Master of Science in Statistics A Proposal

Transcription

1 1 Master of Science in Statistics A Proposal Rationale of the Program In order to cope up with the emerging complexity on the solutions of realistic problems involving several phenomena of nature it is felt that there is a need to come up with a relevant and responsive curriculum in the field of Statistics for the graduate level. This is premised to the fact that statistical analysis is one of the primary tools wherein precise conclusions can be drawn from the data collected in the presence of uncertainty. Moreover, statistical analysis is useful in almost all disciplines for the analysis and interpretation of data. Consequently in order to be assured that valid inferences are made on any research endeavor using statistical tools, there is a demand for well educated statisticians equipped with extensive and intensive knowledge and skills on both theory and techniques on how to apply the different statistical concepts. At present, the Mathematics Department of the College of Science and Mathematics is offering the undergraduate courses of Bachelor of Science in Mathematics and Bachelor of Science in Statistics. However, it was observed that these curricula have some deficiencies on the course contents for them to qualify for admission to the Master of Science in Statistics. To level off the background knowledge, BS in Math graduates seeking for admission must take courses in Statistics including statistical packages whereas those with the BS Statistics degree must enroll in Mathematics courses on Measure theory and Mathematics for Statistics. Graduates in Engineering can enroll provided that they have taken the basic mathematics and statistics required for the proposed program. This proposed program differs from that of Master of Applied statistics wherein the treatment of the courses is more on how to apply the techniques using available stat packages without in depth treatment on the theoretical concepts and derivations of the different formulae. Moreover, unlike the MAS which is a terminal program in Statistics, this program is a prerequisite for those who intend to pursue PhD is Statistics. It has been found out that there is no other institutions in Mindanao which offers a Master of Science in Statistics. This proposed program is timely and relevant in as much as the country is trying to encourage quality researches on various topics which can help alleviate the economy, peace and order conditions and preservation of environment and natural resources. The sustainability of the program can be guaranteed as long as there are graduates of the BS in Math and Statistics and Engineering in all the different colleges and universities of Mindanao. Program of Study The proposed program consists of 6 units of prerequisite courses, 15 units of core courses such as: Theory of Probability, Theory of Statistical Inference, Linear Models, Sampling Designs and Multivariate Analysis. The major subjects are grouped into 12 units of Computational Statistics and Modeling and 12 units of Mathematical Statistics courses which the students can choose for their field of concentration. Completion of the degree requires 30 graduate units with an average grade of 2.0 or better. Written comprehensive examination on the core courses is required and the completion of a thesis.

2 2 Admission Requirements Application for admissions must be filed with the Dean of the Graduate School. 1. An applicant must possess a BS degrees either in Statistics and Mathematics. Those without these degrees must be able to satisfy the minimum requirements as determined by the Graduate Committee. 2. An applicant must take the 6 units requirement for the prerequisite courses. 3. For those who are not mathematics and statistics major can enroll in the Master in Applied Statistics. Course work Units Summer (6 units) Stat 202 Calculus and Matrix Algebra for Statistics ** 3.0 Stat 205 Introduction to Mathematical Statistics* 3.0 Stat 203 Statistical Software * 3.0 Stat 204 Measure Theory ** 3.0 * For BS Math graduates ** For BS Stat and Engineering Graduates First Year First Semester ( 9 units) Stat 331 Introductory Probability 3.0 Stat 342 Sampling Designs 3.0 Stat 321 Statistical Computing 3.0 Second Semester ( 9 units) Stat 332 Introduction to Inference 3.0 Stat 352 Linear Models 3.0 Stat Elective 3.0 Second Year First Semester (9 units) Stat 358 Applied Multivariate Analysis 3.0 Second Semester (6 units) Stat 399 Masters Thesis 6.0 Total Number of Units 37 units

