# Date Topics Slides Matlab Homework (not graded) Videos 1 Aug 22 Class logistics.  Two reasons we need probability and statistics in computational bioengineering. Lecture_1 2 Aug 24 Random experiments. Sample space. Events. Venn diagrams. Definitions of probability: statistical Lecture_2 coin_toss_template.m coin_toss.m 3 Aug 29 Definitions of probability: inductive or logical. Combinatorics. Birthday problem. Combinatorics: Polya Urn problem. Lecture_3 4 Aug 31 Axioms of probability. Conditional probability. Event independence. Circuits Lectire_4 circuit_template.m 5 Sep 5 Circuits (continued) Bayes theorem. Secretary problem. Simpson's paradox Lecture_5 6 Sep 7 Simpson's paradox Monty Hall problem Discrete random variables: PMF, CDF, CCDF, average, variance, standard deviation, skewness, geometric mean Lecture_6 monty_hall_template.m monty_hall.m hw1.pdf 7 Sep 12 Random variables: skewness, geometric mean Discrete distributions: Uniform The distribution of Ct values of a viral PCR test Lecture_7 uniform_discrete_template.m uniform_discrete.m 8 Sep 14 Binomial distribution Poisson distribution Genome assembly (start) Lecture_8 poisson_template.m poisson.m 9 Sep 19 Genome assembly (continued) Geometric distribution Lecture_9 geometric_template.m geometric.m 10 Sep 21 Mitochondrial Eve Negative Binomial Distribution Cancer drivers and passengers Lecture_10 negative_binomial_template.m negative_binomial.m hw1_with_solutions.pdf hw2.pdf 11 Sep 26 Review of discrete distributions. Continuous random variables: PDF, CDF, CCDF, mean, variance. Constant rate process. Exponential distribution Lecture_11 12 Sep 28 Constant rate process (continued) Memoryless property of the exponential distribution Erlang and Gamma distributions Lecture_12 exponential_template.m exponential.m erlang_template.m erlang.m hw2_with_solutions.pdf Log-normal 13 Oct 3 Work in class on Group_Project_1 Videos relevant for this project: Log-normal 14 Oct 5 Gaussian distribution Standardization Work in class on Group_Project_2 Videos relevant for this project: Gaussian_and_Standardization 15 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 cancer_wdbc.mat 16 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 17 Oct 17 Descriptive statistics. Samples, i.i.d. random variables,  Histograms. Median, quartiles, boxplot, probability plots Lecture_17 18 Oct 19 Central Limit Theorem Parameter estimators: method of moments Lecture_18 central_limit_theorem_template.m central_limit_theorem.m hw3.pdf 19 Oct 24 Sample variance S^2 (unbiased estimator)  Maximum Likelihood Estimator (MLE) Confidence Intervals - with known population variance, sigma^2 Lecture_19 moment_estimators_template.m moment_estimators.m 20 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 Lecture_20 confidence_intervals_template.m confidence_intervals.m hw3_with_solutions.pdf 21 Oct 31 Hypothesis tested (one- and two-sided). One sample and two samples hypotheses Bonferroni correction for multiple hypotheses Lecture_21 dark_vs_milk_chocolate_analysis_template.m 22 Nov 2 Midterm review Lecture_22 Nov 7 MIDTERM 23 Nov 9 Linear regression  (single variable) Lecture_23 expression_table.mat regression_template.m 24 Nov 14 Chi-squared Goodness of Fit Test. M&M colors exercise Lecture_24 m_and_m_analysis_template.m hw4.pdf 25 Nov 16 Multiple Linear Regression. adjusted R-squared Use of testing and training samples to avoid overfitting.  Double descent Lecture_25 regression_multiple_template.m 26 Nov 28 Supervised and unsupervised machine learning. Clustering Lecture_26 clustering_template.m hw4_with_solutions.pdf 27 Nov 30 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 Lecture_27 coexpression_network_random start.gephi disease_disease_random_start.gephi gephi_network_analysis_exercise.pdf hw5.pdf 28 Dec 5 Final exam review Lecture_28 hw5_with_solutions.pdf FINAL EXAM