c) Multiple Submissions are allowed BEFORE THE DEADLINE are allowed for both the report, and the code.

However, multiple submissions are NOT ALLOWED AFTER THE DEADLINE.

YOU WILL NOT BE ABLE TO MAKE ANY CHANGES TO YOUR SUBMISSION AFTER THE DEADLINE.

Nevertheless, if you did not submit anything before the deadline, then you can still submit

your work after the deadline, but late penalties will apply. The timing of the late penalties will be determined by the time you have submitted BOTH the report, and the code (i.e. whichever was submitted later counts).

We illustrate these rules by some examples:

Alice has spent a lot of time and effort on her assignment for BDA. Unfortunately, before

submission, she has accidentally introduced a typo in her code in the first question, and it did

not run using Run All in RStudio. - Alice will get 0 for the questions that do not run in her

code (we will try to run each code block individually), with the only feedback “Results are not reproducible from the code”.

Bob has spent a lot of time and effort on his assignment for BDA. Unfortunately he forgot to

submit his code. - Bob will get no personal reminder to submit his code. Bob will get 0 for

the whole assignment, with the only feedback “Results are not reproducible from the code, as

the code was not submitted.”

Charles has spent a lot of time and effort on his assignment for BDA. He has submitted both

his code and report in the correct formats. However, he did not include any explanations in the report. Charles will get 0 for the whole assignment, with the only feedback “Explanation is missing.”

Denise has spent a lot of time and effort on her assignment for BDA. She has submitted

her report in the correct format, but thought that she can include her code as a link in the

report, and upload it online (such as Github, or Dropbox). - Denise will get 0 for the whole assignment, with the only feedback “Code was not uploaded on Learn.”

3) Group work: This is an INDIVIDUAL ASSIGNMENT, like a 2 week exam for the course. Communication between students about the assignment questions is not permitted. Students who submit work that has not been done individually will be reported for Academic Mis- conduct, that can lead to serious consequences. Each problem will be marked by a single instructor, so we will be able to spot students who copy.

Problem 1

In this problem, we study a dataset about car insurance. This data set is based on one-year vehicle insurance policies taken out in 2004 or 2005. In total, there are 67856 policies, of which 4624 have claims.

require (insuranceData)

##  Loading  required  package:  insuranceData

data (dataCar)

#You may need to set the working directory first before loading the dataset #setwd("location of Assignment 1")

#The first 6 rows of the dataframe

print.data.frame (dataCar[1:6,])

##    ##  1 ##  2 ##  3 ##  4 ##  5 ##  6 ##    ##  1 ##  2 ##  3 ##  4

veh_value    exposure  clm  numclaims

1 .06  0 .3039014      0                  0

1 .03  0 .6488706      0                  0

3 .26  0 .5694730      0                  0

4 .14  0 .3175907      0                  0 0 .72  0 .6488706      0                  0

2 .01  0 .8542094      0                  0

agecat                       X_OBSTAT_

2  01101        0        0        0

4  01101        0        0        0

2  01101        0        0        0

2  01101        0        0        0

claimcst0 0 0 0 0 0 0

veh_body

HBACK HBACK  UTE STNWG HBACK HDTOP

veh_age

3

2

2

2

4

3

gender

F F F F F M

area

C

A

E

D

C

C

##  5

##  6

2  01101

4  01101

0

0

0

0

0

0

Description of the columns.

veh_value: vehicle value in $10000s

exposure: maximum portion of the vehicle value the insurer may need to pay out in case of an incident

claimcst0: claim amount (0 if no claim)

clm: whether there was a claim during the 1 year duration

numclaims: number of claims during the 1 year duration

veh_body types: BUS = bus CONVT = convertible COUPE = coupe HBACK = hatchback

HDTOP = hardtop MCARA = motorized caravan MIBUS = minibus PANVN = panel van

RDSTR = roadster SEDAN = sedan STNWG = station wagon TRUCK = truck UTE =

utility

gender: F- female, M - male

area: a factor with levels A,B,C,D,E, F

agecat: age category, 1 (youngest), 2, 3, 4, 5, 6

You can use either JAGS, Stan, or INLA for this question.

a)[10 marks] Fit a Bayesian logistic regression model on the dataset dataCar with

● clm as response,

● a link function of your choice,

● using veh_value, exposure, veh_body, veh_age, gender, area, and agecat as covariates (you can use categorical covariates by converting integers to factors if appropriate).

Center and scale the non-categorical covariates.

