This block will only be visible in your HTML output, but will be hidden when rendering to PDF with quarto for the submission. Make sure that this does not get displayed in the PDF!
This is the template for assignment 3. You can download the qmd-files (full, simple) or copy the code from this rendered document after clicking on </> Code in the top right corner.
Please replace the instructions in this template by your own text, explaining what you are doing in each exercise.
The following will set-up markmyassignment to check your functions at the end of the notebook:
Loading required package: markmyassignmentassignment_path = paste("https://github.com/avehtari/BDA_course_Aalto/",
"blob/master/assignments/tests/assignment3.yml", sep="")
set_assignment(assignment_path)Assignment set:
assignment3: Bayesian Data Analysis: Assignment 3
The assignment contain the following (6) tasks:
- mu_point_est
- mu_interval
- mu_pred_interval
- mu_pred_point_est
- posterior_odds_ratio_point_est
- posterior_odds_ratio_intervalThe following installs and loads the aaltobda package:
if(!require(aaltobda)){
install.packages("aaltobda", repos = c("https://avehtari.github.io/BDA_course_Aalto/", getOption("repos")))
library(aaltobda)
}Loading required package: aaltobdaThe following installs and loads the latex2exp package, which allows us to use LaTeX in plots:
Loading the library and the data.
data("windshieldy1")
# The data are now stored in the variable `windshieldy1`.
# The below displays the data:
windshieldy1[1] 13.357 14.928 14.896 15.297 14.820 12.067 14.824 13.865 17.447The below data is only for the tests, you need to change to the full data windshieldy1 when reporting your results.
Write your answers here!
Write your answers and code here!
Keep the below name and format for the functions to work with markmyassignment:
# Useful functions: mean(), length(), sqrt(), sum()
# and qtnew(), dtnew() (from aaltobda)
mu_point_est <- function(data) {
# Do computation here, and return as below.
# This is the correct return value for the test data provided above.
14.5
}
mu_interval <- function(data, prob = 0.95) {
# Do computation here, and return as below.
# This is the correct return value for the test data provided above.
c(13.3, 15.7)
}You can plot the density as below if you implement mu_pdf to compute the PDF of the posterior \(p(\mu|y)\) of the average hardness \(\mu\).
mu_pdf <- function(data, x){
# Compute necessary parameters here.
# These are the correct parameters for `windshieldy_test`
# with the provided uninformative prior.
df = 3
location = 14.5
scale = 0.3817557
# Use the computed parameters as below to compute the PDF:
dtnew(x, df, location, scale)
}
x_interval = mu_interval(windshieldy1, .999)
lower_x = x_interval[1]
upper_x = x_interval[2]
x = seq(lower_x, upper_x, length.out=1000)
plot(
x, mu_pdf(windshieldy1, x), type="l",
xlab=TeX(r'(average hardness $\mu$)'),
ylab=TeX(r'(PDF of the posterior $p(\mu|y)$)')
)
Write your answers and code here!
Keep the below name and format for the functions to work with markmyassignment:
# Useful functions: mean(), length(), sqrt(), sum()
# and qtnew(), dtnew() (from aaltobda)
mu_pred_point_est <- function(data) {
# Do computation here, and return as below.
# This is the correct return value for the test data provided above.
14.5
}
mu_pred_interval <- function(data, prob = 0.95) {
# Do computation here, and return as below.
# This is the correct return value for the test data provided above.
c(11.8, 17.2)
}You can plot the density as below if you implement mu_pred_pdf to compute the PDF of the posterior predictive \(p(\tilde{y}|y)\) of a new hardness observation \(\tilde{y}\).
mu_pred_pdf <- function(data, x){
# Compute necessary parameters here.
# These are the correct parameters for `windshieldy_test`
# with the provided uninformative prior.
df = 3
location = 14.5
scale = 0.8536316
# Use the computed parameters as below to compute the PDF:
dtnew(x, df, location, scale)
}
x_interval = mu_pred_interval(windshieldy1, .999)
lower_x = x_interval[1]
upper_x = x_interval[2]
x = seq(lower_x, upper_x, length.out=1000)
plot(
x, mu_pred_pdf(windshieldy1, x), type="l",
xlab=TeX(r'(new hardness observation $\tilde{y}$)'),
ylab=TeX(r'(PDF of the posterior predictive $p(\tilde{y}|y)$)')
)
Write your answers here!
Write your answers and code here!
