STAT 300 Model building Andrzej Polanski Duncan Hall

STAT 300 Model building Andrzej Polanski Duncan Hall, Room 2091 http: //www. stat. rice. edu/~mathbio/stat 300 polanski@stat. rice. edu

Textbook D. Brown, P. Rothery Models in Biology: Mathematics, Statistics and Computing Wiley, 1994

Homework, tests • (50% of the final score) Project work – every two weeks. Cooperation concerning understanding and discussing the material is encouraged. Some individual study and elaborating - testing simple computer programs, is expected. • (50% of the final score) 2 tests – one in the middle of the semester, one in the end of the semester. Closed book, one sheet of notes admissible, approximately 4 hours.

Software Matlab Simulink other ?

Plan • Introductory comments • PART I: Models for single populations and processes • PART II: Modeling interactions • PART III: Selected advanced topics

Introductory comments • What is (mathematical) modeling ? • How do we derive (elaborate) models ? • What is the benefit of using mathematical models ? • What is computer simulation and what do we use it for ?

What is (mathematical) modeling ? “ … a model is a peculiar blend of fact and fantasy, of truth, halftruth and falsehood. In some ways a model may be reliable, in other ways only helpful and at times and in respects thoroughly misleading…” (our textbook)

How do we elaborate models ? • Hypotheses, principles of conservation, laws of physics, chemistry. • Empirical observations

What is the benefit of using mathematical models ? • Better understanding and verifying biological mechanisms • Predicting future events • Optimizing control and design actions

Computer simulation • Setting a computer program that would mimic reality • Deterministic and stochastic • Easy, modeling = drawing block diagrams

What is specific in modeling in biology ? • Complexity of modeled phenomena • Extent of simplifications in the models • Element of randomness

Research work in modeling • • • Model building Model learning Model understanding Applying a model to data Model modification

Models • Deterministic and stochastic • Descriptive and mechanistic • Dynamic and non-dynamic