Choose your own prior distributions (do not use default priors), and explain the rationale your prior choices, and ensure that the posterior is not too sensitive to your prior choice [Hint: look at the induced prior on the linear predictor and on the response.]

Compute the posterior means of the model parameters, and discuss the results.

Explanation (min 300 characters in your own words, otherwise -5 marks for insufficient explanation):

b)[10 marks] Fit a Bayesian Poisson regression model on numclaims as response with

● log link function,

● using veh_value, exposure, veh_body, veh_age, gender, area, and agecat as covariates. Center and scale the non-categorical covariates.

Choose your own prior distributions (do not use default priors), and explain the rationale your prior choices, and ensure that the posterior is not too sensitive to your prior choice [Hint: look at the induced prior on the linear predictor and the response.]

Compute the posterior means of the model parameters, and discuss the results.

Explanation (min 300 characters in your own words, otherwise -5 marks for insufficient explanation):

c)[10 marks] Fit a zero-inflated Bayesian Poisson regression model (https://en.wikipedia.org /wiki/Zero-inflated_model) on

● numclaims as response,

● with log link function,

● using veh_value, exposure, veh_body, veh_age, gender, area, and agecat as covariates. Center and scale the non-categorical covariates.

Choose your own prior distributions (do not use default priors), and explain the rationale your prior choices, and ensure that the posterior is not too sensitive to your prior choice [Hint: look at the induced prior on the linear predictor and the response.]

Compute the posterior means of the model parameters, and discuss the results.

Explanation (min 300 characters in your own words, otherwise -5 marks for insufficient explanation):

d)[10 marks] Fit a new model on numclaims in terms of the same covariates to improve on the models in part b) or part c) by considering interactions between covariates, as well as random effects. Describe your new model and justify your choices.

Choose your own prior distributions (do not use default priors), and explain the rationale your prior choices, and ensure that the posterior is not too sensitive to your prior choice [Hint: look at the induced prior on the linear predictor and the response.]

Compute the posterior means of the model parameters, and discuss the results.

Explanation (min 300 characters in your own words, otherwise -5 marks for insufficient explanation):

e)[10 marks] Perform posterior predictive model checks for your models b, c, d (i.e. using replicates).

As test functions, use the number of rows in the dataset with numclaims equal 0, 1, 2, 3, and 4 (5 test functions).

Compute the RMSE values for predicting numclaims based on all 3 models. Discuss the results.

Explanation (min 300 characters in your own words, otherwise -5 marks for insufficient explanation):

Problem 2 - Barcelona study

In this problem, we will use a dataset from the CitieS-Health project that provides insight

into the impact of air pollution on humans. It is comprised of data collected in Barcelona,

Spain, and examines various environmental variables, such as air pollution levels, and their

effects on mental health and wellbeing. In addition to environmental factors, this dataset also captures self-reported survey data on mental health, physical activity, diet habits, and more. From performance in a Stroop test (a type of psychological test evaluating attention capacity and processing speed) to information on total noise exposure at 55 dB - this dataset contains interesting information to understand the link between air pollution and human health.

We start by loading the dataset.

study<-read .csv ( "Barcelona .csv")

head(study)

##      Person_ID  date_all  year  month  day  dayoftheweek  hour  sadness  wellbeing  energy

##  1              115        22222  2020        11      3                        1      18            14                  3            2 ##  2              212        22247  2020        11    28                       5      18             4                  9            9 ##  3              104        22208  2020        10    20                        1      20              1                  6            6 ##  4              216        22247  2020        11    28                       5      18              2                  8            8 ##  5                94        22213  2020        10    25                       6      19            12                  8           4

##  6               215         22258  2020         12      9                          2      20               4                    7             7

##      stress  sleep  hours_out  physical_activity  computer_use  on_a_diet  alcohol  drugs

##  1            5          2                  5                               No                   Yes             Yes           No        No ##  2            1          9                  5                             Yes                     No               No         Yes        No ##  3            7          9                11                               No                   Yes             Yes           No        No ##  4            1          3                  2                             Yes                     No             Yes         Yes        No ##  5            2          8                  1                               No                   Yes               No           No      Yes

##  6 ##    ##  1 ##  2 ##  3 ##  4 ##  5 ##  6 ##    ##  1 ##  2 ##  3 ##  4 ##  5 ##  6 ##    ##  1 ##  2 ##  3 ##  4 ##  5 ##  6 ##    ##  1 ##  2 ##  3 ##  4 ##  5 ##  6 ##    ##  1 ##  2 ##  3 ##  4 ##  5 ##  6 ##    ##  1 ##  2 ##  3 ##  4 ##  5 ##  6