BIOS6170
10 units
6000 level
Course handbook
Description
The first half of the course covers the foundations of probability theory including: probability laws, conditional probability, random variables, probability distributions, expectation and variance, independence, covariance and correlation. Commonly used families of probability distributions and their properties will be discussed. Large sample results such as the Central Limit Theorem will be used to approximate sampling distributions. The second half of the course introduces the basics of statistical inference including: likelihood, point and interval estimation, properties of estimators (such as bias), and hypothesis testing paradigms. Emphasis is placed on theoretical understanding combined with problem solving using basic simulation methods such as Inverse Transform Sampling and Monte Carlo. Practical exercises will include estimating probabilities theoretically and empirically, investigating the performance of basic statistical methods under different assumptions, and interpreting the use of probability and inference in medical statistics research.
Availability2024 Course Timetables
Online
- Semester 2 - 2024
Learning outcomes
On successful completion of the course students will be able to:
1. Calculate probabilities by applying probability laws and theoretical results.
2. Identify an appropriate probability distribution for a given discrete or continuous random variable and use its properties to calculate probabilities.
3. Calculate statistics such as the mean and variance of common probability distributions.
4. Calculate probabilities for joint distributions including marginal and conditional probabilities.
5. Determine whether random variables are independent and find their covariance and correlation.
6. Apply results from large-sample theory and the Central Limit Theorem to approximate a sampling distribution.
7. Explain the desirable properties of estimators.
8. Calculate and interpret maximum likelihood estimates and their confidence intervals.
9. Explain the role of probability in hypothesis testing and describe issues related to interpreting statistical significance.
10. Implement basic simulation methods using statistical software to investigate sampling distributions.
Content
- Module 1 - Probability
- Module 2 - Random variables and probability distributions
- Module 3 - Properties of probability distributions
- Module 4 - Joint distributions
- Module 5 - Sampling distributions and the Central Limit Theorem
- Module 6 - Likelihood and estimation
- Module 7 - Hypothesis testing
This course also includes practical exercises in simulation using statistical software (Stata, SAS, and R).
Assumed knowledge
Basic computer skills, high-school level mathematics (pre-calculus)
Assessment items
Quiz: Quiz 1
Written Assignment: Assignment 1
Written Assignment: Assignment 2
Written Assignment: Assignment 3
Contact hours
Semester 2 - 2024 - Online
Online Activity-1
- Online 2 hour(s) per week(s) for 13 week(s) starting in week 1
Self-Directed Learning-1
- Self-Directed 8 hour(s) per week(s) for 13 week(s) starting in week 1
Course outline
Course outline not yet available.
The University of Newcastle acknowledges the traditional custodians of the lands within our footprint areas: Awabakal, Darkinjung, Biripai, Worimi, Wonnarua, and Eora Nations. We also pay respect to the wisdom of our Elders past and present.