# Statistics

- Department Information
- Program Description
- M.S. in Statistics
- Other Degree Requirements
- Certificate Programs
- Post-baccalaureate Courses
- Graduate Courses

## Department Information

**Department of Statistics and Biostatistics College of Science Office: North Science 229 Phone: (510) 885-3435**

*Professors*

Eric A. Suess (Chair), Ph.D. University of California, Davis

Mitchell R. Watnik, Ph.D. University of California, Davis

*Associate Professors*

Lynn Eudey, Ph.D. University of California, Berkeley

Shenghua (Kelly) Fan, Ph.D. University of Minnesota

Joshua D. Kerr, Ph.D. University of California, Davis

YanYan Zhou, Ph.D. University of Maryland

*Assistant Professor*

Ayona Chatterjee, Ph.D. University of Edinburgh (United Kingdom)

*Graduate Coordinator:* Lynn Eudey

## Program Description

The Department of Statistics and Biostatistics offers graduate study leading to the degree Master of Science in Statistics. The program is flexible in order to serve the needs of students with varying backgrounds (including statistics, mathematics, computer science, engineering, business, economics and other quantitative fields) and with different career objectives. The program includes options in Applied Statistics, Computational Statistics, Mathematical Statistics, and Actuarial Science. All students are expected to master a wide variety of applied statistical, computational, and probabilistic techniques and the theoretical foundations upon which these techniques are based. Students are expected to be familiar with recent developments in the field and to be able to use the statistical literature to learn new techniques and theories throughout their professional careers. In addition to the general requirements stated elsewhere in this catalog, students must satisfy the departmental requirements stated in the following paragraphs.

Students interested in pursuing an M.S. degree in Biostatistics should see the Biostatistics chapter in the university catalog.

**Student Learning Outcomes**

Students graduating with an M.S. in Statistics from Cal State East Bay will be able to:

- Apply statistical methodologies, including a) descriptive statistics and graphical displays, b) probability models for uncertainty, stochastic processes, and distribution theory, c) hypothesis testing and confidence intervals, d) ANOVA and regression models (including linear, and multiple linear) and analysis of residuals from models and trends.
- Derive and understand basic theory underlying these methodologies
- Formulate and model practical problems for solutions using these methodologies
- Produce relevant computer output using standard statistical software and interpret the results appropriately
- Communicate statistical concepts and analytical results clearly and appropriately to others; and
- Understand theory, concepts, and terminology at a level that supports lifelong learning of related methodologies.

### Admission Requirements

- A baccalaureate degree or equivalent.
- Differential and Integral Calculus, including multiple integration and infinite series (MATH 1304, 1305, 2304).
- Departmental approval.
- For "Classified Graduate" status, fulfillment of the University Writing Skills Requirement. For information on meeting the University Writing Skills Requirement, see the Testing Office website at www.csueastbay.edu/testing or call 510.885.3661.

In addition to the above minimal requirements for admission, if students have some of the following background they will be at an advantage both as to selection for admission to the program and optimal progress toward the degree if admitted:

- basic statistics and probability at the level of STAT 3401, 3502 (or beyond)
- additional mathematics at the level of MATH 2101 (or beyond)
- knowledge of a computer programming language
- experience in a setting where studies or experiments are conducted for the collection of data.

### Advancement to Candidacy Requirements

- Completion of at least 15 quarter units of approved coursework beyond the baccalaureate, with an average of "B" (3.0) or higher.
- Departmental approval.

## M.S. in Statistics

### Degree Requirements

Successful completion of the following unit, grade, and course requirements.

