Model Risk & Decision Support: Bayesian Framework for High-Stakes Infrastructure Investments

The Hidden Risk in Multi-Million Dollar Decisions

Every organization deploying machine learning in high-stakes contexts faces a paradox: to justify investing in better data (sensors, measurements, labeled datasets), you need to calculate the ROI of information you don't yet possess. Value of Information (VoI) analysis is the established framework for solving this problem, promising data-driven justification for multi-million dollar investments in sensor networks, monitoring systems, and data acquisition.

But there's a dangerous flaw lurking in the standard methodology.

During my doctoral research, I discovered that conventional VoI frameworks make a critical, unstated assumption: the underlying predictive models are perfect representations of reality. When highway authorities use VoI to decide whether to invest $2M in bridge sensors, or when ML teams calculate the ROI of labeling more training data, they're implicitly trusting that their models are unbiased and accurate.

They never are.

All models are approximations containing inherent biases and errors. If a decision framework can't account for the risk of its own predictive models being wrong, its outputs become dangerously misleading—potentially causing organizations to either massively under-invest when data would be valuable, or massively over-invest when data adds little value.

I architected a novel framework that explicitly corrects for this "model risk," preventing mis-estimations exceeding 200% and establishing new best practices for responsible analytics deployment. This work directly parallels modern concerns in ML safety: how do we trust imperfect models in high-stakes decisions?

The Initial Investigation

My research began by implementing standard Bayesian pre-posterior analysis for a realistic use case: a highway authority deciding whether to invest in Structural Health Monitoring (SHM) sensors for aging bridge infrastructure. The decision had clear financial stakes:

Do nothing: Risk catastrophic failure (potential loss: $10M+ in liability, public safety crisis)
Repair preemptively: Avoid failure but incur massive costs ($1M-$5M depending on intervention type)
Install sensors first: Gather data to make informed decision (sensor system cost: $200K-$500K)

The VoI framework promises to calculate the expected monetary benefit of the sensor data, providing clear ROI justification.

I built a physics-based simulation for fatigue crack growth in steel (Paris' Law), representing a high-consequence failure mode where the decision to "repair" or "do nothing" carries significant financial implications. Using nested Monte Carlo simulation, I calculated the Expected Value of Information (EVI):

EVI = E[Cost without Data] - E[Cost with Data]

This metric quantifies how much the organization would save, on average, by making decisions informed by sensor data rather than relying on uncertain prior knowledge.

The Sensitivity Analysis That Changed Everything

To understand what drove information value, I conducted Global Sensitivity Analysis (GSA) using Sobol' indices—a variance-based method that decomposes model output variance and attributes it to input parameters.

I treated the physical parameters of the fatigue model (initial crack size, stress range, critical crack size) as input variables and ran thousands of simulations to calculate how much each parameter influenced the final EVI.

The results were clear: The EVI was overwhelmingly sensitive to the parameters of the physical model itself. This made logical sense—if you don't know the true stress range on the structure, the value of sensor data changes dramatically.

But this sparked a critical realization: What if the model that told us those parameter values was wrong?

The standard framework had no answer. It was completely blind to the uncertainty in the model of those parameters. I had discovered a fundamental gap.

The Flaw: Implicit Perfect-Model Assumption

Every VoI analysis relies on a predictive model to simulate how the system behaves. In infrastructure contexts, these are physics-based models (finite element analysis, fatigue crack growth equations). In ML contexts, these are trained statistical models (neural networks, gradient boosting ensembles).

The standard VoI framework assumes these predictive models are unbiased and accurate. But in reality:

Physics models simplify complex phenomena with approximations
Statistical models trained on limited data contain systematic biases
Calibration errors introduce multiplicative scaling issues
All models have random error components

If you can't account for these model imperfections, your VoI estimates become unreliable. You might justify a $2M sensor investment based on predicted $5M value, only to discover the model was biased and the actual value is $500K. Or worse: you might reject a valuable data strategy because a biased model underestimated its worth.

Act II: The Innovation - A Comprehensive Error Framework

I set out to architect a solution that would make VoI analysis robust to model imperfection.

Separating Truth, Prediction, and Measurement

The breakthrough came from recognizing three distinct entities in any decision-making context:

The True Physical State: The actual, unobservable reality (e.g., the true stress on a bridge, the true conversion rate of a marketing campaign)
The Model's Prediction: An imperfect, biased estimate of reality
The Instrument's Measurement: An imperfect, biased observation of reality (or the model's prediction)

Standard VoI conflates entities #1 and #2, assuming the model perfectly represents truth. My framework explicitly separates them and models the transformation from truth → prediction → measurement.

