Section 3 Masters Degree Requirements
Students work toward Masters Degrees in Probability and Statistic in a number of different ways. It depends on which program you are in, what is your background coming into statistics, and what your career goals are.
Doctoral students in Statistics who do not already have a MA in statistics will often complete the MA in Mathematical Statistics which can be satisfied by completing the Core Courses and then passing two Qualifying exams along with 6 additional units of coursework.
Masters Students in Statistics who are working towards an MA in Applied Statistics as a terminal degree. It makes some difference in choosing your courses as to what your goals are. If you are interested in applying to PhD programs after you have completed the MA, then you may want to take some of the other doctoral core courses (207ABC, 213ABC) in order to demonstrate your aptitude. If you are more interested in directly finding employment in industry, then focusing on more applied courses is recommended.
BS/MS Students in Actuarial Science have a completely separate set of requirements for the joint degree. Only UCSB undergraduates are elgible to join this program.
Doctoral Students from other Departments frequently are looking for an MA in Applied Statistics in addition to their doctoral degree. They should look to complete the Course Requirements for MA in Applied Statistics.
You can consult the Department Grad Handbook for some alternative degree options.
3.1 Course Requirements for MA in Applied Statistics
This is an outline of the requirements for the most common paths towards a terminal MA degree. This information is relevant to either the Applied Statistics or Data Science track in the MA degree. If you have questions or would like to see if an exception can be made to these requirements, the Faculty Graduate Advisor is happy to discuss that with you.
3.1.1 Required Courses
There are 5 require courses within each option for the MA. All of these required courses must be passed with a letter grade of B or better.
- 220A,B,C Advanced Statistical Methods
Prerequisites: PSTAT 126 Regression, PSTAT 122 Designed Experiments, Math 108A Linear Algebra
Applied statistical techniques including graphical methods; estimation and inference; diagnostics; and model selection. R/SAS Computation.
- Regression; analysis of variance of fixed, random, and mixed effects models; analysis of covariance; and experimental design.
- Generalized linear models; log-linear models with application to categorical data; and nonlinear regression models.
- Multivariate analysis. Topics selected from factor analysis; canonical correlation analysis; classification and discrimination; clustering; and data mining.
- 230 Statistical Consulting
Prerequisites: 220ABC, can be taken concurrently with 220C
Students participate in the discussions and consulting projects in the statistics laboratory. They are assigned project(s) to work on and write a report on statistical aspects of the project.
PSTAT 230 features a major project on a real data set which will be assessed to complete the MA Applied Statistics Area Requirement as a sort of combination of a qualifying exam and Masters thesis.
3.1.1.1 Applied Statistics Track Requirement
This course is required if you are following the Applied Stats option:
122 Design and Analysis of Experiments
An introduction to statistical design and analysis of experiments. Covers: principles of randomization, blocking and replication; fixed, random and mixed effects models; block designs, factorial designs and nested designs; analysis of variance and multiple comparison.
3.1.1.2 Data Science Track Requirement
This course is required if you are pursuing the Data Science option:
234 Statistical Data Science
Prerequisites: 126 Regression , 131/231 Machine Learning
Overview and use of data science tools in R and/or Python for data retrieval, analysis, visualization, reproducible research and automated report generation. Case studies will illustrate practical use of these tools.
3.1.2 Electives
You must also complete 5 elective courses plus two additional units. At least 4 of the courses are required to be graduate level courses in the department (specifically, PSTAT 2xx courses.)
