msa830: introduction petter mostad [email protected]
TRANSCRIPT
MSA830 homepage
http://www.math.chalmers.se/Stat/Grundutb/GU/MSA830/H07/
Chapter 1: Scientific investigation
• Scientific investigations – In a research group– In an organization, workplace, factory…
• Empirical basis of science– Making observations– Experimenting
Inductive – Deductive learning
Model, theory, idea.. Model, theory, idea..
Data DataDeduction DeductionInduction
• Model for science: Inductive – deductive iteration
• Increasingly good prediction/explanation of data (i.e., the real world)
Induction
…
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
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
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
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
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
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
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
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.
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
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