**Unit and Grade Requirements**

The M.S. in Statistics program consists of at least 48 quarter units of approved upper division and graduate work. The university requirement for the minimum number of 6000-level units applies. All work applied toward the 48 units must be at an average grade of "B" (3.0) or higher. No graduate-level required course may be at a grade below "B-."**Course Requirements (48 units)**

Elective courses referred to in section 2 below must be chosen with advanced written approval of an advisor.*Required Graduate Level Courses (28 units)*- STAT 6204 Probability Theory (4)
- STAT 6205 Statistical Theory (4)
- STAT 6304 Advanced Statistical Inference (4)
- STAT 6305 Analysis of Variance Models (4)
- STAT 6501, 6502 Mathematical Statistics I and II (4, 4)
- STAT 6509 Theory and Application of Regression (4)

*Elective Courses (20 units)*

Select one of the options below or complete 20 units of advanced courses chosen with the advanced written approval of an advisor:*Option in Applied Statistics (20 units)*

Topics include a broad background in the practice of statistics, including data modeling and the use of computing packages for data analysis.*Required Courses:*

- Choose at least one course from:
- STAT 6250 SAS Programming (4)
- STAT 6260 R Programming (4)

- Additional three to four graduate electives in statistics or biostatistics, approved by a graduate advisor. (12-16)

- Choose at least one course from:
*Option in Computational Statistics (20 Units)*

Topics include regression modeling, multivariate statistics, factor analysis, Monte Carlo simulations, Markov Chain, Monte Carlo methods, bootstrapping, data mining, and other computationally intensive methods.*Required Courses:*

Choose three courses from:- STAT 6250 SAS Programming (4)
- STAT 6260 R Programming (4)
- STAT 6310 Advanced Stochastic Processes and Simulation (4)
- STAT 6515 Advanced Multivariate Analysis (4)
- STAT 6550 Bayesian Statistics (4)
- STAT 6555 Statistical Time Series Analysis (4)
- STAT 6601 Advanced Statistical Computing (4)
- STAT 6610 Data Visualization (4)
- STAT 6620 Statistical Learning with R (4)

Choose two additional courses from those not taken above, or:

- One approved course from STAT 6860-6864 Selected Topics in Graduate Probability and Statistics (4)
- STAT 6865 Mathematical Modeling (4)
- One approved upper-division or graduate level course in computer science (4) (graduate level preferred)

*Option in Mathematical Statistics (20 units)*

Advanced coursework in mathematics is strongly recommended, particularly MATH 3100 Linear Algebra and MATH 3300 Analysis I (real analysis).*Required Courses:*- STAT 6310 Advanced Stochastic Processes and Simulation (4)
- STAT 6401 Advanced Probability I (4)

Choose three additional approved upper-division or graduate level courses in mathematics or graduate level courses in statistics. Ordinarily, these would be at the 4000- or 6000-level. (12)
*Option in Actuarial Science (20 units)*

Graduate coursework in the College of Business and Economics relevant to insurance, finance, and operations research is recommended. Areas of interest include stochastic modeling, force of mortality, life tables, and other topics from actuarial mathematics.

*Required Courses:*

- Choose one course from:
- STAT 6310 Advanced Stochastic Processes and Simulation (4)
- STAT 6401 Advanced Probability I (4)

- One course from STAT 6851-6859 Selected Topics in Actuarial and Decision Science (4)

- One approved 6000-level course from the College of Business and Economics (4)
- One additional approved 6000-level course from statistics (4)

- Choose one course from:

### Comprehensive Examination

Successful completion of a departmental examination is required. This written examination will cover the contents of the courses in the candidate's approved program. Other material may be included, the general nature of which will be specified in advance. The examination is given only in the Fall and Spring quarters, and will cover both applied and theoretical topics.

In each quarter of offering, the department Chair will appoint three or more members of the graduate faculty to administer the examination. Each student will generally take the Comprehensive Examination in the quarter of intended graduation or in the preceding quarter, after consulting with the graduate advisor. Students enrolled in the Actuarial Science Option may substitute a passing grade on an approved national actuarial exam for a designated portion of the comprehensive examination, with the approval of the graduate advisor. The examination committee is the final departmental authority in deciding eligibility to take the examination.

