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Confidence in working with probabilities, distributions, and risk measures
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Ability to apply decision-making criteria under uncertainty (Maximin, Hurwicz, Laplace, etc.)
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Skills to calculate and interpret confidence intervals, likelihoods, and expected values
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Using new evidence to update risk profiles
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Practical experience using Monte Carlo simulation to model risk profiles
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Awareness of techniques such as EVPI, sensitivity analysis, fan charts, and tornado charts
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Clearer communication of uncertainty to support robust, evidence-based
Course Topics
• Foundations of probability, distributions, and confidence intervals
• Decision theory: comparing alternative strategies under uncertainty
• Risk measures and the value of information (EVPI/EVPPI)
• Using Bayes to maintain and update risk profiles
• Monte Carlo simulation for quantifying risk in real-world problems
• Sensitivity analysis: identifying the drivers of uncertainty
• Visualising and communicating risk with fan charts and tornado diagrams
• Applied case studies from healthcare, logistics, and policy planning
Who is this Course For
• Operational Researchers seeking practical methods to address uncertainty in their models
• Analysts and decision support professionals who must quantify and communicate risk
• Practitioners in government, defence, healthcare, finance, or industry where risk-informed strategies are critical
• Data analysts and forecasters wanting to go beyond averages and point estimates
• Anyone working in strategy, planning, or operations who needs confidence in making decisions under uncertainty
Outline content (1 day programme)
Introduction: Why Quantify Risk?
Risk vs. uncertainty.
OR contexts: healthcare demand, logistics disruption, investment planning.
Today’s goals & overview.
Probabilities, Distributions & Confidence Intervals
Refresher on basic probability & common distributions (Normal, Poisson, Exponential).
Calculating confidence intervals & interpreting uncertainty in estimates.
Quick worked examples with small datasets.
Decision Making under Uncertainty
Payoff matrices & decision rules: Maximax, Maximin, Minimax Regret, Laplace, Hurwicz.
Hands-on group exercise: apply rules to a simple project choice scenario.
Bayesian Updating: Revising Risk with New Evidence
Why update probabilities, Prior → Posterior.
Bayes’ Theorem explained intuitively.
Worked example: interpreting a diagnostic test.
Short group exercise: update probabilities from observed data.
Risk Measures & the Value of Information
Variance, standard deviation, coefficient of variation.
Expected Value of Perfect Information (EVPI) & Expected Value of Partial Perfect Information (EVPPI).
Link to Bayesian updating perfect vs. incremental learning.
Monte Carlo Simulation: Building Risk Profiles
Random sampling from distributions.
Estimating likelihood of thresholds being crossed.
Demonstration in Excel/Python.
Group activity: simulate outcomes for a small decision problem.
Sensitivity Analysis & Communicating Risk
Which assumptions matter most?
Tornado diagrams, fan charts.
Practical illustration with project or healthcare example.
Mini Case Study & Wrap-Up
Groups tackle a realistic scenario (e.g. capacity planning under uncertain demand).
Apply tools: probability, Bayesian updating, decision rules, simulation, sensitivity analysis.
Discussion: which tools gave the most insight?
Closing reflections on applying risk quantification in OR practice.