The below data is only for the tests:
Keep the below name and format for the functions to work with markmyassignment:
# Useful function: mean(), quantile()
posterior_odds_ratio_point_est <- function(p0, p1) {
# Do computation here, and return as below.
# This is the correct return value for the test data provided above.
2.650172
}
posterior_odds_ratio_interval <- function(p0, p1, prob = 0.95) {
# Do computation here, and return as below.
# This is the correct return value for the test data provided above.
c(0.6796942,7.3015964)
}Write your answers and code here!
Loading the library and the data.
data("windshieldy2")
# The new data are now stored in the variable `windshieldy2`.
# The below displays the first few rows of the new data:
head(windshieldy2)[1] 15.980 14.206 16.011 17.250 15.993 15.722Write your answers here!
Write your answers and code here!
Write your answers here!
This block will only be visible in your HTML output, but will be hidden when rendering to PDF with quarto for the submission. Make sure that this does not get displayed in the PDF!
The following will check the functions for which markmyassignment has been set up:
✔ | F W S OK | Context
⠏ | 0 | task-1-subtask-1-tests
⠏ | 0 | mu_point_est()
✖ | 1 3 | mu_point_est()
────────────────────────────────────────────────────────────────────────────────
Failure ('test-task-1-subtask-1-tests.R:17:3'): mu_point_est()
mu_point_est(data = 1:10) not equivalent to 5.5.
1/1 mismatches
[1] 14.5 - 5.5 == 9
Error: Incorrect result for vector 1:10
────────────────────────────────────────────────────────────────────────────────
⠏ | 0 | task-2-subtask-1-tests
⠏ | 0 | mu_interval()
✖ | 2 3 | mu_interval()
────────────────────────────────────────────────────────────────────────────────
Failure ('test-task-2-subtask-1-tests.R:15:3'): mu_interval()
mu_interval(data = 1:10, prob = 0.95) not equivalent to c(3.3, 7.7).
2/2 mismatches (average diff: 9)
[1] 13.3 - 3.3 == 10
[2] 15.7 - 7.7 == 8
Error: Incorrect result for 1:10 using a 95% interval.
Failure ('test-task-2-subtask-1-tests.R:16:3'): mu_interval()
mu_interval(data = 1:10, prob = 0.8) not equivalent to c(4.2, 6.8).
2/2 mismatches (average diff: 9)
[1] 13.3 - 4.2 == 9.1
[2] 15.7 - 6.8 == 8.9
Error: Incorrect result for 1:10 using a 80% interval.
────────────────────────────────────────────────────────────────────────────────
⠏ | 0 | task-3-subtask-1-tests
⠏ | 0 | mu_pred_interval()
✖ | 2 3 | mu_pred_interval()
────────────────────────────────────────────────────────────────────────────────
Failure ('test-task-3-subtask-1-tests.R:16:3'): mu_pred_interval()
mu_pred_interval(1:10, 0.95) not equivalent to c(-1.7, 12.7).
2/2 mismatches (average diff: 9)
[1] 11.8 - -1.7 == 13.5
[2] 17.2 - 12.7 == 4.5
Error: Incorrect result for 1:10, (95%)
Failure ('test-task-3-subtask-1-tests.R:18:3'): mu_pred_interval()
mu_pred_interval(1:10, 0.8) not equivalent to c(1.1, 9.9).
2/2 mismatches (average diff: 9)
[1] 11.8 - 1.1 == 10.7
[2] 17.2 - 9.9 == 7.3
Error: Incorrect result for 1:10, (80%)
────────────────────────────────────────────────────────────────────────────────
⠏ | 0 | task-4-subtask-1-tests
⠏ | 0 | mu_pred_point_est()
✖ | 1 3 | mu_pred_point_est()
────────────────────────────────────────────────────────────────────────────────
Failure ('test-task-4-subtask-1-tests.R:16:3'): mu_pred_point_est()
mu_pred_point_est(data = 1:10) not equivalent to 5.5.
1/1 mismatches
[1] 14.5 - 5.5 == 9
Error: Incorrect result for vector 1:10
────────────────────────────────────────────────────────────────────────────────
⠏ | 0 | task-5-subtask-1-tests
⠏ | 0 | posterior_odds_ratio_point_est()
✖ | 3 3 | posterior_odds_ratio_point_est()
────────────────────────────────────────────────────────────────────────────────
Failure ('test-task-5-subtask-1-tests.R:18:3'): posterior_odds_ratio_point_est()
posterior_odds_ratio_point_est(p1, p0) not equivalent to 0.5307909.
1/1 mismatches
[1] 2.65 - 0.531 == 2.12
Error: Incorrect result for p1 = rbeta(100000, 5, 95), p0 = rbeta(100000, 10, 90).
