Tutorial 11 Problem Set
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Tutorial 11 Problem Set
The zero-inflated Poisson model is defined as follows:
p ~ U (0, 1)
λlp ~ Γ(a, b)
rilp, λ ~ Ber(p)
xilr, λ ~ Pois(λri)
where a, b are known.
1. Simulate drawing 1000 integers y = (y1 , . . . , y1000 ) from a zero-inflated Poisson data model with p = 0.1 and λ = 10. (You should already have code to do this from Q3a of the Tutorial 7 Problem Set.)
2. Let k(y) be the number of zeroes in your data set and let S(y) = yi . Show that k and S are sufficient
for θ = (p, λ).
3. Write code to implement ABC and use it to draw 100 values of θ from the approximate posterior distribution pe(θly), where e = 10. Plot marginal distributions for p and λ .
4. Improve the estimates of θ obtained in Question 3 using regression adjustment, and again plot marginal distributions for p and λ .
5. Repeat Question 3 with MCMC ABC.
6. Repeat Question 3 with SMC ABC.
2023-06-03