Statistics
145.
Introduction to Statistics.
(3)
Techniques for the visual presentation of numerical data, descriptive statistics, introduction to probability and basic probability models used in statistics, introduction to sampling and statistical inference, illustrated by examples from a variety of fields. Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics (NMCCN 1113). (I)
Prerequisite: ACT = >22 or SAT = >510 or (MATH 118 and MATH 119) or MATH 120 or 121 or 123 or 150 or 162 or 163 or 180 or 181 or 264.
{Summer, Fall, Spring}
**345.
Elements of Mathematical Statistics and Probability Theory.
(3)
An introduction to probability including combinatorics, Bayes’ theorem, probability densities, expectation, variance and correlation. An introduction to estimation, confidence intervals and hypothesis testing.
Prerequisite: MATH 181 or MATH 163
425 / 525.
SAS® Programming.
(3)
A detailed introduction to the SAS® programming language. Topics covered include reading data, storing data, manipulating data, data presentation, graphing, and macro programming. SAS® software will be used.
Prerequisite: 345 and 427
427 / 527.
Advanced Data Analysis I.
(3)
Statistical tools for scientific research, including parametric and non-parametric methods for ANOVA and group comparisons, simple linear and multiple linear regression, and basic ideas of experimental design and analysis. Emphasis placed on the use of statistical packages such as Minitab® and SAS®.
Prerequisite: 145
{Fall}
428 / 528.
Advanced Data Analysis II.
(3)
A continuation of 427 that focuses on methods for analyzing multivariate data and categorical data. Topics include MANOVA, principal components, discriminant analysis, classification, factor analysis, analysis of contingency tables including log-linear models for multidimensional tables and logistic regression.
Prerequisite: 427
434 / 534.
Contingency Tables and Dependence Structures.
(3)
This course examines the use of log-linear models to analyze count data. It also uses graphical models to examine dependence structures for both count data and measurement data.
Prerequisite: 345 and 427
440 / 540.
Regression Analysis.
(3)
Simple regression and multiple regression. Residual analysis and transformations. Matrix approach to general linear models. Model selection procedures, nonlinear least squares, logistic regression. Computer applications.
Prerequisite: 427
{Fall}
445 / 545.
Analysis of Variance and Experimental Design.
(3)
A data-analytic course. Multifactor ANOVA. Principles of experimental design. Analysis of randomized blocks, Latin squares, split plots, etc. Random and mixed models. Extensive use of computer packages with interpretation, diagnostics.
Prerequisite: 440
{Spring}
453 / 553.
Statistical Inference with Applications.
(3)
Transformations of univariate and multivariate distributions to obtain the special distributions important in statistics. Concepts of estimation and hypothesis testing in both large and small samples with emphasis on the statistical properties of the more commonly used procedures, including student’s t-tests, F-tests and chi-square tests. Confidence intervals. Performance of procedures under non-standard conditions (i.e., robustness).
Prerequisite: 461
{Spring}
461 / 561.
Probability.
(3)
(Also offered as MATH 441)
Mathematical models for random experiments, random variables, expectation. The common discrete and continuous distributions with application. Joint distributions, conditional probability and expectation, independence. Laws of large numbers and the central limit theorem. Moment generating functions.
Prerequisite: MATH 264
{Fall}
470 / 570.
Industrial Statistics.
(3)
Basic ideas of statistical quality control and improvement. Topics covered: Deming’s 14 points and deadly diseases, Pareto charts, histograms, cause and effect diagrams, control charts, sampling, prediction, reliability, experimental design, fractional factorials, Taguchi methods, response surfaces.
Prerequisite: 345
472 / 572.
Sampling Theory and Practice.
(3)
Basic methods of survey sampling; simple random sampling, stratified sampling, cluster sampling, systematic sampling and general sampling schemes; estimation based on auxiliary information; design of complex samples and case studies.
Prerequisite: 345
{Alternate Falls}
474 / 574.