3 3 List of Electives Option 1: Computational Statistics Econometric Methods Statistics for Ecology Neural Networks Biostatistics Stat Computing II Time Series Survival Analysis Statistical Quality Control Nonparametric Statistics Option 2: Mathematical Statistics Stochastic Processes Robust Estimation Bayesian Theory Fuzzy Sets Chaos Theory Decision Theory Information Theory Categorical Data Analysis Course Description Stat 202 Calculus and Matrix Algebra for Statistics Differential and Integral Calculus, Infinite Series, Matrix Algebra and Differentiation. Stat 233. Introduction to Mathematical Statistics Probability Distribution, Sampling Distribution, Parametric and Nnonparametric Inference. Stat 203. Statistical Software Programming using Statistical Package for Social Sciences (SPSS), Statistical Analysis Systems (SAS) and other statistical packages for simulation and computing. Stat 204. Measure Theory Lebesgue and Outer Measure Theories, Probability Measure Stat 321. Statistical Computing I Algorithms for Statistical Computing; Numerical Analysis for Linear and Nonlinear Models. Stat 322. Statistical Computing II (Simulation) Random Number Generation; Monte Carlo Methods, Simulation using Programming Languages and Statistical Packages. Stat 331. Probability Theory

4 4 Combinatorial Analysis; Sample Space and Random Variables; Probability Distribution Function; Expectation; Common Probability Distributions, Convergence of Sequences of Random Variables, Laws of Large Numbers and Characteristic Functions. Stat 332. Statistical Inference Sampling Distributions; Point and Interval Estimation; Properties of Estimators, Tests of Hypothesis. Stat 355. Time Series Analysis Classical Procedures; Stationarity, Box Jenkins Designs, Stat 358. Applied Multivariate Analysis Multivariate normal distributions, multivariate analysis of variance, multivariate regression, principal component analysis; factor analysis; discriminant analysis; cluster analysis; multidimensional scaling; correspondence analysis; canonical correlation analysis; graphical and data oriented techniques; applications. Stat 352. Linear Models Subspaces and Projections; multivariate normal distributions; non central distribution, distribution of quadratic forms, the general linear model of full column rank, tests about the mean, tests about the variance, the general linear model with full and not of full column rank; estimability and testability. Regression Analysis Stat 342. Sampling Designs Concepts in designing sample surveys; non sampling errors; simple random sampling;; systematic sampling; sampling with varying probabilities; stratification; use of auxiliary information; cluster sampling; multi stage sampling and adaptive sampling. Stat 353. Econometric Methods Distributed lag models, structural change; simultaneous equations; limited dependent variables; ARCH, GARCH processes; co integration; applications. Stat 343. Categorical Data Analysis. Cross classified tables, multidimensional tables; loglinear model; logit models, measures of association; inference for categorical data; applications, Stat 354. Survival Analysis Functions of Survival Time; estimation and survival functions; survival distributions and their applications; distribution fitting and goodness of fit test. Stat 361. Nonparametric Methods Distribution free statistics, U statistics; power functions; asymptotic relative efficiency of tests; confidence intervals and bounds; point estimation; linear rank statistics; other methods of constructing distribution free distributions.

5 5 Stat 362. Bayesian Analysis Bayesisn inference; empirical and hierarchical analysis; robustness; numerical procedures. Stat 363. Robust Statistics Breakdown point and robust estimators; M, R, and L estimates; robust tests; robust regression and outlier detection. Stat 364. Statistical Quality Control Statistical methods used for quality assurance; statistical process control; control chart for variable and attributes; cusum chart; multivariate chart; process capability analysis; acceptance sampling; MIL SYD and JIS tables; off line quality control; introduction to response surface analysis; Taguchi method and applications. Stat 365. Statistical Communication Theory Theory of normed linear spaces; probability measures on Borel sets of sequence in Banach spaces; characteristic functionals; Gaussian Measure; signal detection; filtering theories; modulation theory. Stat 366. Stochastic Processes Markov chains; Markov processes; Poisson Processes; Renewal Processes; Martingales. Stat 367. Decision Theory Basic concepts, Risk function; Bayes and minimax solutions of decision problems; statistical decision problems; statistical decision functions; information of general decision problems. Stat 355. Neural Networks Intoduction. Neural Network, component and structure, Application of Neural Network, Artficial Neural Networks. Stat 356. Chaos Theory Introduction to chaos, Sensitive dependence, Critical points, Strange attractors, applications of chaos. Stat 357. Fuzzy Sets Fuzzy systems, introduction to fuzzy logic, operations on fuzzy sets, fuzzy relations, the extension principle. Stat 358. Biostatistics Statistics for Ecology and biology, Spatial sampling; Pri ncipal Component Regression; Cluster Analysis; Discriminant Analysis. Stat_399. Masters Thesis