Course Module

UNDERGRADUATE PROGRAMME FOR A FOUR-YEAR B.Sc. DEGREE IN STATISTICS/DATA SCIENCE

CURRICULUM COURSE OUTLINE

100 LEVEL

FIRST SEMESTER

Course Code	Course Title	CU	STATUS	LH	PH
STA 111	Descriptive Statistics	3	C	45	–
STA 112	Probability I	3	C	45	–
GST 111	Communication in English	2	C	15	45
GST 112	Nigerian Peoples and Culture	2	C	30	–
CSC 101	Introduction to Computing Science	3	C	30	45
MTH 101	Elementary Mathematics I	2	C	30
GSS 113	Physical & Health Education	1	C	15	15
GSS 116	Use of Library	1	C	20
PHY 112	Elementary Physics I	2	C	30
PHY 117	Physic Laboratory 1	1	C	–	30
CHM 113	General Chemistry l	3	C	45
UGC 111	Farm Practice	1	C	–	30

TOTAL		24

100 LEVEL

SECOND SEMESTER

Course Code	Course Title	CU	STATUS	LH	PH
STA 121	Statistical Inference I	3	C	45	–
STA 122	Statistical Computing I	3	C	15	90
MTH 102	Elementary Mathematics II	2	C	45	–
STA 123	Introduction to R Programming software	2	C	15	60
STA 124	Introduction to Structured Query Language	2	C	15	60
CSC 123	Problem Solving	3	C	30	45
PHY 122	Elementary Physics I	2	C	45	–
PHY 127	Physic Laboratory 1	1	C	15	30
GSS 121	Use of English II	2	C	45	–
GSS 126	Social Sciences	2	C	45	–
UGC 121	Farm Practice II	1	C	15	30

TOTAL		23

200 LEVEL

FIRST SEMESTER

Course Code	Course Title	CU	STATUS	LH	PH
STA 211	Probability II	3	C	45	–
STA 212	Introduction to Social & Economic Statistics	3	C	45	–
GST 212	Philosophy, Logic, and Human Existence	2	C	30	–
STA 202	Statistics for Physical Sciences & Engineering	3	C	45	–
MTH 201	Mathematical Methods I	2	C	30	–
MTH 204	Linear Algebra I	2	C	30	–
MTH 212	Introduction to modern Algebra	3	C	45	–
COS 211	Computer programming I	3	C	30	45

TOTAL		18

200 LEVEL

SECOND SEMESTER

Course Code	Course Title	CU	STATUS	LH	PH
STA 221	Statistical Inference II	3	C	45	–
STA 231	Statistical Computing II	2	C	–	90
STA 299	Industrial Attachment I (12 Weeks)	3	C
ENT 211	Entrepreneurship and Innovation	2	C	15	45
MTH 205	Linear Algebra II	1	C	15	–
MTH 207	Real Analysis I	2	C	30	–
MTH 209	Introduction to Numerical Analysis	2	C	30
STA 222	Survey and Census Statistics	2	C	30
STA 220	Introduction to Data Science	2	C	15	30
TOTAL		19

300 LEVEL

FIRST SEMESTER

Course Code	Course Title	CU	STATUS	LH	PH
STA 311	Probability III	3	C	45	–
STA 312	Distribution theory I	3	C	45	–
STA 313	Statistical Quality Control	2	C	30
STA 314	Multivariate Analysis I	2	C	30
STA 315	Operations Research I	2	C	30
GST 312	Peace and Conflict Resolution	2	C	30
ENT 312	Venture Creation	2	C	15	45
STA 310	Introduction to Python programming	2	C
TOTAL		16

300 LEVEL

SECOND SEMESTER

Course Code	Course Title	CU	STATUS	LH	PH
STA 321	Statistical Inference III	3	C	45	–
STA 322	Regression and Analysis of Variance I	2	C	30	–
STA 324	Survey methods and sampling theory	3	C	45	–
STA 399	Industrial Attachment II (12 Weeks)	3	C
STA 326	Demography I	2	C	30
STA 327	Elements of Econometrics	2	C	30
STA 331	Statistical Computing III	3	C	–	90
STA 320	Machine Learning I	2	C	15	45
TOTAL		20

400 LEVEL

FIRST SEMESTER

Course Code	Course Title	CU	STATUS	LH	PH
STA 401	Project Seminar	2	C
STA 411	Probability IV	3	C	45	–
STA 412	Distribution Theory II	3	C	45	–
STA 413	Statistical Inference IV	3	C	45
STA 414	Time Series Analysis	2	C	30
STA 415	Regression and Analysis of Variance II	3	C	45	–
STA 417	Biometric Methods	2	E	30	–
STA 418	Demography II	2	E	30	–
STA 419	Artificial Intelligence	2	C	15	30
TOTAL		18

400 LEVEL

SECOND SEMESTER

Course Code	Course Title	CU	STATUS	LH	PH
STA 499	Research Project	4	C
STA 421	Design and Analysis of Experiments	3	C	45
STA 422	Logical Background of Statistics & Decision Theory	3	C	45	–
STA 423	Machine Learning II	2	C	15	45
STA 424	Sampling Theory and Survey Methods II	2	E	30
STA 425	Multivariate Analysis II	2	E	30
STA 426	Operations Research II	2	E	30
STA 427	Stochastic Processes	2	C	30
TOTAL		21

COURSE DESCRIPTION

STA 111: Descriptive Statistics (3 Units C: LH 45)
Learning Outcomes
At the end of the course, students should be able to:
1. explain the basic concepts of descriptive statistics;
2. present data in graphs and charts;
3. differentiate between measures of location, dispersion and partition;
4. describe the basic concepts of Skewness and Kurtosis as well as their utility function in a
given data set;
5. differentiate rates from ratio and how they are use; and
6. compute the different types of index number from a given data set and interpret the output.

Course Contents
Statistical data. Types, sources and methods of collection. Presentation of data. Tables chart and graph. Errors and approximations. Frequency and cumulative distributions. Measures of location, partition, dispersion, skewness and Kurtosis. Rates, ratios and index numbers.