## Other Degree Requirements

In addition to departmental requirements, every student must also satisfy the university requirements for graduation which are described in the Graduate Degree Information chapter in this catalog. These include the 32-unit residence requirement, the five year rule on currency of subject matter, the minimum number of units of 6000-level courses, the 3.00 grade point average, and the University Writing Skills requirement.

## Certificate Programs

### Applied Statistics

The Certificate in Applied Statistics combines basic work in statistics, which is required for many majors and graduate degree programs, with additional coursework in applied statistics. The coursework is designed to broaden the abilities of scientists and social scientists who already have degrees, but who need more training in applying statistics to their research and employment activities.

The minimum required GPA for the awarding of the certificate is 2.0. Consult an advisor in the Department of Statistics and Biostatistics for clarification and interpretation of requirements. The certificate consists of 24-25 units, plus 4-5 units of prerequisites. At least 4 units must be at the graduate level.

*Prerequisites:*

- STAT 2010
- STAT 3010 (requires STAT 1000)
- STAT 3031 (requires MATH 1130)
- STAT 3502 (requires MATH 1305)
- STAT 3601 (requires MATH 1305)

**Core Courses (12-13 units)**

*Applied Statistical Methodology (8-9 units)*

Choose one of the following five pairs of courses:- STAT 2010 Elements of Statistics for Business and Economics (5) and STAT 4000 Analysis of Variance in the Behavioral Sciences (4)
- STAT 3010 Statistical Methods in the Social Sciences (4) and either STAT 4000 Analysis of Variance in the Behavioral Sciences (4) or STAT 6010 Applied Analysis of Variance (4)
- STAT 3031 Statistical Methods in Biology (4) and either STAT 4000 Analysis of Variance in the Behavioral Sciences (4) or STAT 6010 Applied Analysis of Variance (4)
- STAT 3502 Statistical Inference I (4) and STAT 3503 Statistical Inference II (4)
- STAT/ENGR 3601 Statistics and Probability for Science and Engineering I (4) or STAT/ENGR 5601 Introductory Statistics and Probability for Science and Engineering (4) and STAT/ENGR 3602 Statistics and Probability for Science and Engineering II (4)

*Data Analysis Using Statistical Packages (4 units)*- STAT 3900 Data Analysis Using Statistical Packages (4) or STAT 4950 Advanced Statistical Packages for Data Analysis (4). A person skilled in statistical programming may provide evidence of such proficiency and substitute a course for one of these, with the approval of an advisor.

**Electives (12 units)**

Choose from the following courses not taken above:- ENGR/STAT 5300 Quality Engineering (4)
- ENGR/STAT 6300 Applied Quality Assurance (4)
- STAT 3050 Statistics: from Data to Decisions (4)
- STAT 3415 Introduction to Decision Theory (4)
- STAT 3510 Sampling Procedures for Surveys (4)
- STAT 3910 Statistical Software Usage (4) or STAT 4910 Advanced Statistical Package Usage (4)
- STAT 4515 Applied Multivariate Analysis (4) or STAT 6515 Advanced Multivariate Analysis (4)
- STAT 4601 Regression or STAT 6509 Theory and Application of Regression (4)
- STAT 4603 Operations Research II (4)
- STAT 4610 Introduction to Nonparametric Statistical Methods (4)
- STAT 4860-69 Undergraduate Seminar (4)
- STAT 6010 Applied Analysis of Variance (4)
- STAT 6011 Statistical Modeling for Management and Economics (4)
- STAT 6020 Statistical Methods in Clinical Trials (4)

### Mathematical Statistics

The Certificate in Mathematical Statistics is designed to enhance a student's understanding of theoretical statistics and probability in preparation for employment in the engineering, information science, and technology sectors. The certificate also prepares students for further graduate study.

The minimum required GPA for the awarding of the certificate is 3.0. Consult an advisor in the Department of Statistics and Biostatistics for clarification and interpretation of requirements. The certificate consists of 16 graduate level units, plus any necessary prerequisites. All required courses are cross-listed with Mathematics.