Mathematical Error Modeling

I designed a versatile linear error model capturing the full range of potential inaccuracies:

Model Prediction = α_Mo + β_Mo × (True Value) + ε_Mo Measurement = α_Me + β_Me × (Model Prediction) + ε_Me

Where: - α (additive bias): Constant offset error (e.g., a fatigue model that systematically under-predicts stress by 10 MPa) - β (multiplicative bias): Scaling error (e.g., a model that predicts values 80% of the true magnitude, β = 0.8) - ε (random error): Zero-mean stochastic noise (e.g., sensor precision, σ = 5%)

The Mo subscript denotes the predictive model's error, while Me denotes the measurement system's error.

This formulation is powerful because it's general enough to capture: - Perfect models: α_Mo = 0, β_Mo = 1, ε_Mo = 0 - Biased but consistent models: α_Mo ≠ 0, β_Mo ≠ 1 - Noisy but unbiased sensors: α_Me = 0, β_Me = 1, ε_Me > 0

Implementation: From Theory to Scalable Computation

Implementing this framework required solving a computationally massive problem. To rigorously test the framework, I needed to run VoI analysis across the full parameter space of potential errors.

The challenge: Each VoI calculation involves nested Monte Carlo simulations (outer loop simulates possible measurement outcomes, inner loop evaluates expected costs for each measurement). Now I needed to repeat this thousands of times for different combinations of α_Mo, β_Mo, σ_Mo, α_Me, β_Me, σ_Me.

The solution: I built a parallelized Python pipeline deployed on a SLURM-managed Linux HPC cluster:

Surrogate Modeling for Computational Tractability: The nested Monte Carlo was prohibitively expensive (~10 hours per VoI calculation). I implemented Polynomial Chaos Expansion (PCE) surrogate models to replace the expensive physics simulation, achieving >95% computational speedup while preserving accuracy (R² > 0.999).
GSA Implementation: Used the SALib Python library to implement Sobol' sensitivity analysis, requiring N × (k + 2) VoI simulations where k = 6 error parameters and N = 1000 samples. Total: 8,000 full VoI analyses.
Parallel Execution: Distributed computation across HPC cluster nodes using SLURM job arrays, reducing wall-clock time from weeks to days.
Validation: Compared results from two different GSA estimation schemes (Saltelli and FAST) to ensure robustness.

The entire codebase was built in Python using NumPy, SciPy, Pandas, SALib, and custom Monte Carlo engines I wrote from scratch.

Act III: The Results - Model Bias Dominates Everything

The Critical Finding: 200%+ Mis-Estimation Risk

When I compared the EVI from my comprehensive error-aware framework to the EVI from standard analysis (which implicitly assumes α_Mo=0, β_Mo=1, σ_Mo=0), the results were shocking:

Standard VoI analysis produced estimates ranging from 5% to 230% of the true information value.

In practical terms: if the true ROI of a $500K sensor system is $2M (4x return), the standard framework might tell you it's only $100K (0.2x return, reject the investment) or $4.6M (9x return, vastly overpromising).

This isn't a small margin of error. It's the difference between strategic blunders and sound decisions.

The Dominant Factor: Model Bias, Not Sensor Precision

The Sobol' indices from the GSA revealed an unequivocal pattern:

The additive and multiplicative biases of the predictive model (α_Mo, β_Mo) were the dominant factors driving EVI. Their sensitivity indices were consistently orders of magnitude higher than those for the measurement system's precision (σ_Me).

Specific quantified results: - α_Mo (model additive bias): Sobol' index ≈ 0.45 (explains 45% of output variance) - β_Mo (model multiplicative bias): Sobol' index ≈ 0.35 (explains 35% of output variance) - σ_Me (sensor random error): Sobol' index ≈ 0.03 (explains only 3% of output variance)

Translation: Whether your sensor has 1% precision or 10% precision barely matters if your underlying predictive model has a 20% multiplicative bias or a systematic 50 MPa offset.

A New Paradigm for Data Strategy

This finding fundamentally changes how organizations should think about analytics investments:

Old paradigm: "We need ultra-precise sensors to make good decisions."

New paradigm: "We need unbiased, well-calibrated models. Sensor precision is secondary."

Practical implications:

Invest in model calibration first: Before spending millions on high-precision sensors, invest in validating and calibrating your predictive models against ground truth data.
"Good enough" sensors are often sufficient: A $50K sensor with 10% error feeding into an unbiased model delivers better decisions than a $500K sensor with 1% error feeding into a biased model.
Model risk is the hidden cost: The biggest threat to analytics ROI isn't sensor noise—it's systematic model bias that you're unaware of.

This directly parallels modern ML deployment challenges: companies obsess over model accuracy (the ML equivalent of sensor precision) while ignoring systematic biases in training data or model architecture (the ML equivalent of α_Mo and β_Mo).