Biostatistical Methods: Survival Analysis and Logistic Regression.
(3)
A detailed overview of methods commonly used to analyze medical and epidemiological data. Topics include the Kaplan-Meier estimate of the survivor function, models for censored survival data, the Cox proportional hazards model, methods for categorical response data including logistic regression and probit analysis, generalized linear models.
Prerequisite: 428 or 440
476 / 576.
Multivariate Analysis.
(3)
Tools for multivariate analysis including multivariate ANOVA, principal components analysis, discriminant analysis, cluster analysis, factor analysis, structural equations modeling, canonical correlations and multidimensional scaling.
Prerequisite: 428 or 440
{Offered upon demand}
477 / 577.
Introduction to Bayesian Modeling.
(3)
An introduction to Bayesian methodology and applications. Topics covered include: probability review, Bayes’ theorem, prior elicitation, Markov chain Monte Carlo techniques. The free software programs WinBUGS and R will be used for data analysis.
Prerequisite: 461 and (427 or 440)
{Alternate Springs}
479.
Topics in Statistics.
(3, no limit Δ)
Modern topics not covered in regular course offerings.
481 / 581.
Introduction to Time Series Analysis.
(3)
Introduction to time domain and frequency domain models of time series. Data analysis with emphasis on Box-Jenkins methods. Topics such as multivariate models; linear filters; linear prediction; forecasting and control.
Prerequisite: 461
{Alternate Springs}
495.
Individual Study.
(1-3 to a maximum of 6 Δ)
Guided study, under the supervision of a faculty member, of selected topics not covered in regular course offerings.
520.
Topics in Interdisciplinary Biological and Biomedical Sciences.
(3, unlimited Δ)
(Also offered as ANTH 620, BIOL 520, CS 520, ECE 620)
Varying interdisciplinary topics taught by collaborative scientists from UNM, SFI, and LANL.
524.
Collaborative Interdiciplinary Teaching.
(3)
(Also offered as BIOL 524, CS 524, ANTH 624, ECE 524)
Course designed to develop the methods content and assessment of effective interdisciplinary biological courses; Students will develop and teach an undergraduate interdisciplinary topics course. Topics vary.
Restriction: permission of instructor.
525 / 425.
SAS® Programming.
(3)
A detailed introduction to the SAS® programming language. Topics covered include reading data, storing data, manipulating data, data presentation, graphing, and macro programming. SAS® software will be used.
Prerequisite: 345, 427
**527 / 427.
Advanced Data Analysis I.
(3)
Statistical tools for scientific research, including parametric and non-parametric methods for ANOVA and group comparisons, simple linear and multiple linear regression and basic ideas of experimental design and analysis. Emphasis placed on the use of statistical packages such as Minitab® and SAS®. Course cannot be counted in the hours needed for graduate degrees in Mathematics and Statistics.
Prerequisite: 145
{Fall}
528 / 428.
Advanced Data Analysis II.
(3)
A continuation of 527 that focuses on methods for analyzing multivariate data and categorical data. Topics include MANOVA, principal components, discriminate analysis, classification, factor analysis, analysis of contingency tables including log-linear models for multidimensional tables and logistic regression.
Prerequisite: 527
531.
Statistical Genetics I.
(3)
A detailed examination of the statistical methods used in analyzing genetic data. Topics covered include the estimation of allele frequencies, testing for Hardy-Weinberg equilibrium, classical and complex segregation analysis, linkage analysis for Mendelian and complex diseases, and the detection of allelic association. Popular genetic software will be used for data analysis.
Prerequisite: 345, 427
{Alternate Falls}
532.
Statistical Genetics II.
(3)
A continuation of 531. Topics covered include statistical methods for describing variation in quantitative traits, methods of mapping and characterizing quantitative trait loci and other current topics in statistical genetics, including the analysis of microarray data and phylogenetic methods. Popular genetic software will be used for data analysis.