**Prerequisites**

- STAT 6401 requires MATH 3300 and either STAT 3402 or 4401
- STAT 6501 requires MATH 3300 or MATH 3100, and STAT 6205 or graduate standing in mathematics
- STAT 6510 requires MATH 2101 and STAT 3503

**Core Courses (12 units)**- STAT 6401 Advanced Probability I (4)
- STAT 6501 Mathematical Statistics I (4)
- STAT 6502 Mathematical Statistics II (4)

**Electives (4 units)**

*Choose at least one course from the following (advisor approval required):*- STAT 6510 Analysis of Variance (4)
- STAT 6860-69 Selected Topics in Probability and Statistics (4)

## Post-baccalaureate Courses

Course Number | Course Information |
---|---|

5300 |
Quality Engineering (4)(See ENGR 5300 for course description.) |

5601 |
Introductory Statistics and Probability for Science and Engineering (4)Basic probability rules (independence, Bayes' Theorem), distributions (binomial, Poisson, normal, exponential), reliability. Descriptive, inferential statistics (control charts, estimation, hypothesis testing: one, two samples), correlation, regression. Emphasizes: computer analysis, simulation; science, engineering applications. Prerequisite: MATH 1305 or departmental approval. Not open to students with credit for STAT/ENGR/MATH 3502. Cross-listed with ENGR 5601. |

## Graduate Courses

Course Number | Course Information |
---|---|

6010 |
Applied Analysis of Variance (4)Elementary analysis of variance including multiple comparisons. Factorial analysis of variance, interactions, repeated measures designs, random effects designs. Computer-facilitated analyses. Analysis of real data and written report required. Prerequisites: STAT 3010, 3031, or 3502. Not for credit in Statistics M.S. degree. |

6011 |
Statistical Modeling for Management and Economics (4)Concepts in statistics for management and economics. Probability and statistical models. Rare events, waiting time, qualitative and quantitative models. Bayes theorem. Estimation, inference. Linear and nonlinear models. Emphasis on computer estimation of models with statistical analysis of errors and attention to model assumptions. Restricted to post-baccalaureate students. Co-requisite: MATH 1810. Not for credit toward M.S. in Mathematics or Statistics. |

6020 |
Statistical Methods in Clinical Trials (4)Experimental designs, statistical analyses, and clinical-scientific-regulatory issues common to clinical trials research. Includes writing analysis plan, conducting statistical analysis meeting constraints of regulatory agencies, reporting results, and data monitoring. Prerequisites: STAT 3503, 4000, or 6010. Not for credit in Statistics M.S. degree. |

6059 |
Advanced Statistical Methods Using Computing Packages (4)Using computer packages (e.g., SPSS) and interpreting output applied to social science and education. Data preparation, descriptive statistics, graphs, checks for normality, t-tests, F-tests, ANOVA, cross tabulations, chi-squared tests, and correlation. Report preparation. Prerequisites: STAT 2010, 3010, 3031, or STAT/MATH 3502; postbaccalaureate/graduate standing. Not for credit in Statistics graduate program. |

6204 |
Probability Theory (4)Theory of probability. Random variables; joint, marginal, conditional distributions; important distributions (binomial, Poisson, normal, etc.); moments; moment generating functions. Multivariate distributions. Inequalities; limit theorems. Multidimensional transformations; derivation of random variables. Prerequisite: MATH 2304 or admission to the graduate program. |

6205 |
Statistical Theory (4)Maximum likelihood and least squares estimation, applications to one-sample, two-sample and regression problems, hypothesis testing, confidence intervals, significance level, bias, precision. Prerequisite: Stat 6204. A-F grading only. |

6250 |
SAS Programming (4)Professional SAS programming techniques. Data management and processing. Data integrity. Graphical presentation of data. Data reporting techniques. Topics in applied statistics and biostatistics. Introduction to SAS data step, SAS Macros, SAS Reports, SAS SQL, and other relevant programming topics. Report Writing. Prerequisites: Current enrollment or completion of a graduate level course in statistics. |

