logisticbeta-reproduce

Code to reproduce figures, simulation results, and real data analysis results from the paper

Lee, C. J., Zito, A., Sang, H., & Dunson, D. B. (2024). Logistic-beta processes for dependent random probabilities with beta marginals. arXiv preprint arXiv:2402.07048. https://arxiv.org/abs/2402.07048

Codes for reproducing figures

• Figure 1 (density of univariate logistic-beta and Polya):
  • figure/figure_1.R
• Figure 2 (density of bivariate logistic-beta):
  • figure/figure_2.R
• Figure 3 (LBP prior example and latent LBP):
  • figure/figure_3.R
• Figure 4 (correlation lower bounds of bivariate betas and LB-DDP):
  • figure/figure_4_and_scatter.R
• Figure 5 (preterm birth probability plot for smoking group):
  • real_analysis/DDEexposure_smoking.R
• Figure B.1 (correlation lower bounds of LB-DDP and bivariate scatterplots):
  • figure/figure_4_and_scatter.R
• Figure D.1 (effect of feature map normalization):
  • figure/figure_basis.R
• Figure D.2 (preterm birth probability plot for nonsmoking group):
  • real_analysis/DDEexposure_nonsmoking.R

Codes for reproducing simulation results

Scenario 1, Scenario 2, Scenario 3 correspond to rho = 0.1, 0.2, 0.4, respectively, for data generation settings with different Matern range parameters.

• See simul/execute_simul_copula*.R for running all simulations with data generation based on Gaussian copula.
• See simul/execute_simul_lbp*.R for running all simulations data generation based on latent LBP.
• simul/simul_data_copula.R and simul/simul_data_lbp.R are scripts to generate data under Gaussian copula and latent LBP models, respectively.
• run_copula.R and run_lbp.R are scripts to run a single simulation for Gaussian copula and latent LBP models, respectively.
• Stan code and associated prediction code for the Gaussian copula model can be found in the folder simul/copula_codes.

Codes for reproducing real data analysis results

• Smoking group: real_analysis/DDEexposure_smoking.R
• Nonsmoking group: real_analysis/DDEexposure_nonsmoking.R

R codes

1. R/lb.R: basic functions for logistic-beta

• Random variate generation: univariate rulb(), multivariate rmlb().
• Density evaluation: univariate dulb(), multivariate dmlb() (warning: unstable!).
• Others: mlb_cov(), pulb()

2. R/polya.R: basic functions for Polya distribution

• Random variate generation: rpolya() (requires dqrng package for fast random number generation)
• Density evaluation: dpolya() (warning: unstable!)
• Adaptive Polya proposal: find_polya_proposal() to find a’, b’ with moment matching criterion
• Others: mean epolya(), variance vpolya().

3. Functions for latent LBP model for binary data

• R/LBBer_Matern.R implements Algorithm 1 (blocked Gibbs sampler) with Matern correlation kernel.
  • Can handle both 1 and 2-dimensional covariates
  • Fixed smoothness parameter. Discrete uniform prior is assumed on the Matern range parameter.
  • If adapt = TRUE, it utilizes the adaptive Polya proposal (see find_polya_proposal() in R/polya.R)
  • If nparticle = 0, it runs independent M-H for sampling the Polya mixing parameter. Otherwise, it runs particle Gibbs.
  • For the unblocked version, see R/LBBer_Matern_unblocked.R
• R/LBBer_Matern_predict_LB.R is a function to get posterior predictive samples of success probabilities.

4. R/LBDDP_basis.R and R/LBDDP_postprocess.R: functions for LB-DDP mixture model

• R/LBDDP_basis.R implements Algorithm 2 (blocked Gibbs sampler) with normalized basis.
• R/LBDDP_postprocess.R is a function to get posterior predictive samples of conditional density and cumulative probability.

5. R/LSBP_basis.R and R/LSBP_postprocess.R: functions for logit stick-breaking mixture model, implemented in R.

6. R/dmvn_lowrankstr.R: functions for MVN density evaluation with low-rank structure