Prerequisite: 531
{Alternate Springs}
534 / 434.
Contingency Tables and Dependence Structures.
(3)
This course examines the use of log-linear models to analyze count data. It also uses graphical models to examine dependence structures for both count data and measurement data.
Prerequisite: 345, 427
538.
Biostatistical Methods I for Public Health and Medical Sciences.
(3)
Covers basic statistical methods including statistical summaries and inference. Methods of summarizing data include graphical displays and numerical summaries. Statistical inference includes hypothesis testing and confidence intervals. Methods for continuous and categorical data are studied.
Prerequisite: B or better in MATH 121
{Fall}
539.
Biostatistical Method II for Public Health and Medical Sciences.
(3)
Covers basic models used in the statistical analysis of studies in the medical sciences and public health field, with an emphasis on epidemiology. Linear regression, analysis of variance, logistic regression, and survival models are studied.
Prerequisite: 538
{Spring}
540 / 440.
Regression Analysis.
(3)
Simple regression and multiple regression. Residual analysis and transformations. Matrix approach to general linear models. Model selection procedures, nonlinear least squares, logistic regression. Computer applications.
Prerequisite: 527
{Fall}
545 / 445.
Analysis of Variance and Experimental Design.
(3)
A data-analytic course. Multifactor ANOVA. Principles of experimental design. Analysis of randomized blocks, Latin squares, split plots, etc. Random and mixed models. Extensive use of computer packages with interpretation, diagnostics.
Prerequisite: 540
{Spring}
546.
Theory of Linear Models.
(3)
Theory of the Linear Models discussed in 440/540 and 445/545. Linear spaces, matrices, projections, multivariate normal distribution and theory of quadratic forms. Non-full rank models and estimability. Gauss-Markov theorem. Distribution theory for normality assumptions. Hypothesis testing and confidence regions.
Prerequisite: 553, 545, linear algebra.
{Alternate Falls}
547.
Multivariate Analysis and Advanced Linear Models.
(3)
Hotelling T2, multivariate ANOVA and Regression, classification and discrimination, principal components and factor analysis, clustering, graphical and computational techniques, topics in linear models.
Prerequisite: 546
{Alternate Springs}
553 / 453.
Statistical Inference with Applications.
(3)
Transformations of univariate and multivariate distributions to obtain the special distributions important in statistics. Concepts of estimation and hypothesis testing in both large and small samples with emphasis on the statistical properties of the more commonly used procedures, including student’s t-tests, F-tests and chi-square tests. Confidence intervals. Performance of procedures under non-standard conditions (i.e., robustness).
Prerequisite: 561
{Spring}
556.
Advanced Statistical Inference I.
(3)
Theory and methods of point estimation, sufficiency and its applications.
Prerequisite: 553, 561 and MATH 510
{Alternate Falls}
557.
Advanced Statistical Inference II.
(3)
Standard limit theorems, hypothesis testing, confidence intervals and decision theory.
Prerequisite: 556
{Alternate Springs}
561 / 461.
Probability.
(3)
Mathematical models for random experiments, random variables, expectation. The common discrete and continuous distributions with application. Joint distributions, conditional probability and expectation, independence. Laws of large numbers and the central limit theorem. Moment generating functions.
Prerequisite: MATH 264
{Fall}
565.
Stochastic Processes with Applications.
(3)
(Also offered as MATH 540)
Markov chains and processes with applications. Classification of states. Decompositions. Stationary distributions. Probability of absorption, the gambler’s ruin and mean time problems. Queuing and branching processes. Introduction to continuous time Markov processes. Jump processes and Brownian motion.
Prerequisite: 561
{Offered on demand}
567.
Advanced Probability.
(3)
(Also offered as MATH 541)
A measure theoretic introduction to probability theory. Construction of probability measures. Distribution and characteristic functions, independence and zero-one laws. Sequences of independent random variables, strong law of large numbers and central limit theorem. Conditional expectation. Martingales.
