Monte Carlo ICU Risk Model

An absorbing Markov chain fit to 14,000+ ICU transitions, with a Monte Carlo engine for tail risk in mortality and length of stay.

• Modeled daily ICU states with an absorbing Markov chain fit to 14,000+ observed transitions across 186 hospitals; derived closed-form mortality and length-of-stay estimates, matching observed mortality (8.32% vs. 8.31%).
• Built a vectorized Monte Carlo engine for VaR₉₉/expected shortfall; control variates cut estimator variance 2.6x, common random numbers cut scenario variance 2.5–3.7x, and ignoring parameter uncertainty understated VaR₉₉ by 12% at n=50.
• Compared 7 models with patient-level walk-forward/cross-validation and Bayesian shrinkage, reducing out-of-sample log-loss 19% vs. no-change baseline; a bootstrap likelihood-ratio test rejected one-day memory (p=0.002).