STA 112: Probability 1 (3 Units C: LH 45)
Learning Outcomes
At the end of the course, students should be able to:
1. explain the differences between permutation and combination;
2. explain the concept of random variables and relate it to probability and distribution
functions;
3. describe the basic distribution functions; and
4. explain the concept exploratory data analysis.

Course Contents
Permutation and combination. Concepts and principles of probability. Random variables.
Probability and distribution functions. Basic distributions: Binomial, geometric, Poisson, normal and sampling distributions; exploratory data analysis.

STA 120: Statistical Computing I (3 Units C: LH 15; PH 90)
Learning Outcomes
At the end of the course, students should be able to:
1. explain the fundamentals of computer;
2. acquire knowledge of the applications and use of computers and calculators in relation to
computing the measures of locations and dispersions;
3. explain the organizations of computations to access, transform, explore, analyse data and
produce results; and
4. demonstrate the use of Microsoft excel and the installation of the analysis tool pack.

Course Contents
Introduction to computer: structure, type, uses and applications; computations (using
computers and calculators), involving topics in STA111 and 121; organizations of computations
to access, transform, explore, analyze data and produce results. Concepts and vocabulary of
statistical computing. Microsoft excel and specifically the installation and the utility function of
the analysis tool pack.

STA 121: Statistical Inference I (3 Units C: LH 45)
Learning Outcome
At the end of the course, students should be able to:
1. differentiate population from sample as well as point from interval estimate;
2. test for hypothesis concerning population mean and proportions for large and small
samples;
3. compute regression and obtain the fitted line. Likewise, the computation for correlation
coefficient well understood; and
4. describe the fundamentals of time series analysis.

Course Contents
Population and samples. Random sampling distributions. Estimation (point and interval) and
tests of hypotheses concerning population mean and proportion (one and two large sample
cases). Regression and correlation. Elementary time series analysis.

STA 122: Statistical Computing I (3 Units C: LH 15; PH 90)

Learning Outcomes

At the end of the course, students should be able to:

explain the fundamentals of computer;
acquire knowledge of the applications and use of computers and calculators in relation to computing the measures of locations and dispersions;
explain the organizations of computations to access, transform, explore, analyse data and produce results; and
demonstrate the use of Microsoft excel and the installation of the analysis tool pack.

Course Contents

Introduction to computer: structure, type, uses and applications; computations (using computers and calculators), involving topics in STA111 and 121; organizations of computations to access, transform, explore, analyze data and produce results. Concepts and vocabulary of statistical computing. Microsoft excel and specifically the installation and the utility function of the analysis tool pack.

STA 123: Introduction to R Programming software (2 Credits C: L= 15 P=45)

Learning Outcomes

On completion of the course, students should be able to:

generate reproducible and simple analysis of quantitative data using statistical and visualization tools
adapt existing computational methods and tools to complete a target task
engage with unfamiliar data problems and identify relevant solution strategies to solve them
have obtained a handy programming platform and acumen to handle any new mathematical and statistical equations that comes in higher level courses
understand R sessions for Statistics
understand simple R operations in R; and
use R for simple statistical modelling

Course Contents

Introducing the R system for Statistical computing. Downloading the R system. The R Console in windows environment. Regular expressions in R. Objects in R. Reading data files into R. Sample R sessions for statistics. Working with RStudio. Simple R operations. Simple R functions. Introducing traditional R graphics. Graph and chat plotting. Othe data visualization tools. Data presentation and organization using R. Other descriptive Statistics with R. Simple statistical modelling with R. Simple time series analysis with R. Regression analysis with R.

STA 124: Introduction to Structured Query Language (2 Units C: LH 30)

Learning outcomes

By the end of this course, students should be able to:

be familiar with some database management systems;
design a relational database using entity relationship diagrams and following the principles of normalization;
effectively and efficiently query a database management system;
update, insert and delete a table in a database;
join tables from different databases; and
carry out a statistical analysis for a given table in a database.

Course contents

Introduction to Databases and Database management systems (DBMS). Database analysis and design by normalization- 1NF, 2NF, 3NF. SQL operations: SELECT, UPDATE, INSERT and DELETE. Subqueries: IN, EXISTS and inline views. Stored procedures. Functions, triggers, JOINS, NULL handling. The data query language (DQL) command. Select, aggregate functions using group by Count, average. Having, cube, and rollup SQL statements. The data control language (DCL) commands: grant, revoke. The transaction control language (TCL): commit, rollback, save point. SQL merge. SQL operators: +, >, like, concat, union. SQL join, SQL nested queries. SQL stored procedure. SQL exception handling.

STA 211: Probability II (3 Units C: LH 45)
Learning Outcomes
At the end of the course, students should be able to:
1. explain further permutation and combination;
2. define probability laws, conditional probability, and independence;
3. describe Bayes’ theorem and explain some of the basic probability distribution for discrete
and continuous random variables;
4. compute expectations and moments of random variables;
5. explain Chebyshev’s inequality and apply it to real life situations;
6. explain joint marginal and conditional distributions and moments as well as Limiting
distributions;
7. describe standard distributions, moments and moment-generating functions; and
8. explain laws of large numbers and the central limit theorem.

Course Contents
Further permutation and combination. probability laws. conditional probability, independence. Bayes’ theorem. probability distribution of discrete and continuous random variables: binomial, Poisson, geometric, hypergeometric, rectangular (uniform), negative exponential, binomial. Expectations and moments of random variables. Chebyshev’s inequality. joint marginal and conditional distributions and moments. limiting distributions. discrete and continuous random variables, standard distributions, moments and moment-generating functions. laws of large numbers and the central limit theorem.

STA 212: Introduction to Social and Economic Statistics (3 Units C: LH 45)

Learning Outcomes

At the end of the course, students should be able to:

highlight the statistics systems and explain the nature, types, sources, methods of collection and problem of official statistics;
compute index numbers using the different types;
describe descriptive statistics and Basic principles of probability;
differentiate discrete from continuous random variables considering binomial, normal, t, chi-square, Poisson, other univariate distributions;
explain joint distributions and sampling distributions;
demonstrate central limit theorem;
explain the properties of an estimators and linear combinations of random variables;
explain the basic concept of testing of hypotheses;
identify the socio-economic indicators: nature, types, uses and computation; and
explain the nature, sources, contents and problems of official statistics in selected sectors.