6260 |
R Programming (4)Data input, data output, data manipulation, use of libraries, simulation, data analysis methods, programming interfaces, graphics, functions using R. Prerequisites: STAT 6304 or consent of instructor. |

6300 |
Applied Quality Assurance (4)(See ENGR 6300 for course description.) |

6304 |
Advanced Statistical Inference (4)Random variables, sampling distributions, conditional probability. Expectation. Estimation, method of moments, maximum likelihood. Confidence intervals. Hypothesis testing. Computer-aided computations and simulations. Topics include: t-tests, correlation, regression, proportions, chi-squared, ANOVA, nonparametrics, bootstrapping. Prerequisite: MATH 1305 or admission to graduate program. |

6305 |
Analysis of Variance Models (4)Models for factorial designs: expected mean squares, random effects, nesting, power/sample size, missing data, ANOVA. Model assessment. Computer-aided analysis. Report writing. Prerequisite: STAT 6304. |

6310 |
Advanced Stochastic Processes and Simulation (4)Theory of stochastic models. Markov chains: classification, limiting behavior. Continuous-time Markov processes: Poisson, birth-death. Simulations of processes and probability modeling. May include: additional limit theorems, queues, renewal theory, applications. Prerequisite: STAT 6205. |

6401 |
Advanced Probability I (4)Advanced treatment of probability theory and its applications. May include: conditioning, generating/characteristic functions, modes of convergence, limit theorems, renewal theory, Markov processes, combinatorial techniques, measure and integration. Prerequisites: MATH 2304 and either STAT 3402 or 4401; or admission to graduate program and STAT 6204. Cross-listed with MATH 6401. |

6501, 6502 |
Mathematical Statistics I, II (4 units each)Theory of point and interval estimation and hypothesis testing, from the Neyman-Pearson point of view. May include: decision theory, non-parametric inference, sequential analysis, multivariate analysis, robustness, Bayesian methods, computer intensive methods. Prerequisites: STAT 6205 or graduate standing in mathematics. Cross-listed with MATH 6501, 6502. |

6509 |
Theory and Application of Regression (4)Theory of least squares in model fitting. Computational methods in regression, including variable selection, ANOVA and ANCOVA. Model assessment, graphical techniques and assumption checking. Computer-assisted analysis. Report writing. Prerequisite or co-requisite: STAT 6305. A-F grading only. |

6510 |
Analysis of Variance (4)The theory and application of the general linear model, the analysis of variance and covariance, application of generalized inverses and decomposition theorems from linear algebra. Prerequisites: MATH 2101, and either STAT 3503 or STAT 6305. Cross-listed with MATH 6510. |

6511 |
Advanced Applied Econometrics (4)(See ECON 6511 for course description.) |

6515 |
Advanced Multivariate Analysis (4)Advanced, computer-intensive applications of multivariate analysis. Applications of linear algebra. Topics may include ANOVA, canonical correlation, discriminant functions, factor/cluster/spatial analysis. Emphasis on actual data, report writing. Prerequisites: STAT 6305, and STAT 4950 or 6250, and MATH 2101. |

6550 |
Bayesian Statistics (4)Bayes Theorem, subjective probability, conjugate priors, non-informative priors, posterior estimation, credible intervals, prediction, sensitivity analysis, comparison to classical procedures, MCMC, Gibbs sampling, hierarchical Bayesian analysis. Use of statistical software. Report writing. Prerequisites: a graduate level course in Statistics or probability and an upper division course in computational statistics or computer science or consent of instructor. Co-requisite: one of prerequisites allowed as co-requisite. |

6555 |
Statistical Time Series Analysis (4)Analysis of correlated data in time, trends, seasonal patterns, periodicity, autocorrelation, spectral analysis, filtering, time domain versus spectral domain. Decomposition, autoregression, ARIMA, state-space models, forecasting. Applications to data in economics, engineering, seismology. Use of statistical software. Report writing. Prerequisites: one course in upper division statistics or probability and statistical computing or consent of instructor. |

