SIT743: Bayesian Learning and Graphical Models - IT Computer Science Assignment Help

Assignment Task

Q1)

For this question, use the dataset given as a CSV file, named “DataMyrmindon2023.csv”. You can download this from the Assignment folder in CloudDeakin (Unit site). Below is the description of this dataset.

This dataset, comprising air and sea water measurements, has been collected from Myrmindon Reef , which is located in the Great Barrier Reef, North Queensland, Australia.

This data gives 10 minutes sample measurements collected over an approximately one-year period between March 2022 and March 2023.

The dataset includes the following variables, in the same order of columns as appear in the file DataMyrmindon2023.csv:

o AirTemperature: Air temperature in degree Celsius o Pressure: Air pressure in Hectopascals

o Humidity: Relative Humidity in percentage.

o WaterTemperature: Water temperature (at 14.7m below the surface of the sea water) in degrees Celsius.

o WindSpeed: Average wind speed in kilometers per hour

 

• Download the data file “DataMyrmindon2023.csv” and save it to your R working directory.
• Assign the data to a matrix, e.g. using

the.fulldata <- as.matrix(read.csv("DataMyrmindon2023.csv", header = TRUE, sep = ","))

• Generate a sample of 30,000 data using the following:

my.data <- the.fulldata [sample(1: 52561, 30000), c(1:5)]

Save “my.data” to a text file titled “name-StudentID-MyrmMyData.txt" using the following R code (NOTE: it is ‘mandatory’ to upload this data text file and the R code along with your submission. If not, ZERO marks will be given for this whole question).

 write.table(my.data,"name-StudentID-MyrmMyData.txt")

 

Use the sampled data (“my.data”) to answer the following questions.

1.1) Draw a histogram and a box plot for the ‘Humidity’ variable. Provide a five number summary for the Humidity values. Use these to comment about the distribution of the Humidity variable.

1.2) Which summary statistics would you choose to summarize the center and the spread for the ‘Humidity’ variable? Why?

1.3) Draw a parallel box plot for variables ‘AirTemperature’ and ‘WaterTemperature’. Compare and comment on the results.

1.4) Draw a scatterplot of ‘Pressure’ (as x) and ‘AirTemperature‘ (as y). Name the axes.

Fit a linear regression model to the above two variables, and plot the (regression) line on the same scatter plot.

Write down the linear regression equation.

Compute the correlation coefficient and the coefficient of Determination.

Explain what these results reveal.

1.5) Create three new variables, as defined below:

• ‘WaterTB’: This takes the value “High” when the WaterTemperature is above 28 degrees Celsius, “Moderate” when the WaterTemperature is between 25 and 28 (both inclusive), and “Low” when the WaterTemperature is below 25.
• ‘PreB’: This takes the value “High” when the pressure is above 1013 Hectopascals, otherwise it is "Low".
• ‘WSB’: This takes the value “High” when the WindSpeed is above 30 km/h, otherwise it is "Low".

1. Write R program to construct a cross table (cross tabulation) using the above three new variables (WaterTB, PreB, and WSB).

Show the obtained cross table.

1. Use the above obtained cross table to answer the following questions. Show all the steps/workings clearly.

Consider that a record (row) is selected from the data at random,

1. what is the probability that the WSB is low?
2. what is the probability that the WaterTB is moderate given that the WSB is high?

• what is the probability that the WaterTB is low given that the WSB is high and the PreB is low?

1. Are low WaterTB and high PreB mutually exclusive? Explain.
2. Are high WSB and low WaterTB independent events? Explain.

 

Q2)

2.1) a) State two differences between frequentist way and the Bayesian way of estimating a parameter

b) How the uncertainty (or variance/error) in an (parameter) estimate is computed using the frequentist approach?

c) Why are conjugate priors useful in Bayesian statistics? Give an example of a Conjugate pair.

2.2 ) A basket contains four red marbles and six black marbles. John performed three selections (trials) from the basket in a sequence. In each selection (trial), if he picks a red marble, he keeps it with him (i.e., he does not put it back in the basket). If he picks a black marble, he returns two black marbles to the basket (i.e., he returns one more ‘additional’ black marble to the basket). At the end of three selections, compute the following probabilities.

Show all the steps/workings clearly.

a) Draw a tree diagram and mark all the probabilities in the branches.

b) What is the probability that John ended up keeping two black marbles with him?

c) What is the probability that only the third one john has chosen is the red marble?

d) What is the probability that john gets at least one red marble?

e) Given that his 3rd selection was a black marble, what is the probability that his 2nd selection was a black marble?

 

Q3) Frequentist and Bayesian estimations

 

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