Prerequisite: MATH 563
{Alternate Springs}
569.
Selected Topics in Probability Theory.
(3, no limit Δ)
(Also offered as MATH 549)
570 / 470.
Industrial Statistics.
(3)
Basic ideas of statistical quality control and improvement. Topics covered: Deming’s 14 points and deadly diseases, Pareto charts, histograms, cause and effect diagrams, control charts, sampling, prediction, reliability, experimental design, fractional factorials, Taguchi methods, response surfaces.
Prerequisite: 345
572 / 472.
Sampling Theory and Practice.
(3)
Basic methods of survey sampling; simple random sampling, stratified sampling, cluster sampling, systematic sampling and general sampling schemes; estimation based on auxiliary information; design of complex samples and case studies.
Prerequisite: 345
{Alternate Falls}
574 / 474.
Biostatistical Methods: Survival Analysis and Logistic Regression.
(3)
A detailed overview of methods commonly used to analyze medical and epidemiological data. Topics include the Kaplan-Meier estimate of the survivor function, models for censored survival data, the Cox proportional hazards model, methods for categorical response data including logistic regression and probit analysis, generalized linear models.
Prerequisite: 528 or 540
576 / 476.
Multivariate Analysis.
(3)
Tools for multivariate analysis including multivariate ANOVA, principal components analysis, discriminant analysis, cluster analysis, factor analysis, structural equations modeling, canonical correlations and multidimensional scaling.
Prerequisite: 528 or 540
{Offered upon demand}
577 / 477.
Introduction to Bayesian Modeling.
(3)
An introduction to Bayesian methodology and applications. Topics covered include: probability review, Bayes’ theorem, prior elicitation, Markov chain Monte Carlo techniques. The free software programs WinBUGS and R will be used for data analysis.
Prerequisite: 561 and (527 or 540)
{Alternate Springs}
579.
Selected Topics in Statistics.
(3, no limit Δ)
581 / 481.
Introduction to Time Series Analysis.
(3)
Introduction to time domain and frequency domain models of time series. Data analysis with emphasis on Box-Jenkins methods. Topics such as multivariate models; linear filters; linear prediction; forecasting and control.
Prerequisite: 561
{Alternate Springs}
585.
Nonparametric and Robust Methods.
(3)
Statistical methods that are insensitive to the distribution of the data. Sign tests, Kolmogorov-Smirnov tests, rank tests including the Wilcoxon, Mann-Whitney, Kruskal-Wallis and Friedman tests. Robust estimation including M estimators, L estimators and R estimators.
Prerequisite: 561
{Offered upon demand}
586.
Nonparametric and Robust Methods.
(3)
Nonparametric regression, density estimation, filtering, spectral density estimation, image reconstruction and pattern recognition. Tools include orthogonal series, kernels, splines, wavelets and neural networks. Applications to medicine, engineering, biostatistics and economics.
Prerequisite: 561
{Offered upon demand}
590.
Statistical Computing.
(3)
A detailed examination of essential statistical computing skills needed for research and industrial work. Students will use S-Plus, Matlab and SAS® to develop algorithms for solving a variety of statistical problems using resampling and simulation techniques such as the bootstrap, Monte Carlo methods and Markov chain methods for approximating probability distributions. Applications to linear and non-linear models will be stressed.
Prerequisite: 528
595.
Problems.
(1-3, no limit Δ)
599.
Master’s Thesis.
(1-6, no limit Δ)
Offered on a CR/NC basis only.
605.
Graduate Colloquium.
(1 to a maximum of 4 Δ)
Students present their current research.
649.
Seminar in Probability and Statistics.
(1-3, no limit Δ)
(Also offered as MATH 649)
650.
Reading and Research.
(1-6 to a maximum of 12 Δ)
699.
Dissertation.
(3-12, no limit Δ)
Offered on a CR/NC basis only.
