# MATH09004 2017 Applied Statistics and Probability

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**Description**

This module covers the statistics and probability required for a Masters in Engineering. The learner will gain the expertise to interpret the probabilistic models used in the engineering literature. It will cover statistical methods to analyse and quantify processes. It will enable learners to model problems using probabilistic and statistical mathematical methods.

### Learning Outcomes

*On completion of this module the learner will/should be able to;*

**1.**

*Apply probability theory to analsye the centrality, dispersion and relationships within and between datasets and distributions. *

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*Apply experimental design and statistical inference to make inferences from data.*

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Analyse the bias and variance of maximum likelihood and Bayesian estimators.

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Analyse stochastic processes (including Markov processes).

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*Evaluate, select and apply appropriate statistical techniques to problems in the application field of study. *

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*Interpret the probability and statistics used in state of the art research publications and reproduce findings.*

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*Model an application specific problem with statistics and probability techniques.*

### Teaching and Learning Strategies

A lecture will be provided each week. In advance of the lecture, the learner will be asked to material that is relevant to the lecture so that they get the maximum learning from that lecture.

The project work will challenge the learner to master concepts beyond those covered in the theory lecture.

### Module Assessment Strategies

A terminal exam and continuous assessment will be used to assess the module.

To reinforce the theoretical principles covered in lectures, learners will participate in project work.

The learner will complete a final exam at the end of the semester.

The learner is required to pass both the continuous assessment and terminal examination element of this module.

### Repeat Assessments

Repeat Exams will be set for Autumn of each year.

Repeat continuous assessment can be submitted at the end of August each year.

### Indicative Syllabus

Probability Theory

- Random Variables
- Probability Distributions
- Marginal Probability
- Conditional Probability
- The Chain Rule of Conditional Probabilities
- Independence and Conditional Independence
- Expectation, Variance and Covariance
- Common Probability Distributions
- Useful Properties of Common Functions
- Technical Details of Continuous Variables
- Random Vectors

Estimation Theory

- Estimators, Bias and Variance.

MMSE, MAP, BLUE estimators

Bias/Variance trade-off

- Design of Experiments
- Statistical Inference & Inferential thinking
- Bayes’ Theorem
- Maximum Likelihood
- Stochastic Processes

### Coursework & Assessment Breakdown

**Coursework & Continuous Assessment**

**End of Semester / Year Formal Exam**

### Coursework Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
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1 | CA 1 | Continuous Assessment | Assessment | 30 % | Week 6 | 1,2,3,4 |

2 | Project | Continuous Assessment | Project | 30 % | Week 12 | 1,2,3,4,5,6,7 |

### End of Semester / Year Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
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1 | Final Exam | Final Exam | Closed Book Exam | 40 % | End of Semester | 1,2,3,4,5,6,7 |

### Full Time Mode Workload

Type | Location | Description | Hours | Frequency | Avg Workload |
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Lecture | Lecture Theatre | Lecture | 2 | Weekly | 2.00 |

Laboratory Practical | Computer Laboratory | Laboratory Practical | 2 | Fortnightly | 1.00 |

Independent Learning | Not Specified | Independent Learning | 7 | Weekly | 7.00 |

### Online Learning Mode Workload

Type | Location | Description | Hours | Frequency | Avg Workload |
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Lecture | Online | Theory Lecture | 1 | Weekly | 1.00 |

Independent Learning | Not Specified | Independent Learning | 8.5 | Weekly | 8.50 |

Laboratory Practical | Online | Laboratory Practical | 0.5 | Weekly | 0.50 |

### Required & Recommended Book List

**Recommended Reading**

2016-03-28

*Python for Probability, Statistics, and Machine Learning*Springer

ISBN 3319307150 ISBN-13 9783319307152

This book covers the key ideas that link probability, statistics, and machine learning illustrated using Python modules in these areas. The entire text, including all the figures and numerical results, is reproducible using the Python codes and their associated Jupyter/IPython notebooks, which are provided as supplementary downloads. The author develops key intuitions in machine learning by working meaningful examples using multiple methods and codes thereby connecting theoretical concepts to concrete implementations. This book is suitable for anyone with an undergraduate-level exposure to probability, statistics, and machine learning and with rudimentary knowledge of Python programming.

**Recommended Reading**

2007-02-01

*Pattern Recognition and Machine Learning (Information Science and Statistics)*Springer

ISBN 0387310738 ISBN-13 9780387310732

The dramatic growth in practical applications for machine learning over the last ten years has been accompanied by many important developments in the underlying algorithms and techniques. For example, Bayesian methods have grown from a specialist niche to become mainstream, while graphical models have emerged as a general framework for describing and applying probabilistic techniques. The practical applicability of Bayesian methods has been greatly enhanced by the development of a range of approximate inference algorithms such as variational Bayes and expectation propagation, while new models based on kernels have had a significant impact on both algorithms and applications. This completely new textbook reflects these recent developments while providing a comprehensive introduction to the fields of pattern recognition and machine learning. It is aimed at advanced undergraduates or first-year PhD students, as well as researchers and practitioners. No previous knowledge of...

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