Models and statistics Statistical estimation methods Finse Friday

Models and statistics Statistical estimation methods, Finse Friday 10. 9. 2010, 9. 30– 10. 00 Andreas Lindén 1

Outline • What are models? • Kinds of models • Stochastic models • Basic concepts: parameters and variables 2

What 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) 3

Examples of models http: //education. jlab. org/qa/atom_model_02. gif 4

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Anything 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 9

Stochastic 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 10

Variables • 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 11

Examples 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 12

Parameters • 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 13

Examples of parameters • Population characters of the flycatcher population – Intrinsic growth rate – Carrying capacity • The average clutch size • The variance of clutch size 14

Variables vs. parameters • Important to distinguish… – Variables are observable/measurable and varies – Parameters are often imaginary defining model properties • In linear regression Variable Parameter • …but there are grey zones – Stochastic, time-varying parameters – Latent variables – State-variables (e. g. populations size) 15