Fit product partition (PPM; Hartigan, 1990) and covariate-dependent product partition (PPMx; Muller, Quintana, and Rosner, 2011) models using Markov chain Monte Carlo (MCMC). Covariates are currently assumed to be of continuous type. They may optionally contain missing values (Page, Quintana, and Muller, 2022; Heiner, Page, and Quintana, 2023).
First create a model object with Model_PPMx. Then run MCMC with mcmc! on the model object. For example, using a vector of responses y and covariate matrix X, fit the model with
model = Model_PPMx(y, X, 0, similarity_type=:NN, sampling_model=:Reg)
sims = mcmc!(model, 1000)
The object sims is a vector of dictionaries, with each dictionary indexed by symbols. Access a list of dictionary keys with
keys(sims[1])
Posterior samples of parameter values or other quantities in the keys list can be extracted by collecting them into arrays
sims_llik = [ sims[i][:llik] for i in 1:length(sims) ]
Posterior draws can also be used for in-sample prediction
Ypred_is, Cpred_is, Mpred_is = postPred(model, sims)
or out-of-sample prediction
Ypred_oos, Cpred_oos, Mpred_oos = postPred(Xpred, model, sims)
Model objects can be initialized with user-defined priors and similarity functions. They can also be modified prior to running MCMC, for example
model.state.similarity = Similarity_NNiChisq_indep(0.0, 0.1, 10.0, 0.5^2)
model.prior.baseline.mu0_mean = 1.0
model.state.baseline.sig_upper = 1.5
See documentation on Model_PPMx, mcmc!, and postPred for additional options, or run
model |> typeof |> fieldnames
model.prior |> typeof |> fieldnames
model.state |> typeof |> fieldnames
to explore the fields in each object.
See CITATION.bib.