Course Contents

Statistics systems. nature, types, sources, methods of collection and problem of official statistics. index numbers, theory, construction and problems. descriptive statistics. Basic principles of probability. discrete and continuous random variables (binomial, normal, t, chi-square, Poisson, other univariate distributions). joint distributions. sampling distributions. central limit theorem. properties of estimators. linear combinations of random variables. testing and estimation.

STA 202: Statistics for Physical Sciences and Engineering (3 Units C: LH 45)

Learning Outcomes

At the end of the course, students should be able to:

highlight the scope for statistical methods in physical sciences and engineering;
define the measures of location, partition and dispersion;
explain the elements of probability; probability distribution: binomial Poisson, geometric, hypergeometric, negative-binomial, normal poisson, geometric, hypergeometric, negative-binomial, normal, Student’s t and chi-square distribution;
differentiate point from internal estimation and could be able to tests for hypotheses concerning population means proportions and variances;
compute for regression and correlation as well as conduct some non–parametric tests with reference to contingency table analysis; and
explain the elements of design of experiments and analysis of variance.

Course Contents

Scope for statistical methods in physical sciences and engineering. Measures of location, partition and dispersion. Elements of probability. Probability distribution: binomial Poisson, geometric, hypergeometric, negative-binomial, normal poisson, geometric, hypergeometric, negative-binomial, normal, Student’s t and chi-square distributions. Estimation (point and internal) and tests of hypotheses concerning population means proportions and variances. regression and correlation. non-parametric tests. contingency table analysis. introduction to design of experiments. analysis of variance.

STA 221: Statistical Inference II (3 Units C: LH 45)
Learning Outcomes
At the end of the course, students should be able to:
1. explain sampling and sampling distribution;
2. differentiate point from interval estimation;
3. outline the principles of hypotheses testing; test hypotheses concerning population means,
proportions and variances; of large and small samples, large and small sample cases; and
4. conduct a goodness fit tests using the analysis of variance.

Course Contents
Sampling and sampling distribution. point and interval estimation. principles of hypotheses
testing. tests of hypotheses concerning population means, proportions and variances of large
and small samples, large and small sample cases. Goodness –fit tests. analysis of variance

STA 222: Survey and Census Statistics (2 Units C: LH 30)

Learning Outcomes

At the completion of the course, students should be able to:

understand the basic concepts of Survey and Census
understand the concept of Survey design and use it to design a simple Survey.
identify and explain the traditional and innovative methods of data collection
design a questionnaire and any other data collection instruments
develop basic steps for planning and execution of a Survey or census
process data from a survey or census
know how to monitor and evaluate a simple survey
use modern statistical packages to analyse survey data; and
learn how to report survey results.

Course Contents

Census and sample Survey. Population and target population. Population and housing census. Sampling frames. Enumeration and enumeration procedures. Enumerator, households, housing units, head of household, building or structures, family, compound, etc. Sampling units. Post-enumeration. Pilot survey. Monitoring of Surveys through re-interview. Traditional and innovative data collection. Design of a questionnaire and other instruments. Basic steps in planning and execution of any survey or census. Data processing. Design of simple surveys. Monitoring and evaluation techniques. Errors in sample surveys and censuses. Analysis of field data. Report writing.

STA 231: Statistical Computing II (2 Units C: PH 90)

Learning Outcomes

At the end of the course, students should be able to:

explain the uses of computers in statistical computing;
demonstrate various statistical package;
use some statistical packages in solving problems in statistical methodology;
to demonstrate the use of spread sheet in application software; and
use packages such as SPSS, STATA, MINITAB etc, to demonstrate their abilities in statistical methodology.

Course Contents

Uses of computers in statistical computing. introduction to various statistical packages. use of statistical packages in solving problems in statistics. spread sheet applications. Such as SPSS, STATA, MINITAB etc.

STA 299: Industrial Attachment I (12 Weeks) (3 Units C)
Learning Outcomes

At the end of the course, students should be able to:
1. exhibit laboratory and field knowledge of subjects taught;
2. demonstrate knowledge of technical report writing and presentation; and
3. carryout research on specific topic, collect and evaluate information on specific subject
matter while at the attachment.

Course Contents
Students should be attached to some relevant organizations for 12 Weeks at the 200 Level
preferably during the long vacation for industrial experience. Students are to be assessed based on seminar presentation, their reports and assessment by supervisors

STA 220: Introduction to Data Science (2 Units C: LH 15, PH 30)

Senate-approved relevance to mission, vision, strategic goals, uniqueness, and contextual peculiarities of the University.

The course provides a foundational overview of key concepts and techniques in the field of data science and statistical computing. Students are introduced to the fundamental principles of data analysis, visualization and interpretation using R. Michael Okpara University of Agriculture, Umudike prides itself in the production of professionally competent and confident graduates that will work to meet the national goals of self-sufficiency in addressing challenges specific to agriculture. This will be done by training students who can collect, cleaning, and manipulating agricultural data, employing statistical techniques to extract meaningful insights.

Overview

Introduction to Data Science is a comprehensive course designed to equip students with the fundamental knowledge and practical skills required to analyze and interpret data in the context of agricultural research and innovation. This course integrates principles of data science and statistical computing, emphasizing their application in addressing complex challenges in industries, companies, and agricultural sector.

Objectives

The objectives of the course are to:

Understand the fundamental concepts and principles of data science.
Develop proficiency in data manipulation, cleaning, and pre-processing.
Gain hands-on experience with data visualization tools and techniques.
Use of statistical packages / R programming language in solving problems in inference.

Learning Outcomes

At the completion of the course, students should be able to:

explain common data science concepts.
collect, clean, manipulate and pre-process data.
use appropriate visualization techniques for a given data type.
set up a hypothesis test and engage in data storytelling to provide more context.
Implement statistical theories in R programming language or any other statistical software.