Restricted Electives in the Data Science Track
If you are working on the Data Science option then you must complete at least 2 out of these 5 elective courses:
231 Introduction to Statistical Machine Learning
Prerequisite: 126 Regression
Statistical Machine Learning is used to discover patterns and relationships in large data sets. Topics will include: data exploration, classification and regression trees, random forests, clustering and association rules. Building predictive models focusing on model selection, model comparison and performance evaluation.232 Computational Techniques in Statistics
Prerequisite: 126 Regression
Explores computationally-intensive methods in statistics. Topics covered include Fundamentals of Optimization, Combinatorial Optimization, EM algorithm, Monte Carlo simulation, Markov Chain Monte Carlo methods.235 Big Data Analytics
Prerequisite: 126 Regression, 231, and 234
Basics in distributed data storage, retrieval, processing and cloud computing. Overview of methods for analyzing big data from both high dimensional statistics and machine learning - topics chosen from penalized regression, classification/clustering, dimension reduction, random projections, kernel methods, network clustering, graph analytics, supervised and unsupervised learning.237 Uncertainty Quantification
Prerequisite: 126 Regression
Statistical and machine learning approaches to computational uncertainty quantification in mathematical models with applications to computer simulations, images, and time-series, spatio-temporal, and functional data. Topics include computer model emulation and design, reproducing kernel Hilbert spaces, Gaussian processes, dynamic systems, the Kalman filter, inverse problems, and Bayesian optimization.215A Bayesian Inference
Prerequisite: 220A (may be taken concurrently)
Fundamentals of the Bayesian inference, including the likelihood principle, the discrete version of Bayes theorem, prior and posterior distributions, Bayesian point and interval estimations, and predictions. Bayesian computational methods such as Laplacian approximations and Markov Chain Monte Carlo (MCMC) simulation.
Suggested Elective
263 Research Seminars in Probability and Statistics (1 unit)
Weekly research talks presented by faculty, visiting scholars, and invited speakers on current research topics. This 1 unit course may be repeated to give you 2 units towards the 22 elective units.
Regularly Offered Electives in Applied Statistics
225 Linear and Nonlinear Mixed Effects Models
Prerequisite: 220A
Linear and nonlinear mixed effects models. Topics include fixed effects, random effects, several size experimental units, design structure, treatment structure, randomized block design, nested design, split plot design, repeated measures, growth curves, longitudinal and spatial data, BLUP, ML, and REML estimates.226 Nonparametric Regression and Classification Methods
Prerequisite: 220A
Introduction to some statistical regression and classification techniques including kernel smoothing, smoothing splines, local-linear regression, generalized additive models, neural networks, wavelets, decision tree and nearest neighbor methods.227 Bootstrap and Resampling Methodology
Prerequisite: 207B and 220A
Parametric and nonparametric bootstrap simulation; confidence limit methods; resample significance tests, including Monte Carlo and bootstrap; resampling for improved regression model selection and prediction; diagnostics for bootstrap validity228 Spline Smoothing and Applications
Prerequisite: 207C and 220A
Model building, multivariate function estimation and supervised learning using reproducing kernel Hilbert space, regularization and splines. Smoothing splines for Gaussian and non-Gaussian data. Bayesian models and data-driven turning parameter selection. Emphasis on methodology, computation and application.236 Spatial Statistics
Prerequisite: 126 Regression, 274 Time Series
Spatial Covariance Functions, Variograms, Kriging, Gaussian Processes, Estimation Methods and Uncertainty Quantification. Stationary and Non-Stationary Models, Selected Topics from Non-Gaussian Spatial Models, Spatial Point Processes, Areal Data Models, Spatial Networks, Hierarchical Models, Spatio-Temporal Models, and Recent Advances.274 Time Series
Stationary and non-stationary models, seasonal time series, ARMA models: calculation of ACF, PACF, mean and ACF estimation. Barlett’s formula, model estimation: Yule-Walker estimates, ML method. Identification techniques, diagnostic checking, forecasting, spectral analysis, the periodogram. Current software and applications.275 Survival Analysis
Prerequisite: 220A
Basic concepts: survival functions, hazard functions, cumulative hazard functions, and censoring types. Kaplan-Meier and Nelson-Fleming-Harrington estimates. Log-rank tests. Exponential and Weibull models. Cox proportional hazards and accelerated failure time regression models. Current software and applications.
Other Graduate Courses
Other 200 level courses such as 207ABC, 213ABC, and 23x courses which are not required are also very good options for completing the elective requirements.
Undergraduate Courses
Only 4 units of 100-level undergraduate courses can be counted towards the degree (in addition to the 4 units from 122 for those in the Applied track.) However, the undergraduate courses offer an opportunity to fill in any holes in your background, and they can give you an introduction to a wider range of topics.
