Inroduction to aim, scope and content of the course.
Syllabus.
The importance of critical thinking and reasoning.
Overview of coursework
requirements (six assignments,
two exams,
one presentation,
one final report
and class summaries assigned at random)
Probability as an essential ingredient of the course.
Course combines qualitative and quantitative aspects.
The Rootclaim website as a model.
How to ask investigative questions.
Different types of questions:
about definitions,
causal relationships,
events in space and time,
policy questions.
Examples of topics for investigative questions:
Morandi bridge collapse in Genoa, Italy;
Monsanto verdict.
Answering questions and formulating hypotheses.
Going over assignments
#1
and
#2.
Class summary from a student.

Week 2: Sept 3 - no class: Labor day

Office hours on
Wed Sept 5 in CA-365
from noon to 5 PM.
Please stop by to hand in
assignment #1.
We will read it and discuss it together so
that you'll be prepared to do assignment
#2.

Week 3: Sept 10 - no class: Rosh Hashanah

Even if today it's a holiday,
please work on assignment
#2.

Week 4: Sept 17

Review of past assignments #1
and
#2.
Going over new assignment #3.
Discussion of types of evidence:
eywitness testimonies,
scientific studies,
photgraphic evidence,
video evidence,
etc.
Relationship between evidence and hypotheses.
Evidence for/against a hypothesis.
How to assess the reliability of a piece of evidence.
How to summarize, present and document your evidence.
Class summary from a student.

Week 5: Sept 24

Review of assignment #3.
Intuitive ways to weigh evidence.
Student presentations for Stage 1, 2 and 3.
Importance of probability theory to handle uncertainity.
Class summaries from students.

PART 2: Probability Theory

Week 6: Oct 1

Basics of probability theory.
Role of probability in your investigative progejct.
How probable is your hypothesis given the evidence you've collected?
Examples of probability
(video):
tossing a coin;
rollign a dice;
picking names from a deck of cards.
Probability as relative frequency.
Space of equiprobable outcomes.
Probability law:
Pr(A)= #(successful outcomes where A obtains)/#(equiprobable outcomes).
Relative frequency simulator
.
Probability as betting behaviour
and evidence-based subjective estimate.
Sets and Venn diagrams
(video 1
and
video 2):
union, intersection, complementation.

Intro to Probability
(pdf)
Probability with Khan Academy
(link)

Week 7: Oct 8, no class: Columbus day

Keep studying probability theory!

Week 8: Oct 15

Class canceled due to medical emergency.

Week 9: Oct 22

Online class.
Review of set-theoretic operations (video).
How to calculate propabilities and basic properties of probability (video).
Conditional Probability (video 1 and video 2).
Sample exam (pdf) and
solutions (pdf).
Discussion of sample exam: (quest. a,
quest. b and
quest. c).
Distinction between Pr(A|B) and Pr(B|A) (see sample exam
quest. e).
Take-home exam #1 (pdf)
and data (pdf) DUE next Monday.

Week 10: Oct 29

Bayes's theorem (handout).
Mathematical statement of the theorem.
Diagnostic test example.

Week 11: Nov 5

Reveiw of take-home exam #1.
Solutions (pdf).
Keep in mind the difference between Pr(A|B) and Pr(B|A).
More on Bayes's theorem.
Mathematical formulation of the theorem.
Medical diagnosis example.
Witness testimony example.

Handout on Bayes's theorem
(pdf)
Videos on Bayes's theorem
(video 1 and
video 2)

Week 12: Nov 12

More applications of Bayes's theorem, for example, spam filtering (Wikipedia).
Discussion of sample exam (pdf)
and solutions (pdf).
Take-home exam #2 (pdf) DUE next Monday.

PART 3: Applying Probability

Week 13: Nov 19

How to assign prior probabilities to hypotheses.
Base rates.
Objective/subjective estimates.
The Collins case (handout).
Examples from Rootclaim:
see
Usain Bolt
and PEDs.
Stage 4 (pdf) DUE next Monday.

Week 14: Nov 26

Evidence given hypothesis, Pr(E|H).
Not to be confused with hypothesis
given evidence, Pr(H|E).
Relevance of the distinction
for your investigative project.
Stage 5 (pdf) DUE next Monday.

Week 15: Dec 3

Bayes's theorem applied.
Posterior probabilities of each hypthesis given all the pieces of evidence combined,
say, Pr(H|E1 & E2 & E3 & ... & En).
Using probabilistic graphs (known as Bayesian Networks) to compute posterior probabilities.
Program Genie by
BayesianFusion to make calculations easier.
Guide on how to use Genie to costruct probabilistic graphs that connect
evidence and hypotheses
(video).
Stage 6 (pdf) DUE next Monday.