Course contents

Definition and scope of data science. Data cleaning and pre-processing techniques. Handling missing data and outliers. Feature engineering. Hypothesis testing. Effective visualizations for discrete and continuous variables. Communicating insights through visual storytelling. Implementation using R or any other statistical software.

STA 311: Probability III (3 Units C: LH 45)
Learning Outcomes
At the end of the course, students should be able to:
1. define discrete sample spaces and provide rules of probability;
2. explain independence Bayes’ theorem and Um models;
3. determine sampling with and without replacement;
4. explain inclusion-exclusion theorem;
5. explain allocation and matching problems;
6. explain probability generating function; and
7. outline the properties of Bernoulli trials, binomial, Poisson, Hypergeometric negative binomial and multinomial distribution, Poisson process.

Course Contents
Discrete sample spaces. definitions and rules of probability. Independence Bayes’ theorem. Um models; sampling with and without replacement. inclusion-exclusion theorem. allocation and matching problems; probability generating function; Bernoulli trials, binomial, Poisson,
Hypergeometric negative binomial and multinomial distribution, Poisson process.

STA 312: Distribution Theory I (3 Units C: LH 45)
Learning Outcomes
At the end of the course, the students should be able to:
1. identify and/or find distributions using any of the transformation techniques;
2. explain cumulants and their generating functions as well as some special univariate
distribution;
3. explain the central limit theorem;
4. illustrate bivariate moment generating functions of random variable and bivariate
distribution;
5. explain bivariate moment generating functions; and
6. explain bivariate normal distributions associated with the normal, X², t and F distribution.

Course Contents

Transformation techniques, probability integral transformation, order statistics and
their functions. cumulants and their generating functions. some special univariate distribution. central limit theorem. Bivariate moment generating functions of random variable. Bivariate distribution. bivariate normal distributions. distribution associated with the normal, X², t and F distribution.

STA 313: Statistical Quality Control (2 Units C: LH 30)

Learning Outcomes

On completion of the course, students should be able to:

understand the philosophy and basic concepts of quality improvement.
describe the DMAIC processes (define, measure, analyze, improve, and control).
demonstrate the ability to use the methods of statistical process control.
demonstrate the ability to design, use, and interpret control charts for variables.
demonstrate the ability to design, use, and interpret control charts for attributes.
perform analysis of process capability and measurement system capability.
perform basic multivariate statistical quality control analysis
understand and interpret the basic concepts and usage of Lean Six Sigma.

Course Contents

Definition of quality and process. Causes of Variation. Review of important distributions applicable to quality control. Process control procedures. Statistical design of variable and attribute. Control charts. Variable charts. Attribute Charts. Operating Characteristics Curve. Time-weighted control chart processes. Multivariate process control. Process capability indices. Industrial experimentation topics examples. basic concepts and usage of Lean Six Sigma. Acceptance sampling plans. Double acceptance sampling plan. Sequential sampling plan. Use of statistical packages for quality control.

STA 314: Multivariate Analysis I (2 Units C: LH 30)

Learning outcomes

By the end of this course, students should be able to:

understand multivariate and related distributions.
derive the sampling distributions of the mean vector and covariance matrix
make inferences for univariate vector.
draw inferences for multivariate vectors.
test for independence and homogeneity

Course contents

Meaning of multivariate analysis. Review of matrices. Matrix algebra for multivariate analysis. Covariance and correlation matrix. Eigenvectors and Eigen values. Multivariate normal and related distributions. Mean and Variance of Multivariate distribution. Multivariate moment generating function. Characteristic functions. Inference about mean vectors. Mahalanobis distance. Sampling distributions of the mean vector and covariance matrix. Hotelling’s T². Simultaneous inference. Factor analysis. Multivariate analysis of variance. Tests of independence and homogeneity.

STA 315 – Operations Research I (2 Units C: LH 30)

Learning Outcomes

On completion of the course, students should be able to:

formulate problems and construct mathematical models concerning optimum solution to managerial problems in production, distribution and revenue generation.
provide as well as implement solutions obtained from problems of ‘man-machine’ system.
use the linear programming algorithms in achieving optimum solution using the simplex method, artificial variable techniques and dual simplex method.
use the transportation methods like Vogel’s approximation method, north west corner point solution among others to obtain optimal transportation plan at minimum cost.
Formulate and solve problems involving games theory.

Course Contents

Classical methods of optimization: Maxima and minima. Unconstrained optimization. Constrained optimization. Lagrange’s multipliers. Linear Programming: Convex, sets and functions. Graphical method. Simplex method. Artificial Variable Techniques. Big M method. Revised Simplex Method. Duality theory and applications. Transportation models. Sensitivity analysis in transportation models. Games theory. Two-persons’ zero-sum games. Saddle point, dominance, strategies. Linear programming applications in games theory.

STA 310: Introduction to Python programming (2 Units C: LH 15, PH 30)

Senate-approved relevance to mission, vision, strategic goals, uniqueness, and contextual peculiarities of the University.

Python programming is a powerful programming language used for a wide range of applications, spanning from web development and data analysis to artificial intelligence and scientific computing. Its simplicity and readability make it an ideal choice for beginners, while its versatility and extensive libraries make it a favorite among seasoned developers. Michael Okpara University of Agriculture, Umudike prides itself in the production of professionally competent and confident graduates that will work to meet the national goals of self-sufficiency in developing AI web applications for optimizing agricultural production. Students will be taught how to translate real world problems into computational solutions.

Overview

Python is a versatile, high-level programming language known for its readability and simplicity. It emphasizes code readability and ease of use. Python supports both procedural and object-oriented programming paradigms, making it suitable for diverse applications. Its extensive standard library and third-party packages enhance functionality. Python is dynamically typed, interpreted, and features automatic memory management. Widely used in web development, data science, artificial intelligence, and automation, Python’s popularity continues to grow. Hence, a strong background in Python programming will enable students to build data science applications.

