Statistics

This course examines the fundamentals of Bayesian inference, including the specification of prior and posterior distributions, Bayesian decision theoretic concepts, the ideas behind Bayesian hypothesis tests, model choice and model averaging, the capabilities of several common model types, such as hierarchical and mixture models. It also looks at the ideas behind Monte Carlo integration, importance sampling, rejection sampling, Markov chain Monte Carlo samplers such as the Gibbs sampler and the Metropolis-Hastings algorithm, and use of the WinBuGS posterior simulation software.

This course provides an overview of data management architectures and analytics procedures aimed at organizing, describing, and modeling big data, both structured and unstructured. The course discusses both technical aspects of data management/analytics and topics related to analysis managerial evaluation including how to translate the outputs into meaningful business insights. The course examines topics including relational databases such as OLTP, Data warehouse, and SQL language; big data and NoSQL databases, distributed file system, Hadoop, Spark, and Data Lake concept; data understanding and data preparation; models and statistical techniques applied to Big Data; regression and classification trees; ensemble methods (random forest and boosted trees); logistic regression; supervised artificial neural networks; models' performance evaluation; big data ingestion and management; data preparation and cleaning; machine learning algorithms application; and machine learning model evaluation. The course requires students have a basic understanding of descriptive and inferential statistics and basic computer skills as a prerequisite.

In this course, students learn the skills to write Python code to implement statistical and machine learning algorithms that can be applied in a range of contexts. Each week the course covers an aspect of computer coding using examples and exercises that drawn on bioscience contexts. Topics will include: probability, maximum likelihood, Bayes theorem, supervised learning: regression and classification, unsupervised learning: dimensionality reduction and clustering, model evaluation and improvement, reinforcement learning, and neural networks and deep learning.

Does income inequality lead to political polarization? Is social class related to parenting? What accounts for income inequality between ethnic groups in the labor market? We will use statistics and programming to answer these questions throughout the semester. This course introduces tools to summarize the characteristics of data and offers methods to draw conclusions about population from samples. This course focuses on applying statistics, analyzing data, and interpreting results. Although very basic calculation skills are required (e.g., +, -, ×, ÷, √), you do not need further mathematic knowledge to be successful in this class. 

This course offers an introduction to probability theory for students with knowledge of elementary calculus. The course covers not only the mathematics of probability theory but works through diverse examples to illustrate the wide scope of applicability of probability, such as in engineering and computing, social, and management sciences. Topics covered include counting methods, sample space and events, axioms of probability, conditional probability, independence, random variables, discrete and continuous distributions, joint and marginal distributions, conditional distribution, independence of random variables, expectation, conditional expectation, moment generating function, central limit theorem, and weak law of large numbers.

The course provides an introduction to the ideas underlying the calculation of risk from a Bayesian and frequentist standpoint, and the structure of rational, consistent decision making. It is primarily intended for third and fourth year undergraduate students and taught postgraduate students registered on the degree programs offered by the Department of Statistical Science.