BIOE 505  - Computational Bioengineering

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Date

Topics

Slides

Matlab

Homework
(not graded)

Videos

Aug 22

Aug 24

Random experiments.
Sample space.
Events.
Venn diagrams.
Definitions of probability: statistical

coin_toss_template.m

coin_toss.m

Aug 29

Definitions of probability: inductive or logical.
Combinatorics.
Birthday problem.
Combinatorics: Polya Urn problem.

Aug 31

Axioms of probability.
Conditional probability.
Event independence.
Circuits

Sep 5

Circuits (continued)

Bayes theorem.

Secretary problem.

Simpson's paradox

Sep 7 

Simpson's paradox

Monty Hall problem

Discrete random variables:
PMF, CDF, CCDF,
average, variance, standard deviation, skewness, geometric mean

monty_hall_template.m

monty_hall.m

Sep 12

Random variables: skewness, geometric mean

Discrete distributions: Uniform

The distribution of Ct values of a viral PCR test

uniform_discrete_template.m

uniform_discrete.m

Sep 14

Binomial distribution

Poisson distribution

Genome assembly (start)

poisson_template.m

poisson.m

Sep 19

Genome assembly (continued)

Geometric distribution

geometric_template.m

geometric.m

Sep 21

Mitochondrial Eve

Negative Binomial Distribution

Cancer drivers and passengers

negative_binomial_template.m

negative_binomial.m

hw1_with_solutions.pdf

hw2.pdf

Sep 26

Review of discrete distributions.

Continuous random variables: PDF, CDF, CCDF, mean, variance.

Constant rate process.

Exponential distribution

Sep 28

Constant rate process (continued)

Memoryless property of the exponential distribution

Erlang and Gamma distributions

exponential_template.m

exponential.m

erlang_template.m

erlang.m

Erlang and Gamma 

Log-normal

Oct 3

Work in class on

Group_Project_1

Videos relevant for this project:

Erlang and Gamma 

Log-normal

Oct 5

Gaussian distribution

Standardization

Work in class on

Group_Project_2

Videos relevant for this project:

Gaussian_and_Standardization

Oct 10

Multiple variables:
joint, marginal, conditional probabilities.

Statistical independence of variables

Covariation

Correlation coefficients:
Pearson linear, 
Spearman rank

Work in class on

Group_Project_3

Videos relevant for this project:

Joint, Marginal, Conditional probablities, Statistical indepndence of variables

Covariance and correlations

Oct 12

Linear Functions of Random Variables

Principal Component Ananlysis

Work in class on

Group_Project_4

Videos relevant for this project:

Principal Component Analysis

Oct 17

Descriptive statistics.

Samples, i.i.d. random variables, 

Histograms.
Median, quartiles, boxplot, probability plots

  boxplot_template.m

  boxplot_exercise.m

Oct 19

Central Limit Theorem

Parameter estimators:
method of moments

central_limit_theorem_template.m

central_limit_theorem.m

Oct 24

Sample variance S^2 (unbiased estimator) 

Maximum Likelihood Estimator (MLE)

Confidence Intervals

- with known population variance, sigma^2

moment_estimators_template.m

moment_estimators.m

Oct 26

Confidence Intervals

- for population average with estimated population variance via sample variance,  S^2. Student T-distribution

- for  population variance. Chi-squared distribution.

- for population fraction

confidence_intervals_template.m

confidence_intervals.m

 Oct 31

Hypothesis tested (one- and two-sided).

One sample and two samples hypotheses

Bonferroni correction for multiple hypotheses

Nov 2

Nov 7

Nov 9

expression_table.mat

regression_template.m

Nov 14

m_and_m_analysis_template.m

Nov 16

Multiple Linear Regression.

adjusted R-squared

Use of testing and training samples to avoid overfitting. 

Double descent

regression_multiple_template.m

Nov 28

Supervised and unsupervised machine learning.

Clustering

Gene Set Enrichment Analysis (GSE) of biological functions in gene expression clusters using NCI David

Netwoek analysis: hubs, PageRank, betweenness-centrality

Network visualization using Gephi

coexpression_network_random start.gephi

disease_disease_random_start.gephi

gephi_network_analysis_exercise.pdf

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