## Overview

Applications of stochastic models to real-world processes observed over time and space. Topics include Poisson processes, renewal processes, Markov chains, hidden Markov models, geostatistics, spatial point processes, model fitting, forecasting and simulation.

This paper introduces at undergraduate level an important class of statistical methods that is widely used in many areas of research and research-informed decision making. It is an introduction to practical data analysis using statistical methods for processes occurring randomly in time and space. Stochastic models have been applied to natural phenomena such as outbreaks of infectious diseases, crimes, financial downturns, stock market return, transitions between high and low economic growth, accident related insurance claims, earthquakes, volcanic eruptions, and forest fires. Real data from economics, finance, geosciences, neuroscience, social sciences and epidemiology will be used to introduce various stochastic models and their applications.

Paper title Stochastic Modelling Statistics 0.15 18 points Semester 1 (On campus) \$981.75 Tuition Fees for international students are elsewhere on this website.
Prerequisite
STAT 261 or STAT 270
Schedule C
Arts and Music, Science
Contact

ting.wang@otago.ac.nz

Teaching staff

Associate Professor Ting Wang

Dr Conor Kresin

Paper Structure

We will focus on applications of the following models in real-world data analysis (using R), model checking, simulation and forecasting from these models.

• Poisson processes
• Renewal processes
• Discrete-time Markov chains
• Hidden Markov models
• Geostatistics
• Spatial point processes
Textbooks

Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Environmental literacy, Information literacy, Research, Self-motivation, Teamwork.
Learning Outcomes

The aim of this paper is to introduce students to many of the statistical learning techniques that are now used to analyse high-dimensional data. Students will learn the underlying rationale for each method and gain practice in using it on real data in R.

On successful completion of the paper, students will be able to:

1. Apply an important class of modern temporal and spatial stochastic models to real data.
2. Describe the assumptions underlying use of each of these methods.
3. Determine an appropriate type of stochastic models for a given analysis.
4. Describe probabilistic forecast using stochastic processes.
5. Critically appraise research literature in terms of the statistical methods used.
6. Use a standard statistical programming language (R) to analyse data and simulate stochastic processes.

## Timetable

### Semester 1

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

#### Lecture

Stream Days Times Weeks
Attend
A1 Monday 11:00-11:50 9-13, 15-22
Wednesday 11:00-11:50 9-13, 15-22
Friday 11:00-11:50 9-12, 15-22

#### Tutorial

Stream Days Times Weeks
Attend
A1 Thursday 09:00-09:50 9-13, 15-16, 18-22