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: (MATH 101 and MATH 102) or (MATH 118 and MATH 119) or MATH 120 or MATH 121 or MATH 123 or MATH 150 or MATH 162 or MATH 163 or MATH 180 or MATH 181 or MATH 264 or ACT Math =>22 or SAT Math Section =>540 or ACCUPLACER Elementary Algebra =66-103 or ACCUPLACER College-Level Math =37-68.
{Summer, Fall, Spring}
279.
Topics in Introductory Statistics.
(1 to 3 to a maximum of 3 Δ)
**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 163 or MATH 181.
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, no limit Δ)
(Also offered as BIOL, CS 520; ANTH, ECE 620)
Varying interdisciplinary topics taught by collaborative scientists from UNM, SFI, and LANL.
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.
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 and 427.
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}
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}
586.
Nonparametric Curve Estimation and Image Reconstruction.
(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.
