R Bayesian Model Selection/Comparison: calculation of posterior probabilities

DEADLINE
Aug 24, 2022 (Client's timezone: UTC -05:00)


DELIVERABLES
replication of Table 2 (with posterior probabilities for the models) from the paper (Ng & Chick) and provide the R code
ADDITIONAL INFORMATION
Find posterior probabilities of models
Data: from paper Table 1 (Ng & Chick) (sent to Ciro) https://onlinelibrary.wiley.com/doi/10.1002/nav.20046
calculate likelihood using prior for parameters (reference 34)
prior for models (uniform p(M_i)=2^-15)



I am trying to replicate a table of posterior probabilities of a few selected models. Can you please advise if you are familiar with bayesian statistics, specifically bayesian model selection/comparison?

this is paper link.
https://ucarecdn.com/9a559655-e3f9-4ec5-9e1d-d395b2c0ea5d/

I am trying to replicate Table 2 from Table 1


Table 1 has the data where z_i is the response. A,B,C,D,E belongs a factorial design

Table 2 calculates the posterior probabilities of candidate models and listed out the most probable ones

prior for models is uniform: p(M_i)=2^-15 for each model in the model space


https://ucarecdn.com/7c3825e0-7832-4293-b083-5ce19d1fe480/

this article has the prior for parameters

so far I am stuck for the next step

I only have the data matrix

I am stuck to write the loop for integration to calculate model likelihood (junior R programmer here)

https://ucarecdn.com/8307d89e-175d-413b-b3dc-7666f19eba16/

I think if it's possible to write out to loop to calculate the likehood for each model, should be able to replicate easily


https://ucarecdn.com/d32958aa-a982-4a6f-9167-134c19dc905c/

I need basic bayesian formula

Data : table 1 or Box, Hunter, and Hunter
Each model : use the factors (B, D, E, BD, DE) find likelihood
Prior: proposed by reference 34 Raftery, Madigan, and Hoeting
Basic posterior probability formula