Bayesian Modeling of Monthly Upper Record Precipitation Using the Exponentiated Log Logistic Distribution: A Case Study from the Upper Indus Basin - Tahir Mehmood (Winaya Inspirasi Nusantara Foundation, 2026)
Record-breaking precipitation events represent a stochastic process that differs fundamentally from annual maxima and threshold exceedances. This study examines monthly upper record precipitation in the Upper Indus Basin (UIB) using a Bayesian framework based on the Exponentiated Log Logistic distribution (ELLD). Upper records defined as observations exceeding all previously observed values were extracted from observed monthly precipitation series spanning 1980–2020. Bayesian inference via Markov Chain Monte Carlo was employed to estimate model parameters, quantify uncertainty, and derive predictive distributions for the magnitude of the next potential upper record. Model performance and adequacy were evaluated using a combination of likelihood-based measures, posterior summaries, convergence diagnostics, and posterior predictive simulations to assess the ability of the ELLD to represent the observed record magnitudes under sparse data conditions. Exceedance probabilities for selected precipitation thresholds were derived from the posterior predictive distribution to provide an interpretable probabilistic characterization of extreme record magnitudes. Rather than relying on return periods or return levels, which are not applicable to record-based processes, the analysis adopts a predictive probabilistic framework focused on uncertainty quantification. The study is intended as a methodological illustration of Bayesian inference for record-breaking precipitation under severe data scarcity and does not attempt trend detection, attribution, or climate-change assessment.