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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. PropertyPrices.cs 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 In the first part, suppose that SalePrice is distributed as where both of p and o² are unknown. Follow the steps given below to find the Bayesian estimate of mean sale price p in Melboume and its variance o²: 1. Create a model diagram for JAGS showing the distribution of sale prices and prior distributions of p and o2 At this step, please do not forget to consider domains of p and 021 2. Specify non-informative prior distributions for both of p and o2 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 p and its variance o² and draw inferences on their Bayesian point and interval estimates. 1/6 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. Part B 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: 2/6 Property Area Bedrooms Bathrooms CarParks PropertyType No 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-inperiod, thinning are all up to your implementation This can change from one report to the other based on the prior distributions and MCMC diagnostics.

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