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Assignment 2
Assignment Instructions:
In this assignment, you will analyse and estimate property prices in Melbourne by using Bayesian methods. The dataset you will focus on is a fabricated dataset by using real data after a number of other analyses for the population distributions of the variables included in the dataset. Assignment2PropertyPrices.csv includes the following variables:
• SalePrice: Sale price in AUD
• Area: Land size in m2 of the sold property
• Bedrooms: The number of bedrooms
• Bathrooms: The number of bathrooms
• CarParks: The number of car parks
• PropertyType: The type of the property (0: House, 1: Unit)
Part A - Required knowledge to do the tasks in this part is covered by Modules 1 to 5.
In the first part, suppose that SalePrice is distributed as Normal(µ,s2), where both of µ and s2 are unknown. Follow the steps given below to find the Bayesian estimate of mean sale price µ in Melbourne and its variance s2:
1. Create a model diagram for JAGS showing the distribution of sale prices and prior distributions of µ and s2. At this step, please do not forget to consider domains of µ and s2!
2. Specify non-informative prior distributions for both of µ and s2.
3. Create JAGS data and model blocks based on the model diagram at the previous step.
4. Compile your model and create Markov chains using the compiled model.
5. Assess the appropriateness of the chains using the MCMC diagnostics.
6. Display the posterior distribution of mean sales price µ and its variance s2 and draw inferences on their Bayesian point and interval estimates.
Write Part A of your report for this assignment based on your implementation of the steps above and the inferences you draw.
Settings of MCMC sampler such as the number of chains, the length of burn-in period, thinning are all up to your implementation. This can change from one report to the other based on the prior distributions and MCMC diagnostics.
Hint: The task in Part A is just a simple extension of Task 4 of Module 5.
Part B - Required knowledge to do the tasks in this part is covered by Modules 1 to 6.
In the second section, you will model the sale prices in Melbourne using the other predictors given in the dataset and expert knowledge from a real estate agent. For each predictor, expert information and degree of belief in the prior information is given as follows:
• Area: Every m2 increase in land size increases the sales price by 90 AUD. This is a very strong expert knowledge.
• Bedrooms: Every additional bedroom increases the sales price by 100,000AUD. This is a weak expert knowledge.
• Bathrooms: There is no expert knowledge on the number of bathrooms.
• CarParks: Every additional car space increases the sales price by 120,000AUD. This is a strong expert knowledge.
• PropertyType: If the property is a unit, the sale price will be 150,000 AUD less than that of a house on the average. This is a very strong expert knowledge.
Follow the steps given below to build a Bayesian regression model to predict sale prices using the past sales information and expert knowledge:
1. Create a JAGS model diagram showing the multiple linear regression setting in this problem.
2. Specify the prior distributions reflecting the expert information for each predictor.
3. Create JAGS data and model blocks based on the model diagram and prior distributions at the previous steps.
4. Compile your model and create Markov chains using the compiled model.
5. Assess the appropriateness of the chains for each parameter using the MCMC diagnostics.
6. Display the posterior distribution of each parameter and draw inferences on Bayesian point and interval estimates.
7. Use the Bayesian point estimates of the model parameters to write the predictions model.
8. Find the predictions of sale prices for the properties given below:
Property No Area Bedrooms Bathrooms CarParks PropertyType
1 600 2 2 1 Unit
2 800 3 1 2 House
3 1500 2 1 1 House
4 2500 5 4 4 House
5 250 3 2 1 Unit

Write Part B of your report for this assignment based on your implementation of the steps above and the inferences you draw.
Settings of MCMC sampler such as the number of chains, the length of burn-in period, thinning are all up to your implementation. This can change from one report to the other based on the prior distributions and MCMC diagnostics.
Submission Instructions:
• All assignments must be submitted via the Turnitin link on the course Canvas prior to the due date.
• Your submission should be uploaded as a PDF or Microsoft Word file.
• Your report should meet with English language requirements.
• Late submissions will be marked in accordance with the late submission policy explained under “Assessment” title of the course information sheet.
Collaboration vs. Collusion and Plagiarism:
Please make sure that the similarity rate of your report in Turnitin is less than 30%!
You are free to discuss main aspects of the assignment with your classmates. However, keep in mind that this is an individual assignment and you should demonstrate your own effort and understanding. Because assignments will be submitted through Turnitin, all the material you submitted will be checked for plagiarism. If plagiarism is detected, both the copier and the student copied from will be responsible. Therefore, it is your responsibility to ensure you do not copy or do not allow other classmates to copy your work. You should ensure you understand your responsibilities by reading the RMIT University website on academic integrity (Links to an external site.)Links to an external site.