Hazard Structure Dominates Data in Estimating the Long-Horizon Probability of Existential Collapse: A Bayesian Phase-Type Analysis of P(1000)

We ask a deliberately ill-posed question—“what is the probability that human civilization suffersan unrecoverable collapse within 1000 years?”—and show that any defensible answer is determinedmore by the assumed shape of the hazard function than by available evidence. Working ina survival-analytic framework with rates expressed per century, we compare three hazard structures:a time-of-perils model, a phase-type competing-risks continuous-time Markov chain, andan endogenous causal model whose hazard is a functional of latent capability/governance trajectories.We place a correlated joint prior over the rate parameters (via a one-factor Gaussianmodel on the log-rates), anchor the only empirically identified quantity—the natural backgroundrate—to the survival-based bound of [SOB19], and convert the prior pushforward into a genuineposterior by conditioning on elicited extinction-by-2100 forecasts from the Existential RiskPersuasion Tournament [Kar+23] through a hierarchical (partial-pooling) likelihood, sampledby the No-U-Turn Sampler (NUTS) with full convergence diagnostics (ˆR = 1.00). The phasetyperepresentation yields the full first-passage law of collapse, not merely its terminal mass; aleave-one-survey-out analysis quantifies sensitivity to each elicited group; an explicit constructvalidityparameter κ relating elicited extinction to modelled collapse reveals an identifiabilitylimit (posterior ≈ prior); and a prior-loading sensitivity sweep and posterior predictive checksconfirm robustness. Across structures, the posterior median of P(1000) ranges from ≈ 0.01(post-alignment) to ≈ 0.49 (causal, observational), a spread that exceeds the within-model posteriorwidth and is generated almost entirely by structural choice. We argue that any singlequoted figure for long-horizon existential risk is best read as a statement about the modeller’sstructural prior rather than as a measurement, and we make the analysis fully reproducible.