Introduction to Quantitative Methods In Biology

Topics

• Familiarity with basic differential equations and their solutions. Ability to model simple relationships between biological variables using differential equations. Ability to manipulate matrices using multiplication and addition. An understanding of powers of matrices and the inverse of a matrix. Familiarity with the use of matrices to model transitions in a biological system with discrete categories. An understanding of basic probability theory including some of the standard univariate random variables, such as the binomial, geometric, exponential, and normal distribution, and how these variables can be used to model biological systems. Ability to calculate probabilities of discrete events using simple counting techniques, addition of probabilities of mutually exclusive events, multiplication of probabilities of independent events, the definition of conditional probability, the law of total probability, and Bayes’ formula, and familiarity with the use of such calculations to understand biological relationships. Ability to calculate means and variances for a sample and relate it to expectations and variances of a random variable. An understanding of sampling and sampling variance. Ability to classify states in discrete time Markov chains, and to calculate transition probabilities and stationary distributions for simple discrete time, finite state-space Markov chains, and an understanding of the modeling of evolutionary processes as Markov chains. Ability to define likelihood functions for simple examples based on standard random variables. An understanding of the principles used for point estimation, hypothesis testing, and the formation of confidence intervals and credible intervals. Ability to implement simple statistical models in R and to use simple permutation procedures to quantify uncertainty. Familiarity with covariance, correlation, ordinary least squares, and interpretations of slopes and intercepts of a regression line. Ability to implement standard and logistic regression models with multiple covariates in R. Familiarity with the assumptions of regression and methods for investigating the assumptions using R. Familiarity with random effects models and ability to implement them in R. Familiarity with ANOVA and ability to implementation it in R. Familiarity with PCA, other methods of clustering, and their implementation in R. Familiarity with one or more methods used in machine learning/statistics such as hidden Markov models, CART, neural networks, and/or graphical models. Ability to carry out various procedures for data visualization in R. Familiarity with functional programming in R and/or Python and ability to define new functions. Ability to work in a Unix environment and manipulating files in Unix. Familiarity with python allowing students to understand simple python scripts.

Official catalogue course objectives and student learning outcomes