MSA830: Introduction

1. MSA830: Introduction Petter Mostad mostad@chalmers.se

2. MSA830 homepage http://www.math.chalmers.se/Stat/Grundutb/GU/MSA830/H07/

3. Chapter 1: Scientific investigation • Scientific investigations • In a research group • In an organization, workplace, factory… • Empirical basis of science • Making observations • Experimenting

4. Inductive – Deductive learning Data Data • Model for science: Inductive – deductive iteration • Increasingly good prediction/explanation of data (i.e., the real world) Deduction Induction Deduction Induction Model, theory, idea.. Model, theory, idea.. …

5. Alternative formulation: Updating knowledge • At any time, we have a “model for our knowledge about something” • The model may contain probabilities, to indicate uncertainties • When we make observations (either directly or after experimentation) we update our model about reality (changing probabilities, or changing the model) • We make observations to update the parts of the model that interest us • The process is iterative

6. Different paths of discovery • Many different paths can lead to similar models • Goal: An efficient path • Example: 20-questions game • Very different sequences of questions can lead to same result • Efficient investigation: Each question should have equal probability of yes or no answer • No “objective” probabilities: They depend on your current model • Subject matter knowledge: In this case, your opponents cultural background and way of thinking

7. Complexity • Any model models only a small part of reality • Challenge: To simplify away all that is irrelevant in this context • Essential feature: observable predictions • Identify the parts of the model you want to learn more about • Any model predicts only approximately

8. Experimental error • Not that something has been done wrong! • The discrepancy between the model and the observed values • Good models have small experimental errors (while still being as simple as possible) • Statistical models can be used to formulate models that contain experimental errors

9. Designing experiments • Idea of experiment: To learn as much as possible about what you have questions about • The effects you want to learn about must not be obscured (confounded) by experimental error • Objective: Design experiment so that observing outcomes is likely to give as much information as possible about the questions you have

10. Link between experimental design and statistical analysis • In order to optimize the experiment, you necessarily have to consider how you are going to learn from the experiment • Considering the statistical analysis before the experiment is performed • Possible framework: Update of statistical model

11. Correlation versus causation • Examples: • Storks cause births? • Smoking causes depression? • … • Problem: Several different causal models can explain the same data • Often: An underlying unobserved factor influence both the observed factors, making them correlated

12. The advantage of experiments over just making observations • In an experiment, the experimenter goes in and decides some of the experimental parameters • The way this happens may make some causal explanatory models very unlikely • Example: The experimenter rolls a dice to decide which patients will receive which treatment. • The key is to refute certain explanatory models versus others. Example: Mendelian randomization.

13. Experimental versus non-experimental inference • Randomized experiments are generally the “gold-standard” of science • Sometimes, randomized experiments are difficult. Examples: • Effects of social parameters on people • Clinical testing of treatments for fatal diseases • Questions in cosmology, geology, … • We must then find other ways to differentiate between different explanatory models

14. Scientific investigation in practice • Iterative in nature • Models should predict as well as possible, while being as simple as possible • Statistics is a precise way to formulate models with experimental errors • Models should reflect relevant parts of all available knowledge • Define your objective! • The statistical analysis should be considered before designing any experiment