Failure ('test-task-5-subtask-1-tests.R:24:3'): posterior_odds_ratio_point_est()
posterior_odds_ratio_point_est(p0, p1) not equivalent to 1.876519.
1/1 mismatches
[1] 2.65 - 1.88 == 0.774
Error: Incorrect result for p0 = rbeta(100000, 5, 5), p1 = rbeta(100000, 5, 6).
Failure ('test-task-5-subtask-1-tests.R:25:3'): posterior_odds_ratio_point_est()
posterior_odds_ratio_point_est(p1, p0) not equivalent to 1.24902.
1/1 mismatches
[1] 2.65 - 1.25 == 1.4
Error: Incorrect result for p0 = rbeta(100000, 5, 6), p1 = rbeta(100000, 5, 5).
────────────────────────────────────────────────────────────────────────────────
⠏ | 0 | task-6-subtask-1-tests
⠏ | 0 | posterior_odds_ratio_interval()
⠧ | 6 2 | posterior_odds_ratio_interval()
✖ | 6 2 | posterior_odds_ratio_interval() [0.1s]
────────────────────────────────────────────────────────────────────────────────
Failure ('test-task-6-subtask-1-tests.R:17:3'): posterior_odds_ratio_interval()
posterior_odds_ratio_interval(p0, p1, 0.9) not equivalent to c(0.875367, 6.05911).
2/2 mismatches (average diff: 0.719)
[1] 0.68 - 0.875 == -0.196
[2] 7.30 - 6.059 == 1.242
Error: Incorrect result for p0 = rbeta(100000, 5, 95), p1 = rbeta(100000, 10, 90) and 90%.
Failure ('test-task-6-subtask-1-tests.R:19:3'): posterior_odds_ratio_interval()
posterior_odds_ratio_interval(p1, p0, 0.9) not equivalent to c(0.1650407, 1.142378).
2/2 mismatches (average diff: 3.34)
[1] 0.68 - 0.165 == 0.515
[2] 7.30 - 1.142 == 6.159
Error: Incorrect result for p1 = rbeta(100000, 5, 95), p0 = rbeta(100000, 10, 90) and 90%.
Failure ('test-task-6-subtask-1-tests.R:21:3'): posterior_odds_ratio_interval()
posterior_odds_ratio_interval(p1, p0, 0.8) not equivalent to c(0.2086461, 0.9392956).
2/2 mismatches (average diff: 3.42)
[1] 0.68 - 0.209 == 0.471
[2] 7.30 - 0.939 == 6.362
Error: Incorrect result for p1 = rbeta(100000, 5, 95), p0 = rbeta(100000, 10, 90) and 80%.
Failure ('test-task-6-subtask-1-tests.R:27:3'): posterior_odds_ratio_interval()
posterior_odds_ratio_interval(p0, p1, 0.9) not equivalent to c(0.2714472, 5.5970131).
2/2 mismatches (average diff: 1.06)
[1] 0.68 - 0.271 == 0.408
[2] 7.30 - 5.597 == 1.705
Error: Incorrect result for p0 = rbeta(100000, 5, 5), p1 = rbeta(100000, 5, 6) and 90%.
Failure ('test-task-6-subtask-1-tests.R:29:3'): posterior_odds_ratio_interval()
posterior_odds_ratio_interval(p1, p0, 0.9) not equivalent to c(0.1786667, 3.6839583).
2/2 mismatches (average diff: 2.06)
[1] 0.68 - 0.179 == 0.501
[2] 7.30 - 3.684 == 3.618
Error: Incorrect result for p0 = rbeta(100000, 5, 6), p1 = rbeta(100000, 5, 5) and 90%.
Failure ('test-task-6-subtask-1-tests.R:31:3'): posterior_odds_ratio_interval()
posterior_odds_ratio_interval(p1, p0, 0.8) not equivalent to c(0.252972, 2.633517).
2/2 mismatches (average diff: 2.55)
[1] 0.68 - 0.253 == 0.427
[2] 7.30 - 2.634 == 4.668
Error: Incorrect result for p0 = rbeta(100000, 5, 6), p1 = rbeta(100000, 5, 5) and 80%.
────────────────────────────────────────────────────────────────────────────────
Maximum number of failures exceeded; quitting at end of file.
ℹ Increase this number with (e.g.) `testthat::set_max_fails(Inf)`
══ Results ═════════════════════════════════════════════════════════════════════
Duration: 0.6 s
[ FAIL 15 | WARN 0 | SKIP 0 | PASS 17 ]
══ Terminated early ════════════════════════════════════════════════════════════