6601 |
Advanced Statistical Computing (4)Implementation of computationally-advanced statistical methods. Topics may include: bootstrap, EM algorithm, Bayesian methods, Markov Chain, Monte Carlo, neural networks, recent methodological advances. Prerequisites: senior or graduate standing, and one of STAT 4950, STAT 6250 or STAT 6260. |

6610 |
Data Visualization (4)Methods used in data visualization and interactive exploration of big data. Topics include data merging and exporting, interactive GIS maps, elements of visual perception, effective graphs and charts, and meaningful visual representations of complex statistics and large data sets. Recommended: experience with R or STAT 6260. Prerequisite: STAT 6304 or consent of instructor |

6620 |
Statistical Learning with R (4)Introduction to machine learning, including supervised learning such as regression, logistic regression and classification methods. Re-sampling methods such as cross-validation and bootstrap. Unsupervised learning. Applications to data mining, statistical pattern recognition, and data processing. Experience with R is recommended. Prerequisite: STAT 6509 and STAT 6260. |

6651 |
Analysis of Categorical Data in Biostatistics (4)(See BSTA 6651 for course description.) |

6801 |
Statistical Consulting (4)Professional statistical consulting skills. Technical methods such as design of experiments and analysis of complex data. Professional data management and software practices will be covered. Interpersonal consulting skills will be emphasized. Real-life applications will be explored. Prerequisites: STAT 6250, STAT 6305, STAT 6509 and completion of the University Writing Skills Requirement. A-F grading only. |

6843 - 6849 |
Selected Topics in Biostatistics (4)(See BSTA 6843-6849 for course description.) |

6851 - 6859 |
Selected Topics in Actuarial and Decision Science (4)Methods in actuarial and decision science extending beyond regular courses. Variable content to be specified at time of offering. Prerequisite: STAT 3402 or 4401. May be repeated for credit when content varies, for a maximum of 8 units. |

6860 - 6864 |
Selected Topics in Graduate Probability and Statistics (4)Probability and/or Statistics extending beyond regular courses. Variable content to be specified at time of offering. Prerequisites: graduate standing and consent of instructor. May be repeated once for credit with consent of department and when content varies, for a maximum of 8 units. |

6865 |
Mathematical Modeling (4)(See MATH 6865 for course description.) |

6870 - 6879 |
Seminar in Probability and Statistics (4)An intensive study of a selected topic in probability and/or statistics from current literature emphasizing student participation. Prerequisites: graduate standing and consent of instructor. May be repeated once for credit with consent of department and when content varies, for a maximum of 8 units. |

6895 |
Practicum in Statistics (1-4)Supervised experience tutoring, grading, or consulting through the Statistics Department Consulting Laboratory. Students complete academic assignments integrated with on- or off-campus paid or volunteer activities. Prerequisites: advancement to candidacy, approval of the graduate advisor. May be repeated for credit, for a maximum of 4 units. Five to twenty hrs. act. |

6898 |
Cooperative Education (1-4)Supervised work experience in which student completes academic assignments integrated with off-campus paid or volunteer activities. Prerequisites: at least 3.0 GPA and departmental approval of activity. May be repeated for credit, for a maximum of 8 units. A maximum of 4 units will be accepted toward the M.S. degree in Statistics. |

6900 |
Independent Study (1-4) |

6950 |
Graduate Statistics Capstone (1)Retrospective view of courses required for M.S. degree. Strategies for lifelong learning and contributions to the statistics profession. Preparation for, and completion of, M.S. Comprehensive Examination. Prerequisites: STAT 6501; Advancement to Candidacy. Co-requisite: STAT 6502. |

6999 |
Issues in Statistics (4)Readings, discussion, and research on contemporary and/or significant issues in statistics. May be repeated for credit when content varies, for a maximum of 8 units. |