next?



A formal open standard for quantifying complex uncertainties
Extend to allow continuous distributions
More powerful reasoning, richer representations
UNCERTML
OVERVIEW

Split into three distinct packages (distributions,
statistics & realisations).
DISTRIBUTIONS
<un:Distribution
definition="http://dictionary.uncertml.org/distributions/gauss
ian">
<un:parameters>
<un:Parameter
definition="http://dictionary.uncertml.org/distributions/gauss
ian/mean">
<un:value>34.564</un:value>
</un:Parameter>
<un:Parameter
definition="http://dictionary.uncertml.org/distributions/gauss
ian/variance">
<un:value>67.45</un:value>
</un:Parameter>
</un:parameters>
</un:Distribution>
UNCERTML
An overview
WEAK VS. STRONG
Weak-typed

Benefits
Strong-typed

Benefits
<Distribution
 Genericdefinition=“http://uncertml.org/gaussian”>
features have
 Produces relatively
<parameter definition=“http://uncertml.org/mean”>34.2</parameter>
genericdefinition=“http://uncertml.org/variance”>12.4</parameter>
properties –
simple XML features
<parameter
</Distribution>
extensible

Drawbacks
<GaussianDistribution>
<mean>34.2</mean>
Validation becomes
<variance>12.4</variance>
less meaningful
</GaussianDistribution>

Drawbacks

Not easily extended –
all domain features
must be known a
priori
THE UNCERTML DICTIONARY




Weak-typed designs rely on dictionaries.
Includes definitions of key distributions &
statistics.
URIs link to dictionary entry and provide
semantics.
Could be written in Semantic Web standards
(OWL, RDF etc).
UNCERTML – DICTIONARY
EXAMPLE
<gml:Dictionary xmlns:gml="http://www.opengis.net/gml" gml:id="DISTRIBUTIONS">
<gml:name>All Probability Distributions</gml:name>
<gml:description>Distributions dictionary</gml:description>
<gml:dictionaryEntry>
<un:DistributionDefinition xmlns:un="http://www.intamap.org/uncertml"
gml:id="Gaussian">
<gml:description>Gaussian distribution</gml:description>
<gml:name>Gaussian</gml:name>
<gml:name>Normal</gml:name>
<un:functions>
<un:FunctionDefinition
gml:id="Gaussian_Cumulative_Distribution_Function">
<gml:description>cumulative distribution
function</gml:description>
<gml:name>Cumulative Distribution Function</gml:name>
<un:mathML>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mn>2</mml:mn>
</mml:mfrac>
SEPARATION OF CONCERNS



Several competing standards already exist
addressing the issue of units and location.
Geospatial information not always relevant –
Systems biology.
Do what we know – do it well!
UNCERTML
An applied case study
THE INTAMAP PROJECT



An automatic, interoperable
service providing real time
interpolation between
observations.
EURDEP providing
radiological data as a case
study.
Provide real time predictions
to aid risk management
through a Web Processing
Service interface.
UNCERTML IN INTAMAP


‘Really clever’ Bayesian
inference:

Different sensor errors.

Change of support.
Fast & approximate
algorithms.
COMPARING PREDICTIONS WITH
AND WITHOUT UNCERTML
Without UncertML
With UncertML
CONCLUSIONS
 Currently
no interoperable standard
which fully describes random variables.
 UncertML provides an extensible,
weak-typed, design that can quantify
uncertainty using:



Distributions.
Statistics.
Realisations.
 Provide
richer information for use in
decision support systems.
<om:Observation>
<un:DistributionArray>
<om:procedure
xlink:href="http://www.mydomain.com/sensor_models/temperature"/>
<un:elementType>
<om:resultQuality>
<un:Distribution
<un:Distribution definition="http://dictionary.uncertml.org/distributions/gaussian">
definition="http://dictionary.uncertml.org/distributions/gaussian">
<un:parameters>
<un:parameters>
<un:Parameter
definition="http://dictionary.uncertml.org/distributions/gaussian/parameters/mean">
<un:Parameter
<un:value>0.0</un:value>
definition="http://dictionary.uncertml.org/distributions/gaussian/mean"/>
</un:Parameter>
<un:Parameter
<un:Parameter
definition="http://dictionary.uncertml.org/distributions/gaussian/variance"/>
definition="http://dictionary.uncertml.org/distributions/gaussian/parameters/variance">
</un:parameters>
<un:value>3.6</un:value>
</un:Parameter>
</un:Distribution>
</un:parameters>
</un:elementType>
</un:Distribution>
<un:elementCount>5</un:elementCount>
</om:resultQuality>
<swe:encoding>
<om:observedProperty
xlink:href="urn:x-ogc:def:phenomenon:OGC:AirTemperature"/>
<swe:TextBlock decimalSeparator="." blockSeparator=" "
<om:featureOfInterest>
<sa:SamplingPoint>
tokenSeparator=","/>
<sa:sampledFeature xlink:href="http://www.mydomain.com/sampling_stations/ws-04231"/>
</swe:encoding>
<sa:position>
<swe:values>
<gml:Point>
35.2,56.75
<gml:pos srsName="urn:x-ogc:def:crs:EPSG:4326">
31.2,65.31
52.4773635864 -1.89538836479
</gml:pos>
28.2,54.23
</gml:Point>
35.6,45.21
</sa:position>
41.5,85.24
</sa:SamplingPoint>
</swe:values>
</om:featureOfInterest>
</un:DistributionArray>
<om:result xsi:type="gml:MeasureType" uom="urn:ogc:def:uom:OGC:degC">19.4</om:result>
</om:Observation>
UNCERTML IN INTAMAP