Act IV: Real-World Application - Bridge Permitting Decisions

To demonstrate practical utility, I applied this framework to a real-world infrastructure problem: multi-million dollar permitting decisions for heavy vehicles on aging bridges.

The Business Problem

Highway authorities face a constant high-stakes dilemma: when a heavy "permit load" (e.g., a massive electrical transformer weighing 200+ tons) needs to traverse an aging bridge, they must decide:

Approve: Allow the load, risk catastrophic failure (potential loss: $50M+ in liability, public safety crisis, economic disruption)
Reject: Block the load, cause multi-million dollar economic delays, damage regional competitiveness
Repair preemptively: Strengthen the bridge first (cost: $1M-$5M depending on intervention)
Install sensors & gather data: Deploy SHM to measure actual bridge response under load (cost: $200K-$500K)

The decision is plagued by uncertainty about both the bridge's true capacity and the load's true impact.

The Solution: VoI-Powered Decision Support System

I architected an end-to-end decision support system that calculates the precise dollar value of sensor data in this context.

System architecture:

Tiered Assessment Workflow (mirrors real engineering practice):
Tier 1: Fast, conservative "Rating Factor" check (Australian standard AS 5100)
Tier 2: Full probabilistic reliability analysis (calculates failure probability β against three limit states: cracking, yielding, ultimate)
Each tier has associated costs (Tier 2 involves expensive consulting, ~$50K)
Decision Tree with Rich Action Space:
Do Nothing (cost: $0, risk: potential $50M failure)
Minor Repair (cost: $100K, reduces risk moderately)
Major Repair (cost: $1M, eliminates risk)
Repair with Load Reduction (cost: $500K + economic penalty)
Bayesian Data Assimilation:
Simulate deployment of strain-gauge SHM system (two types: Type A high-accuracy $500K, Type B low-accuracy $200K)
Use MCMC (Markov Chain Monte Carlo) to perform Bayesian updating: given noisy sensor measurement X_m, update probability distribution of true permit load effect V_PL
Calculate posterior distribution f(V_PL | X_m) and use it to re-run the entire decision tree
VoI Calculation:
Prior analysis: Expected cost without sensor data (C_prior)
Pre-posterior analysis: Expected cost with sensor data (C_prepost), averaged over thousands of simulated measurement outcomes
EVI = C_prior - C_prepost: The monetary value of installing the sensor system

The Results: Multi-Million Dollar Insights

Finding #1: Sensors have multi-million dollar value in high-risk scenarios

In borderline cases (where initial assessment was uncertain), the EVI of deploying an SHM system ranged from **$800K to $2.5M**. This value was realized by the system's ability to confidently avoid an unnecessary "Major Repair" ($1M) in favor of a "Minor Repair" ($100K) based on data showing the bridge could safely handle the load.

Finding #2: "Good enough" beats "perfect"

The cheaper, lower-accuracy SHM system (Type B, $200K) provided nearly identical EVI as the expensive, high-accuracy system (Type A, $500K).

Why? The VoI framework revealed that for this specific decision, a small amount of information was enough to tip the scales between "Major Repair" and "Minor Repair." The extra precision of the expensive system added no additional business value because the decision boundary didn't require that level of granularity.

Business impact: This analysis provided data-driven justification to procure the cheaper sensor system, saving $300K on equipment while delivering the same $2M+ decision improvement.

Connecting to Modern ML Safety and Responsible AI

While this research was conducted in infrastructure contexts, the insights directly parallel critical challenges in modern machine learning deployment:

Model Risk in ML Deployment

Infrastructure context: A biased fatigue crack growth model mis-estimates sensor ROI by 200%.

ML context: A biased churn prediction model trained on skewed historical data mis-estimates the ROI of gathering more customer interaction data.

Same problem: Decision frameworks that don't account for model imperfection lead to poor data strategy investments.

The Bias-Variance Tradeoff at Decision Time

Infrastructure context: Model multiplicative bias (β_Mo) matters far more than sensor random error (σ_Me).

ML context: Systematic bias in training data (e.g., demographic imbalance) matters far more than model variance (overfitting noise).

Same insight: Focus calibration and bias correction efforts where they have the most decision impact.

Responsible AI Governance

My framework provides a formal methodology for assessing and managing model risk in high-stakes applications. As ML systems deploy in healthcare, finance, criminal justice, and autonomous vehicles, this becomes critical:

Model auditing: Quantify how much decision quality degrades under different levels of model bias
Robustness testing: Sensitivity analysis on model parameters to understand fragility
Investment prioritization: Data-driven allocation of resources between model improvement vs. data collection

Technical Deep Dive: Global Sensitivity Analysis

Sobol' Indices Explained

Global Sensitivity Analysis decomposes the variance of model output (VoI estimate) into contributions from each input parameter (error terms).