Objectives

The objectives of the course are to:

Develop a strong foundation in Python programming, including syntax, data structures, and control flow.
Enhance problem-solving skills through coding exercises and real-world projects.
Grasp the principles of Object-Oriented Programming and apply them to build modular and reusable code.
Gain the ability to work with data using libraries like NumPy and Pandas.
Understand the basics of python’s GUI framework using Tkinter.

Learning Outcomes

At the completion of the course, students should be able to:

understand how to use variables in Python.
work with common Python data structures like lists, tuples, dictionaries, and sets.
use basic flow control including for loops and conditional statements.
write functions and pass arguments in Python.
design object-oriented programs with Python classes.
perform manipulation and statistical analysis using selected Python libraries.
design and develop a simple database and web application with Python.

Course Contents

Python variables. Basic I/O operations. Control flow. Data collections. Functions. Classes. Exceptions handling. Regular expressions. Lambda and higher order functions. File handling. Modules and Packages. Python libraries – NumPy, pandas, Matplotlib, Statsmodels. Python SQLite, GUI programming with Tkinter.

STA 321: Statistical Inference III (3 Units C: LH 45)

Learning Outcomes

At the end of the course, the students should be able to:

outline the properties of a good estimator consistency unbiasedness, efficiency, minimum variance and sufficiency;
describe the methods of estimation; using maximum likelihood, least squares and method of moments; and
determine confidence intervals for simple and composite hypotheses to compute the likelihood ratio test as well as inferences about means and variance.

Course Contents

Criteria of estimating consistency unbiasedness, efficiency, minimum variance and sufficiency. methods of estimation. maximum likelihood, least squares and method of moments. confidence intervals. simple and composite hypotheses. likelihood ratio test. inferences about means and variance.

STA 322: Regression and Analysis of Variance I (2 Units C: LH 30)

Learning Outcomes

At the end of the course, the students should be able to:

explain total, partial and multiple correlation ratio;
demonstrate simple and multiple linear regression using the variable selection techniques, stepwise regression;
determine the analysis of covariance, influence measures, polynomial regression and orthogonal polynomials;
explain simple non-linear way classification;
demonstrate two-way classification; three-way classification; balanced and unbalanced two factor nested (hierarchical) classifications;
explain multiple comparisons component or variance estimates and tests; and
demonstrate these techniques in computing packages.

Course Contents

Total, partial and multiple correlation ratio. simple and multiple linear regression. variable selection techniques. stepwise regression, analysis of covariance, influence measures, polynomial regression. Orthogonal polynomials. simple non-linear way classification. two-way classification. Three-way classification. balanced and unbalanced two factor nested (hierarchical) classifications. multiple comparisons component or variance estimates and tests. computing packages.

STA 324: Survey Methods and Sampling Theory (3 Units C: LH 45)

Learning Outcomes

At the end of the course, students should be able to:

explain survey design, planning and programming;
identify the methods of data collection;
design questionnaires and collect data so that meaning conclusion can determine.
explain errors and biases;
differentiate probabilities from non-probability sampling and outline the selection procedure;
explain the estimation of mean, totals, ratios and proportions in all the sampling techniques;
identify probability proportion-to-size sampling; and
demonstrate Nigeria’s experience in sampling survey.

Course Contents

Survey design, planning and programming. methods of data collection. design of form and questionnaires. data processing, analysis and interpretation. errors and biases. Probabilities and non-probability sampling: selection procedure. estimation of mean, totals, ratios and proportions in simple random, systematic, stratified cluster and two-stage sampling. Probability proportion-to-size sampling; Nigeria’s experience in sampling survey.

STA 331: Statistical Computing III (2 Units C: PH 90)

Learning Outcomes

At the end of the of the course, students should be able to:

install the R or SAS package;
load data into R package;
gain more experience and confidence in statistics applications;
learn something of the structure of the R statistical software;
obtain practical computation skills through application of statistical theories; and
interface computers to their environment through statistical applications

Course Contents

Use of advanced statistical computing packages. Analysis of statistical and numerical algorithms. Analysis of statistical and numerical algorithms. Introduction to Monte Carlo Methods e.g. SAS, R. Etc.

STA 326: Demography I (2 Units C: LH 30)

Learning outcomes

By the end of this course, students should be able to:

collect population census.
evaluate demographic data.
measure fertility, mortality, nuptiality and migration.
use of life tables.
carry out population projections

Course Contents

Concepts of Demography. Type and sources of demographic data. Methods of collection of population censuses. Sample surveys. vital registration. Evaluation of the quality of demographic data. Measure of fertility and reproduction. Mortality analysis. Nuptiality analysis. Migration measures. Some tools of demographic data analysis. Standardization and decomposition. Life tables. Construction and application. Framework for developing demographic information systems. Stable and quasi-stable population, population projection.

STA 327: Elements of Econometrics (2 Units C: LH 30)

Learning outcomes

By the end of this course, students should be able to:

understand econometric models.
Explain Gauss Markov Theorem
understand models involved lagged variables.
construct simultaneous equation systems.
apply econometric models to demand analysis, production analysis, consumption and investment function.

Course Contents

Nature of econometrics. Econometric model: nature, types and characteristics. Econometric problems related to single equation models. Simple and Multiple Regression Models. Assumptions of Regression models. Gauss Markov Theorem. Construction estimation and tests. Models involving lagged variables. Simultaneous equation systems. Structural form. Reduced form. Identification, estimation and test of econometric models. Application of econometric models. Demand analysis. Production functions. Consumption function. Investment functions.

STA 320: Machine Learning I (2 Units C: LH 15, PH 30)

Senate-approved relevance to mission, vision, strategic goals, uniqueness, and contextual peculiarities of the University.

Machine learning is the use of algorithms to uncover hidden patterns in data and make predictions in real time without involving humans. But statistics provide the theoretical framework upon which machine learning algorithms are built. Michael Okpara University of Agriculture, Umudike prides itself in the production of professionally competent and confident graduates that will work to meet the national goals of self-sufficiency in developing effective and efficient machine learning algorithms for solving health and climate related problems.

