Introduction to Bioinformatics
Christopher Lee September 24, 2009
This course is for people who may want to invent new kinds of bioinformatics
1
Bioinformatics is the study of the inherent structure o
Phylogeny Analysis
Christopher Lee
Phylogeny: Reconstructing Evolutionary History
Goal: infer past history that produced a set of modern characters (sequences, typically). Ingredients:
Characters: e
Ancestral Reconstruction & Selection Pressure
Christopher Lee December 3, 2009
Evolutionary Trees as Markov Chains
Assume were given binary tree as a directed graph G with nodes u, and branch lengths
HMM Training: Baum-Welch Algorithm
Christopher Lee December 1, 2009
How to model gene evolution?
atggggctcagcgacggggagtggcagcaggtgctgaacgtctgggggaa atggggctcagtgatggggagtggcagatggtgctgaacatctgggggaa a
Chapter 3
A Recipe for Inference
3.0.3 Pure Inference
n
The projection operation is very useful for Bayesian inference when expressed in the following form: Pr(A|Bi ) Pr(Bi ) = Pr(A)
i=0
This enables
Chapter 1
What is Inference?
I think the most interesting question in the world is how we think. This is one of the basic questions of life but how well do we understand it? Our difculty is not a shor
C260A Lecture 6: Measuring Evidence for Single Nucleotide Polymorphism
Christopher Lee October 15, 2009
Single Nucleotide Polymorphisms
Every persons genome is unique; on average there is one letter d
C260A Lecture 5: Probabilistic Modeling
Christopher Lee October 7, 2009
Dening Events vs. Variables event: a subset of our total probability space S. p(e) = a number. variable: some slicing of S into
C260A Lecture 4: Probabilistic Modeling
Christopher Lee October 6, 2009
Conditional Probability
p(S C) p(S|C) = p(C)
Call S the subject and C the condition variable.
1
Draw a Venn diagram of the Monty
C260A Lecture 3: A Recipe for Inference
Christopher Lee October 1, 2009
Whats the probability the sun will rise tomorrow?
Pierre-Simon Laplace worked out a clever solution to this problem.
1
The Binom
C260A Lecture 2: Intro to Inference
Christopher Lee September 29, 2009
What is the fundamental difference between math and science?
1
A Diagnostic Test (T) for a Disease (D)
T + total T
D+ 1 9 10 960
Distance Metrics
Cartesian Distance
D( x, y ) = | x i y i |2
i
Manhattan Distance D( x, y ) = | x i y i |
i
Triangle inequality: Dab+DbcDac Additive distances:
D( x, y ) =
d
x y
ij
Clock-like: D(x