Some of our course are generally given cross-listed with a graduate level course (174/274, 131/231, 134/234, 135/235, etc.) You are advised to take the 200-level version of these courses.
- 120 A,B,C Introduction to Probability and Statistics
PSTAT 120ABC are not eligible to be counted as electives towards the MA degree, but they are essential background for almost all of our other courses.
- Concepts of probability; random variables; combinatorial probability; discrete and continuous distributions; joint distributions, expected values; moment generating functions; law of large numbers and central limit theorems.
- Distribution of sample mean and sample variance; t, chi-squared and F distributions; summarizing data by statistics and graphs; estimation theory for single samples: sufficiency, efficiency, consistency, method of moments, maximum likelihood; hypothesis testing: likelihood ratio test; confidence intervals
- Hypothesis tests for means of independent samples and paired data; likelihood ratio tests; nonparametric hypothesis tests: sign, rank, and Mann-Whitney tests; chi-squared goodness-of-fit tests and contingency tables; Bayesian methods of estimating parameters and credible intervals
126 Regression
Linear and multiple regression, analysis of residuals, transformations, variable and model selection including stepwise regression, and analysis of covariance. The course will stress the use of computer packages to solve real-world problems.127 Advanced Regression
Prerequisite: 126
Exponential family and generalized linear models including logistic and Poisson regression, nonparametric regression, including kernel, spline and local polynomials, and generalized additive models. Other topics as time allows: regularization, neural networks, and support vector machines. Emphasis will be on concepts and practical applications.105 Nonparametric Statistics
Basic statistical methods that derive from empirical probability functions. Goodness of fit tests: Chi-squared, Kolmogorov-Smirnov, and related tests Density estimation via histograms and kernels. Kernel estimation techniques in nonparametric regression. Simulation and bootstrap techniques115 Bayesian Data Analysis
Prerequisite: 126
An introduction to the Bayesian approach to statistical inference, its theoretical foundations and comparison to classical methods. Topics include parameter estimation, testing, prediction and computational methods (Markov Chain Monte Carlo simulation). Emphasis on concepts, methods and data analysis. Extensive use of the R programming language and examples from the social, biological and physical sciences to illustrate concepts.123 Sampling Techniques
An elementary development of the statistical methods used to design and analyze sample surveys. Basic ideas: estimates, bias, variance, sampling and nonsampling errors; simple random sampling with and without replacement; ratio and regression estimates; stratified sampling; systematic sampling; cluster sampling; sampling with unequal probabilities, multistage sampling. Examples from various fields will be discussed to illustrate the concepts including sampling of biological populations, opinion polls, etc.160 A,B Stochastic Processes
Discrete probability models. Review of discrete and continuous probability. Conditional expectations. Simulation techniques for random variables. Discrete time stochastic processes: random walks and Markov chains with applications to Monte Carlo simulation and mathematical finance. Introduction to Poisson process.
Continuous models. Continuous time stochastic processes: Poisson process, Markov chains, Renewal process, Brownian motion, including simulation of these processes. Applications to Black-Scholes model, insurance and ruin problems and related topics.175 Survival Analysis
Prerequisite: 126
Properties of survival models, including both parametric and tabular models; methods of estimating them from both complete and incomplete samples, including the actuarial, moment and maximum likelihood estimation techniques, and the estimation of life tables from general population data.
Courses from Other Departments
Students can use courses taken in other departments to count towards the 6 elective units. These courses must receive prior approval from the Graduate Advisor. The general guideline that we use is that the course must have some quantitative content. It also must cover material that is not covered in an existing PSTAT course.
For instance, a Biochemistry course would not be allowed, but Computational Biology might be. Also, an Education School course on regression would not be allowed because that is material that is likely in PSTAT 126 and 220A, but a course on latent variable models might be because it is about a mode of data analysis that is different to the standard PSTAT approach.
Note, if you are pursuing an MA in addition to a degree in another department at UCSB, then any course may only be applied to the requirements of one of those degrees.