Overview

Machine learning (ML) has a wide range of applications across various industries ranging from health, finance, and agriculture. This course builds upon the foundations of statistical computing and extends into the realm of machine learning, equipping students with the tools to handle complex data-driven challenges. Students will be introduced to a diverse set of machine learning algorithms – supervised and unsupervised algorithms. The primary focus is on understanding the underlying principles and selecting appropriate algorithms for specific tasks.

Objectives

The objectives of the course are to:

Gain a solid understanding of the foundational concepts and principles of machine learning, including key algorithms, techniques, and mathematical foundations.
Learn how to formulate real-world problems in a way that can be addressed using machine learning techniques.
Acquire the skills to select and implement appropriate machine learning algorithms for specific tasks.
Understand how to evaluate the performance of machine learning models using appropriate metrics.

Learning Outcomes

At the completion of the course, students should be able to:

define and explain key machine learning concepts, including supervised learning, and unsupervised learning.
explain the difference between training and testing in machine learning.
demonstrate proficiency in data preprocessing techniques, including data cleaning, feature scaling, and handling missing data.
select appropriate machine learning models for different types of problems.
Evaluate machine learning models using appropriate metrics.
Understand the concepts of overfitting and underfitting and apply regularization techniques to improve model performance.

Course Contents

Definition and basic concepts. Supervised learning. Unsupervised learning. Model validation. Model evaluation and selection.

STA 401: Project Seminar (2 Units C: PH 270)

Learning Outcomes

At the end of the course, students should be able to:

Present proposal of research on specific topic.

Course Contents

Present proposal of intended research selected topic and produce a report. Student should be subjected to oral examination on the project seminar.

STA 411: Probability IV (3 Units C: LH 45)

Learning Outcomes

At the end of the course, the students should be able to:

explain the probability spaces measures and distribution;

describe distribution of random variables as measurable functions, product spaces; products of measurable spaces, product probabilities;

explain independence and expectation of random variable;
identify convergence of random variables; Weak convergence almost everywhere, convergence in path mean;
describe central limit theorem, laws of large numbers; and
explain characteristic function and inversion formula.

Course Contents

Probability spaces measures and distribution; distribution of random variables as measurable functions; product spaces; products of measurable spaces, product probabilities; independence and expectation of random variable; convergence of random variables; weak convergence almost everywhere, convergence in path mean. Central limit theorem, laws of large numbers; characteristic function and Inversion formula.

STA 412: Distribution theory II (3 Units C: LH 45)

Learning Outcomes

At the end of the course, students should be able to;

identify the distribution of quadratic forms; Fisher – Cochran theorem, Multivariate normal distributions;
explain the distribution of order statistics from continuous populations;
differentiate characteristic from moment generating functions; and
to identify uniqueness and inversion theorems and limit theorems.

Course Contents

Distribution of quadratic forms. Fisher – Cochran theorem, Multivariate normal distributions. Distribution of order Statistics from continuous populations. Characteristic and moment generating functions. Uniqueness and inversion theorems. Limit theorems.

STA 413: Statistical Inference IV (3 Units C: LH 45)

Learning Outcomes

At the end of the course, students should be able to:

explain the general linear hypothesis and analysis of linear models;
gain further treatment of estimation and hypothesis testing extension of uniparameter results to multiparameter situation; and
describe the basic ideas of distribution – free test; Bayesian Inference.

Course Contents

General linear hypothesis and analysis of linear models. further treatment of estimation and hypothesis testing extension of uniparameter results to multiparameter situation. basic ideas of distribution – free test. Bayesian Inference

STA 414: Time Series Analysis (2 Units C: LH 30)

Learning outcomes

Upon the completion of this course, students should be able to:

determine patterns exhibited by time series via the visual inspection of the time plot and other necessary graphs
decompose a time series into its components using a suitable model
differentiate between stationary and nonstationary time series
identify an appropriate probability model for a time series using the model identification tool(s)
derive mean, variance, autocovariance function and autocorrelation function for stationary processes
make forecast using the time series models under consideration
derive the spectrum for each of the stationary processes

Course Contents

Estimation and isolation of components of time series. Time series relationships. Cyclical behaviour. Periodicity. Spectral analysis. Coherence and filtering. Time series regression. Nonstationary and stationary processes. Theoretical moments, autocorrelation and partial autocorrelation. Sample moments. Autocorrelation and Partial autocorrelation. Univariate time series model. Identification and estimation of autoregressive (AR) processes. Moving average (MA) process. Autoregressive-moving average (ARMA) model. Diagnostic checking of models. Linear prediction and forecasting. Seasonal time series.

STA 415: Regression and Analysis of Variance II (3 Units C: LH 45)

Learning Outcomes

At the end of the course, students should be able to:

explain multicollinearity, autocorrelation and heteroscedasticity;
perform the residual analysis;
describe the transformations;
compare intercepts and slopes;
explain simple non – linear regression and Logistic regression;
use dummy variables;
familiarise with the departures from ANOVA assumptions;
estimate missing values; and
determine the analysis of covariance in one-way, two-way, three-way and nested (hierarchical) classifications as well as analysis of covariance with two concomitant variables.

Course Contents

Multicollinearity, autocorrelation and heteroscedasticity; residual analysis; transformations. comparison of intercepts and slopes; Simple non – linear regression; Logistic regression; Use of dummy variables. Departures from ANOVA assumptions. Transformations. Missing values; analysis of covariance in one-way, two-way, three-way and nested (hierarchical) classifications; analysis of covariance with two concomitant variables.

STA 417 – Biometric Methods (2 Units E: LH 30)

Learning Outcomes

On completion of the course, students should be able to:

estimate the nature, constitution or potency of a material by means of the reaction that follows its application to living matter.
obtain the relative potency of experimental drugs in bioassays.
obtain standard error relative potency of experimental test material in bioassays in relation to a standard material.
obtain fiducial limits of relative potency potency of experimental test material in bioassays in relation to a standard material.
obtain fiducial limits of relative potency material in bioassays using Behrens-Fisher distribution.
differentiate between analytical and comparative dilution assays.
differentiate between direct and indirect assays

Course Contents

Concepts of Biometry. Direct and indirect assays. Efficiency and utility of concomitant measurements. Design and criticisms of direct assays. Fieller’s theorem and its two analogues. The Behrens-Fisher distribution. Fiducial limits in the strophanthus assay. Dilution assays. Adjustment for body weight. Indirect assays. The dose-response regression. The condition of similarity. The condition of Monotony. Linearizing transformations. Assay validity. Preliminary regression investigation.

