Modify model priors when using include.always

[vandenman]

A possible fix for #40.

At the start of an analyses no_prior_inclusion_is_1(p, probs) counts the number of the initprobs that are 1, denoted noInclusionIs1. This number is passed to all calls to compute_prior_probs which reduces the model space and number of predictors by noInclusionIs1.

For example, this PR will change the prior model probabilities to:

res <- bas.lm(Y ~ ., data = Hald, modelprior = beta.binomial(1, 1), 
              include.always = ~ 1 + X1 + X2)
modeldim <- lengths(res$which)
ord <- order(modeldim)
cbind(modeldim, prior = res$priorprobs[ord])
modeldim  prior
    3     0.333
    4     0.167
    4     0.167
    5     0.333

whereas the current master branch returns:

cbind(modeldim, prior = res$priorprobs[ord])
modeldim  prior
    3     0.033
    4     0.050
    4     0.050
    5     0.200 # <- most prior mass on the most complex model!

I also added a unit test to test-model-priors.R that checks this.

I hope this helps, if anything is unclear please let me know. All comments and/ or feedback are welcome!

[codecov]

Codecov Report

Merging #41 into master will increase coverage by 0.02%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master      #41      +/-   ##
==========================================
+ Coverage   91.56%   91.58%   +0.02%     
==========================================
  Files          54       54              
  Lines        5771     5787      +16     
==========================================
+ Hits         5284     5300      +16     
  Misses        487      487

Impacted Files	Coverage Δ
src/lm_sampleworep.c	97.57% <100%> (ø)	⬆️
src/model_probabilities.c	97.61% <100%> (+0.25%)	⬆️
src/glm_sampleworep.c	100% <100%> (ø)	⬆️
src/lm_mcmcbas.c	96.98% <100%> (ø)	⬆️
src/lm_deterministic.c	99.14% <100%> (ø)	⬆️
src/glm_deterministic.c	100% <100%> (ø)	⬆️
src/glm_mcmcbas.c	90.36% <100%> (+0.04%)	⬆️
src/glm_mcmc.c	100% <100%> (ø)	⬆️
src/lm_mcmc.c	97.83% <100%> (ø)	⬆️

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[merliseclyde]

Looks good!