Bayesian Logistic Classification of Synthetic Cholera-related Profiles: A Methodological Simulation Study
L. A. Bichanga *
Department of Mathematics and Physical Sciences, Maasai Mara University, P. O. Box 861 - 20500, Narok, Kenya.
C. Nyakundi
Department of Mathematics and Physical Sciences, Maasai Mara University, P. O. Box 861 - 20500, Narok, Kenya.
H. Imboga
Department of Statistics and Actuarial Science, Jomo Kenyatta University of science and Technology (JKUAT), P. O. Box 62000-00200, Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Background: Some correctional facilities may face an elevated risk of cholera transmission when population density, limitations in water and sanitation infrastructure, and restricted access to timely healthcare occur concurrently. Statistical classification can support methodological development, but simulated analyses must be distinguished from empirical outbreak forecasting.
Methods: A synthetic dataset of 10,000 profiles was generated from ten coded variables representing symptoms, demographic characteristics, water exposure, and environmental conditions. Binary outcomes labelled as susceptible or infected were drawn from a prespecified logistic data-generating model. Regression coefficients were estimated in a Bayesian framework using a random-walk Metropolis-Hastings algorithm with 10,000 iterations and a 1,000-iteration burn-in. Posterior mean probabilities were dichotomised at 0.50, and internal performance was examined using an 80:20 training-test split.
Results: Posterior estimates were generally close to their prespecified generating values, with a mean absolute error of 0.070 and a root-mean-square error of 0.095. All reported 95% credible intervals excluded zero; this result was expected because the simulation used non-zero coefficients and a large sample. Test-set accuracy was 96.60% and sensitivity was 99.37%, but specificity was 41.67% and balanced accuracy was 70.52%. The positive-class prevalence in the test set was 95.20%, so overall accuracy substantially reflected class imbalance.
Conclusion: The analysis demonstrates parameter recovery and internal classification behaviour under a correctly specified synthetic model. It does not estimate a dynamic susceptible-infected-recovered process, establish clinical diagnosis, or validate outbreak prediction in real correctional populations. Empirical longitudinal data, laboratory-confirmed outcomes, multi-chain Bayesian diagnostics, calibration assessment, and external validation are required before operational use.
Keywords: Bayesian logistic regression, binary classification, cholera-related profiles, synthetic data, parameter recovery, Markov chain Monte Carlo, Metropolis–Hastings algorithm, class imbalance, internal validation, correctional facilities