STA 418: Demography II (2 Units E: LH 30)

Learning outcomes

At the completion of the course, students should be able to:

Estimate the probability, mortality and nuptiality from limited and defected data.
Identify and state the various population models
Prepare a life table
Project any given population using mathematical models; and
Carry out path and multiple classification analyses.

Course contents

Rates and Ratios. Estimating probability. Mortality from defected data. Nuptiality from limited and defected data. Stationarity. Stable models. Quasi-stable population models. Theory and applications. Single decrement life tables. Multiple decrement life tables. Population projections. Mathematical models. Components methods. Matrix analysis. Bayesian population projections. Path analysis. Multiple classification analysis.

STA 419: Artificial Intelligence (2 Units C: LH 15, PH 30)

Senate-approved relevance to mission, vision, strategic goals, uniqueness, and contextual peculiarities of the University.

Experts believe that artificial intelligence has the potential to accelerate the SDG goals through a responsible application in climate change, health, environment, and food security. In line with the vision of the University in achieving food security, students in Statistics MOUAU needs to be equipped with the requisite skill set to harness the power of artificial intelligence in analyzing and interpreting complex data related to agriculture, resource management, and food production. This includes advanced training in machine learning algorithms, and computational modeling, empowering them to contribute significantly to sustainable agriculture practices, precision farming, and innovative solutions that align with the University’s commitment to achieving food security and supporting the broader Sustainable Development Goals (SDGs).

Overview

Artificial Intelligence is a multidisciplinary field of study that focuses on creating intelligent agents and systems capable of performing tasks that typically require human intelligence. This course explores the principles, techniques, and applications of AI, covering a wide range of topics such as machine learning, natural language processing, computer vision, and problem-solving.

Objectives

The objectives of the course are to:

Gain a comprehensive understanding of the fundamental concepts and principles that form the basis of Artificial Intelligence (AI).
Explore and master various optimization techniques used in AI, which is essential for enhancing AI model performance.
Develop proficiency in Natural Language Processing, delving into techniques for understanding, interpreting, and generating human language using AI algorithms.
Acquire skills in image processing within the context of AI.
Understand ethical issues in AI.

Learning Outcomes

At the completion of the course, students should be able to:

Define and explain the basic concepts, principles, and goals of artificial intelligence.
Implement and analyze optimization algorithms commonly used in AI, such as gradient descent.
Demonstrate proficiency in processing and analyzing natural language data.
Apply image processing techniques to extract relevant features from visual data.
Recognize and address ethical challenges and considerations in AI development and deployment.

Course Contents

Optimization techniques in AI. Gradient descent, Stochastic gradient descent. Natural Language Processing – text pre-processing, tokenization, text representation and text classification. Image processing – image formation, image filtering, edge detection and feature descriptors. Ethical considerations and societal impacts.

STA 499: Research Project (4 Units C: PH 270)

Learning Outcomes

At the end of the course, students should be able to:

exhibit laboratory and field knowledge of subjects taught while at the attachment;
demonstrate knowledge of technical report writing and presentation; and
carryout research on specific topic, collect and evaluate information on specific subject matter while at the attachment.

Course Contents

Research finding into selected topics in statistics, each student will be expected to carry out independent research into an assigned or selected topic and produce a report. Student should be subjected to oral examination on the project.

STA 421: Design and Analysis of Experiment (2 Units C: LH 30)

Learning outcomes

At the completion of the course, students should be able to:

understand the basic concepts of design of experiments
formulate an appropriate model for any experiment
estimate the model parameters using the list square method
analyze experiment involving three and four factors with Latin square model and Graeco-Latin square model.
learn and understand the methods of calculating the effects in a 2^k factorial designs, like expansion of products, even and odd rule, sign table or the Yate’s techniques.
Design and analyze a 2 ^{– 2} x 2^k fractional factorial experiment
Apply these designs and models to data collected in Agriculture, Biology, industry and other fields of humanity.

Course Contents

Basic principle of experimentation, randomization, replication and blocking. Local control. Concepts of basic designs. Completely Randomized Designs (CRD). Completely Randomized Blocks Designs (CRBD). Latin Squares Designs (LSD). Balanced Incomplete Blocks. Split Plot. Missing value. Relative efficiency. Estimation and tests of variance components. Multiple comparisons. Departures from underlying assumptions. Applications to agriculture, biology and industry. Further split plot design and nested designs. Unbalanced designs. Incomplete block designs. 2ⁿ factorial designs. Yates-algorithm. Confounding and factorial replication. Diallel cross analysis. Introduction to Response Surface methodology.

STA 422: Logical Background of Statistics and Decision Theory

(3 Units C: LH 45)

Learning Outcomes

At the end of the course, students should be able to:

describe empirical sources of knowledge-hypothesis, observation and experiment;
explain deductive sources of knowledge and scientific attitude;
explain the concept of causation; probability, a brief historical treatment and to show conflicting definitions;
explain Bayesian statistics and the notion in inverse probability;
identify the place of statistical methods in science;
define the principles of decision making, utility functions and their properties;
explain the role of uncertainty; Bayes Strategies; problems of prior and posterior distributions: value of prior information minimax strategies; statistical inference; and
describe the theory of games

Course Contents

Empirical sources of knowledge: hypothesis, observation and experiment. Causation: probability. Bayesian statistics and notion in inverse probability. Principles of decision making, utility functions and properties. Bayes strategies, prior and posterior distributions, statistical interference, minimax strategies. Theory of games.

STA 423: Machine Learning II (2 Units C: LH 15, PH 30)

Senate-approved relevance to mission, vision, strategic goals, uniqueness, and contextual peculiarities of the University.

