Models and statistics
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Transcript of Models and statistics
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Models and statisticsModels and statistics
Statistical estimation methods, FinseFriday 10.9.2010, 9.30–10.00
Andreas Lindén
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OutlineOutline• What are models?
• Kinds of models
• Stochastic models
• Basic concepts: parameters and variables
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What are modelsWhat are models• A model is a description of reality
– Models ≠ reality– Usually a simplification– Helps to understand reality
• “All models are wrong, but some are useful” (Box)
• The suitable complexity of models can depend on the purpose (e.g. understanding, prediction)
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Examples of modelsExamples of models
http://education.jlab.org/qa/atom_model_02.gif
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http://plaza.fi/s/f/editor/images/model_expo_08_galleria_3.jpg
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http://images.askmen.com/galleries/model/claudia-schiffer/pictures/claudia-schiffer-picture-3.jpg
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http://www.symscape.com/files/images/navier_stokes_equation.png
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Anything can be modelledAnything can be modelled• “My research system is complex and can not
be described in terms of any model”• The thoughts about how a system works
produce a model• In science mathematics is a common language
used to express these thoughts as models• Mathematical modelling is not always easy or
successful
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Stochastic modelsStochastic models• In deterministic models there are no randomness and the
outcome is totally predictable
• Stochastic models include both deterministic and random (stochastic) components
• Statistical inference based on data — reverse engineering– Based on stochastic models– Trying to quantify the role of chance– Any stochastic model can in principle be confronted with data
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VariablesVariables• A variable is some quantity of interest that shows variation
– Different replicates– Different individuals– Varies in time– Spatial variation
• Typically measurable• Subject to data collection• In a statistical model:
– Explanatory variables– Response variable
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Examples of variablesExamples of variables• The number of migrating sparrowhawks
counted on a particular day
• The number of breeding pairs in a nestbox population of pied flycatchers
• The clutch size (number of eggs) in each nestbox
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ParametersParameters• Defines model properties
• Underlying approximating metrics
• The prefix para- (Ancient Greek). Wiktionary:– 1) beside, near, alongside, beyond;– 2) abnormal, incorrect;– 3) resembling
• In statistics usually unknown and estimated
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Examples of parametersExamples of parameters• Population characters of the flycatcher
population– Intrinsic growth rate– Carrying capacity
• The average clutch size
• The variance of clutch size
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Variables vs. parametersVariables vs. parameters• Important to distinguish…
– Variables are observable/measurable and varies– Parameters are often imaginary defining model properties
• In linear regression
• …but there are grey zones– Stochastic, time-varying parameters– Latent variables– State-variables (e.g. populations size)
Variable
Parameter