Sobol' first-order index S_i measures the fraction of output variance explained by varying parameter i alone:

S_i = Var[E(Y | X_i)] / Var(Y)

Where: - Y = model output (EVI) - X_i = input parameter i (e.g., α_Mo) - E(Y | X_i) = expected output given X_i is fixed

Sobol' total-order index S_Ti measures the total variance contribution including interactions:

S_Ti = E[Var(Y | X_~i)] / Var(Y)

Where X_~i denotes all parameters except i.

Interpretation: - S_i ≈ S_Ti: Parameter i acts independently, no strong interactions - S_Ti >> S_i: Parameter i has strong interaction effects with other parameters - S_i ≈ 0: Parameter i is non-influential, can be fixed without impacting output

Computational Implementation

Sampling strategy: Sobol' quasi-random sequences for low-discrepancy coverage of parameter space (N=1000 base samples, 8000 total model evaluations for k=6 parameters).

Estimation methods: 1. Saltelli scheme: Generates N×(2k+2) model evaluations, provides robust estimates 2. FAST (Fourier Amplitude Sensitivity Test): Frequency-domain approach, validates Saltelli results

Surrogate modeling: Polynomial Chaos Expansion (PCE) with Hermite polynomial basis reduced computational cost from ~80,000 hours to ~4,000 hours of HPC time.

Skills Demonstrated: Bayesian ML & Computational Science

Bayesian Decision Theory: - Value of Information (VoI) analysis - Pre-posterior analysis - Expected utility maximization - MCMC-based Bayesian updating

Computational Statistics: - Global Sensitivity Analysis (Sobol' indices) - Monte Carlo simulation (nested, importance sampling) - Surrogate modeling (Polynomial Chaos Expansions) - Uncertainty quantification

Software Engineering: - Parallelized Python pipelines (NumPy, SciPy, Pandas, SALib) - HPC deployment (SLURM job arrays, distributed computing) - Reproducible research workflows (configuration management, result validation)

Domain Expertise: - Probabilistic modeling of physical systems - Decision tree design for sequential decisions - Error propagation in complex systems

Publications & Impact

This research established new best practices for VoI analysis, with peer-reviewed publications in:

Reliability Engineering & System Safety (flagship journal, impact factor 8.1)
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems
International conferences (IABMAS, ICASP)

Citation impact: The error-aware VoI framework has been adopted by infrastructure agencies and cited in subsequent research on decision-making under model uncertainty.

Business Value: De-Risking Multi-Million Dollar Investments

This framework transforms how organizations approach high-stakes data investments:

Before (traditional VoI): - Single-point estimate of data ROI: "The sensor system will deliver $2M value" - Hidden assumption: model is perfect - Risk: Actual value could be $100K (massive over-investment) or $5M (missed opportunity)

After (error-aware VoI): - Probabilistic estimate accounting for model imperfection: "Given our model uncertainty, sensor ROI ranges from $800K to $2.8M with 90% confidence" - Explicit quantification of how model bias vs. sensor precision drive value - Decision: Invest in model calibration first, then deploy cheaper sensors

Organizational benefits: - Risk mitigation: Understand downside scenarios before committing capital - Resource allocation: Data-driven balance between model improvement and data collection - Procurement optimization: Justify "good enough" sensors vs. premium systems based on actual value drivers - Strategic confidence: Make defensible decisions with quantified uncertainty

Future Directions: ML-Specific Applications

The framework is immediately applicable to modern ML contexts:

Active Learning: Calculate ROI of labeling additional training data when your current model has unknown bias.

A/B Testing: Determine optimal sample size for experiments when conversion rate models have systematic error.

Feature Engineering: Prioritize investment in new features vs. improving existing model calibration.

Model Monitoring: Set thresholds for model retraining based on sensitivity to drift in error parameters.

Fairness-Aware ML: Quantify how demographic bias in training data (α_Mo, β_Mo for subgroup predictions) impacts decision quality vs. overall model variance.

Code Repository: Academic research code available upon request (Python, ~15K lines)

Related Publications: Published in Reliability Engineering & System Safety, ASCE-ASME JRUESE, IABMAS conference proceedings

For questions about applying this framework to ML model risk assessment or modern analytics strategy, contact me.

Related Projects: - Metamodeling for Computational Efficiency - Surrogate modeling techniques enabling this VoI framework - Agentic AI Platform - Practical ML deployment challenges - Queensland Rail Predictive Analytics - Production ML system with calibration considerations