astr 513: statistical methods in (astro)physics spring
TRANSCRIPT
ASTR 513: Statistical Methods in (Astro)Physics
Spring 2018
Tuesdays - Thursdays 11 am-12:15 noon
Instructor: Dimitrios Psaltis
Office: Steward Observatory N324 621-7859
web page: u.arizona.edu/~dpsaltis/Astr513
What is the goal of this class?
There is the obvious issue that, if you look hard enough, you will always find an unusual correlation
As scientists, we profess pride in that we only report results that are highly statistically significant.
P<0.05, 3 sigma, 5 sigma, etc
But is this biasing our results?
Let’s see what happens when we only report “highly likely” results
true underlying likelihood of a hypothetical “measurement”
Let’s see what happens when we only report “highly likely” results
likelihood of measurements reported
you have to be wrong in order to be right
A side remark (or why always being right is not good):
In the predictions, the chance of either candidate winning a given state ranges from 50-90%
Even if all predictions were at the 90% level, the model should have gotten on average 5 predictions wrong. A more careful analysis shows that it should have gotten at least 3 wrong.
However, it got all of them right!
Confusing prior and posterior likelihoods is a very common source of errors
• The license plate paradox (attributed to R. Feynman)
• What are the odds of a polar star in the sky?
Why do priors matter? Or (more importantly), how to count realizations of the outcome
A short parenthesis
Car 1st choice door open switch result
A A B C not win
A A C B not win
A B C A win
A C B A win
there are two places in the game where the stochastic nature appears: • when you make the 1st choice • if you pick the car, which door MH will open
but is this the right way to calculate odds?
Car 1st choice door open switch result
A A B (or C) C (or B) not win
A B C A win
A C B A win
what matters is the player’s choice and not the distribution of possible realizations of the outcome
“the probability that a research finding is indeed true depends on
• the prior probability of it being true (before doing the study),
• the statistical power of the study,
• the level of statistical significance”
The goal of this class is to develop strategies and computational tools that will allow us to address these
three issues in a variety of situations
We will study
• Frequentist and Bayesian methods
• Stationary and time-dependent processes • Non-linear regression, parameter estimation,
and model selection
• Computational methods focusing on efficiency and minimal information loss
Our goal is to push all methods until they break.
• Six assignments (one every other week) and
• A final project (not literature survey but an actual statistics project)
You are encouraged to work on all assignments in groups of up to 3 people (and you must for the project)
This will be a hands-on class. Bring your laptops!
