1. Models and statistics Statistical estimation methods, Finse Friday 10.9.2010, 9.30–10.00 Andreas Lindén

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

3. 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)

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

5. http://plaza.fi/s/f/editor/images/model_expo_08_galleria_3.jpghttp://plaza.fi/s/f/editor/images/model_expo_08_galleria_3.jpg

6. http://images.askmen.com/galleries/model/claudia-schiffer/pictures/claudia-schiffer-picture-3.jpghttp://images.askmen.com/galleries/model/claudia-schiffer/pictures/claudia-schiffer-picture-3.jpg

8. http://www.symscape.com/files/images/navier_stokes_equation.pnghttp://www.symscape.com/files/images/navier_stokes_equation.png

9. 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

10. 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

11. 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

12. 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

13. 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

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

15. Variables 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