Recommended reading from Statistics, Data Mining, and Machine Learning
in Astronomy ("SDMML") and Numerical Recipes ("NR"):
Yet another random number generator problem.
Write a python script that generates a
list of N random zeros and ones, with the probability of
drawing a one is P (in [0..1]}.
Experiment design with Fisher Information.
Using the Fisher Information, determined the minimal number of
trials N_min you need to test whether a coin has this tendency to an
accuracy of 10% at 99.7% confidence (3-=sigma) or better for all P
values (defined as in Exercise 1). Ask someone else in this lab
to pick a P value (w/o telling you!), generate N_min samples w/their
code in Exercise 1, and tell you how many of these samples are heads.
From this information, estimate (to within 10% at 99.7% confidence)
the P that you classmate chose.
"Waiting for the bus"
Suppose you know that a certain city bus always runs on time, and
comes by a certain bus stop every T minutes, but you do not know
what the time interval T is. If you show up at that bus stop at
some time t, and the bus shows up dt=15 minutes later, what is
your best guess at T?
SDMML: 5.1-5.2
A Tutorial on
Fisher Information, Ly et al. (2017).
Exercise 1.
Exercise 2.
Exercise 3.