## STAT370 Statistical Inference

Second Semester |

This course continues to develop theory for making inference from data that was introduced in STAT 270 (or STAT 261). The tools developed by statisticians for analysing data have become a major factor in the advancement of scientific knowledge. Why are these tools so useful? The reason is that they are based on an agreed system of mathematical and statistical reasoning. In order to be confident that the methods used by a statistician are reliable we need an understanding of this theory.

### Paper details

In STAT370 we will use some of the skills that you developed in STAT270 and begin to apply them to important statistical problems. In particular we will start to look at the theoretical basis for the linear models developed in STAT210, STAT310 and STAT311. We will also consider in more detail the theory behind hypothesis testing and estimation, including Bayesian methods.

Much of statistical analysis involves postulating a model for observed data, fitting the model to data and selecting between models, and finally making inference based on the chosen model. The first part of the course will look at matrix methods for the general linear model, an important class of models that is used in regression analysis and ANOVA. It will look at likelihood-based model inference, and conclude with Bayesian methods.

### Potential students

STAT 370 is required for all students majoring in Statistics. It provides an understanding of the statistical approaches used in science and industry and is recommended for all students with a strong mathematics background interested in a career in scientific research.

### Main topics

- The general linear model
- The likelihood function
- Bayesian inference
- Maximum likelihood estimation
- Hypothesis testing using the likelihood function
- Model selection using the likelihood function

### Prerequisites

(STAT 261 or 270), MATH 170

### Required text

A full set of lecture notes is provided.

### Useful references

*Mathematical Statistics with Applications* by Wackerly, Mendenhall and Scheaffer.

*An Introduction to Mathematical Statistics and its Applications* by Larsen and Marx

### Lecturers

Austina Clark, room 117

Ting Wang, room 518

### Lectures

3 lectures per week:

Tuesday at 11am in MA240

Wednesday and Friday at 11am in room MA241.

### Tutorials

Wednesday 3pm-4pm every week

### Internal Assessment

The internal assessment is made up of two parts:

- 3/8 = 37.5% from 6 exercises. Assignments are to be word processed using LaTeX.
- 5/8 = 62.5% from a mid-term test

### Exam format

The final exam will be worth 60% of the final mark. A minimum score of 40% is required on the exam in order to pass the paper.

### Final mark

Your final mark F in the paper will be calculated according to this formula:

**F = (0.6E + 0.15A + 0.25T)**

where:

- E is the Exam mark
- A is the Assignments mark
- T is the Tests mark

and all quantities are expressed as percentages.

### Students must abide by the University’s Academic Integrity Policy

**Academic integrity** means being honest in your studying and assessments. It is the basis for ethical decision-making and behaviour in an academic context. Academic integrity is informed by the values of honesty, trust, responsibility, fairness, respect and courage.

**Academic misconduct** is seeking to gain for yourself, or assisting another person to gain, an academic advantage by deception or other unfair means. The most common form of academic misconduct is plagiarism.

Academic misconduct in relation to work submitted for assessment (including all course work, tests and examinations) is taken very seriously at the University of Otago.

All students have a responsibility to understand the requirements that apply to particular assessments and also to be aware of acceptable academic practice regarding the use of material prepared by others. Therefore it is important to be familiar with the rules surrounding academic misconduct at the University of Otago; they may be different from the rules in your previous place of study.

Any student involved in academic misconduct, whether intentional or arising through failure to take reasonable care, will be subject to the University’s Student Academic Misconduct Procedures which contain a range of penalties.

If you are ever in doubt concerning what may be acceptable academic practice in relation to assessment, you should clarify the situation with your lecturer before submitting the work or taking the test or examination involved.

Types of academic misconduct are as follows:

**Plagiarism**

The University makes a distinction between unintentional plagiarism (Level One) and intentional plagiarism (Level Two).

- Although not intended,
*unintentional plagiarism*is covered by the Student Academic Misconduct Procedures. It is usually due to lack of care, naivety, and/or to a lack to understanding of acceptable academic behaviour. This kind of plagiarism can be easily avoided. *Intentional plagiarism*is gaining academic advantage by copying or paraphrasing someone elses work and presenting it as your own, or helping someone else copy your work and present it as their own. It also includes self-plagiarism which is when you use your own work in a different paper or programme without indicating the source. Intentional plagiarism is treated very seriously by the University.

**Unauthorised Collaboration**

Unauthorised Collaboration occurs when you work with, or share work with, others on an assessment which is designed as a task for individuals and in which individual answers are required. This form does not include assessment tasks where students are required or permitted to present their results as collaborative work. Nor does it preclude collaborative effort in research or study for assignments, tests or examinations; but unless it is explicitly stated otherwise, each students answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer..

**Impersonation**

Impersonation is getting someone else to participate in any assessment on your behalf, including having someone else sit any test or examination on your behalf.

**Falsiﬁcation**

Falsiﬁcation is to falsify the results of your research; presenting as true or accurate material that you know to be false or inaccurate.

**Use of Unauthorised Materials**

Unless expressly permitted, notes, books, calculators, computers or any other material and equipment are not permitted into a test or examination. Make sure you read the examination rules carefully. If you are still not sure what you are allowed to take in, check with your lecturer.

**Assisting Others to Commit Academic Misconduct**

This includes impersonating another student in a test or examination; writing an assignment for another student; giving answers to another student in a test or examination by any direct or indirect means; and allowing another student to copy answers in a test, examination or any other assessment.