Michael Okpara University of Agriculture Umudike is renowned for its keen interest in food proficiency – a vision that can only be driven by developing robust and complex machine learning algorithms to enhance agricultural processes, optimize crop yields, and ensure sustainable food production practices. Graduates with good knowledge of advanced machine learning would be equipped with professional skills in developing machine learning models ranging from crop image segmentation, yield prediction, and disease detection to optimize farming practices. They would also possess the expertise to leverage neural networks for precision agriculture, utilizing data from sensors, satellites, and drones to make informed decisions about irrigation, fertilization, and pest control. This comprehensive skill set enables them to contribute significantly to the ongoing efforts in enhancing crop productivity, resource efficiency, and sustainability in the field of agriculture.

Overview

Machine Learning II is an advanced course designed to deepen student’s understanding and expertise in the field of machine learning. The course focuses on leveraging advanced machine learning libraries, exploring neural networks, understanding model interpretability, and delving into advanced topics in model evaluation and optimization. The course will equip students with the requisite skillset needed to solve problems in computer vision, crop modelling, and climate change solutions.

Objectives

The objectives of the course are to:

Gain proficiency in utilizing advanced machine learning libraries, specifically Tensorflow and PyTorch, for developing and implementing deep learning models.
Explore the foundations of neural networks, emphasizing deep learning architectures.
Acquire knowledge and skills in model interpretability and explainability.
Explore and implement grid search, random search, and Bayesian optimization methods to enhance model performance and efficiency.
Develop the ability to implement deep learning models using Tensorflow and PyTorch for real-world applications.

Learning Outcomes

At the completion of the course, students should be able to:

Demonstrate proficiency in using advanced machine learning libraries, specifically TensorFlow and PyTorch, for deep learning applications.
Analyze and apply various deep learning architectures.
Apply SHAP (SHapley Additive exPlanations) and LIME (Local Interpretable Model-agnostic Explanations) approaches to interpret model predictions and understand feature importance.
Understand the trade-offs involved in selecting appropriate hyperparameters for machine learning models.

Course Contents

Introduction to advanced machine learning libraries for deep learning – Tensorflow, PyTorch. Introduction to neural networks – Deep learning architectures, Convolutional Neural Networks (CNN). Model interpretability and explainability – SHAP and LIME approach. Advanced topics in model evaluation and optimization – Grid search, random search, and Bayesian optimization.

STA 424: Sampling Theory and Survey Methods II (2 Units E: LH 30)

Learning outcomes

At the end of the course, students should be able to:

define the ratio estimator, its bias, expectation and variance
define ratio estimator of the population mean and total, its bias, expectation and mean square error
derive unbiased ratio estimators
define the regression estimator of the population mean and total, its bias and mean square error
show how to derive a gain in precision due to the adoption of stratification
understand the concept of post-stratification
understand the unequal probability sampling
understand the multistage sampling, including two-stage and three-stage sampling
stratified two-stage sampling
apply the concept of ratio and regression estimators to stratified sampling and multistage sampling
understand the double sampling procedures
handle the treatment of non-response using Hansen and Hurwitz as well as Politz and Simon techniques

Course Contents

Unbiased ratio estimator. Multivariate Ratio estimator of the population mean in simple random sampling. Multivariate Regression Estimator. Unequal probability sampling. PPSWR. PPSWOR. Multistage sampling. Two-stage sampling. Three-Stage Sampling. Ratio and regression estimation in stratified sampling. Gain in precision due to stratification. Post stratification. Domain estimation. Double sampling. Double Sampling for ratio estimator. Double sampling for difference estimator. Incomplete response: Hansen and Hurwitz and Simon techniques.

STA 425 : Multivariate Analysis II (2 Units E: LH 30)

Learning Outcomes

On completion of the course, students should be able to:

understand the characteristic features of multivariate data;
confidently use statistical software to perform multivariate analyses
use graphical tools to find patterns in multivariate data;
perform high level multivariate data analysis like principal component analysis, factor analysis, canonical analysis, discriminant and classification analysis, etc.
report results in a comprehensive manner.

Course Contents

Multivariate normal and related distributions. Mean and Variance of Multivariate normal random variates. Other properties of Multivariate normal distributions. Inference about mean vectors. Hoteling’s T^{2 .}Mahalanobis D²statistic. Multivariate Analysis of Variance. Multivariate multiple regression. Principal component analysis. Factor analysis. Canonical correlation analysis. Discriminant analysis. Classification analysis. Cluster Analysis. Use of Statistical Software to perform analysis. Inferences on the analyses.

STA 426: Operation Research II (2 Units E: LH 30)

Learning Outcomes

On completion of the course, students should be able to:

Formulate problems and construct mathematical models for optimum transportation problems at minimum cost.
Construct network plans for projects as well as evaluate project duration.
Obtain optimal solutions of multi-period managerial problems.
Model queues in different systems and determine their performance measures.
Obtain optimal solution of multi-objective ‘man-machine’ problems.
Obtain efficient solution of non-linear programming problems.

Course Contents

Mathematical programming. Integer programming. Dynamic programming. Theory of reliability. Active and passive reliability. Reliability of a system in series, and in parallel. Hazard rate. Mean time to failure. Inventory models. Optimization. Assignment problems. Network analysis. Critical path method. Programme Evaluation Technique. Theory of queues. Single server. Multi-server queues. Non-linear programming. Quadratic programming.

STA 427: Stochastic Processes (2 Units C: LH 30)

Learning outcomes

By the end of this course, students should be able to:

derive and apply the concept of generating functions in tail probabilities and convolutions
understand Random Walks
understand Markov processes in discrete and continuous time.
know the concept of Poisson, branching, birth and death processes; and
use these concepts to model a queueing process.

Course Contents

Concepts of Stochastic Processes. Some examples of a stochastic process. Discrete and Continuous stochastic processes. Generating functions: tail probabilities and convolutions. Recurrent events. Random walk (unrestricted and restricted). Gamblers ruin problem. Markov processes in discrete and continuous time. Poisson process. Branching. Birth and Death processes. Queuing processes and mechanisms. M/M/1 process. M/M/S process. M/A/1 queues. Waiting time distributions of the queue processes.