Deepan Jayaraman

Research

My central theme is data-driven decision making: how choices should be made when the evidence base is thin, the consequences are asymmetric, and the model informing the decision is itself estimated rather than specified. The methods are general, so the work reaches across business and decision support, entrepreneurship, engineering and reliability, statistics, safety, and generative AI — one programme rather than several.

The doctoral contribution

An L-Moment Framework-Based Uncertainty Treatment for Scarce Samples Including Extremes

Ph.D., Department of Engineering Design, IIT Madras, 2023
Advisor: Prof. Palaniappan Ramu

Conventional uncertainty quantification degrades badly when samples are few and contaminated by extreme values — precisely the regime in which the most consequential decisions are made. The thesis develops a distribution-independent treatment built on L-moments, contributing three methodological advances.

Uncertainty quantification for scarce data with extremes

L-moments provide robust statistical characterisation where product-moment estimators become unstable, yielding reliable estimates from limited, extreme-laden samples.

ReliabilityStatistics
  • L-moments
  • Python
  • MATLAB

Bayesian probabilistic risk assessment

A framework integrating Bayesian inference with L-moments, incorporating prior knowledge and using distribution-independent approximations for conditional probabilities to widen applicability under uncertainty.

Risk assessmentReliability
  • Bayesian inference
  • L-moments
  • MATLAB

Machine-learning-driven robust design optimisation

A dual-surrogate formulation in which ML models approximate cost and constraint functions, from which robust optima are derived — handling complex data patterns at substantially reduced computational cost without loss of accuracy.

Design optimisationReliability
  • Surrogate models
  • Optimisation
  • MATLAB
The L-moment framework Scarce samples containing extremes feed an L-moment characterisation, which supports three methods — uncertainty quantification, Bayesian probabilistic risk assessment, and machine-learning-driven robust design optimisation — converging on a decision that holds under uncertainty. Scarce samples containing extremes L-moment characterisation Uncertainty quantification Bayesian probabilistic risk assessment ML-driven robust design optimisation A decision that holds up
Distribution-independent throughout: nothing in the chain requires committing to a parametric family for the underlying data.

Current threads

Prescriptive analytics and the model-to-decision handover

When an optimisation program's objective is a learned model rather than a specified one, the search inherits whatever that model attributes. I am generalising the explanation gate and calibration protocol developed for product design into a method for operational and resource-allocation decisions.

Decision supportOperations
  • Optimisation
  • Explainable AI
  • Python

Inference and model selection from scarce samples containing extremes

Distance-based selection on moment-ratio diagrams is biased by the codimension of the candidate family rather than by the statistic used; the minimum-chi-square correction generalises to a wider class of graphical selection rules.

StatisticsModel selection
  • L-moments
  • Moment-ratio diagrams
  • Python

Tail-risk estimation for rare, high-consequence events

Estimator choice changes small-probability estimates by an order of magnitude where the choice of learning function does not. I am carrying the peaks-over-threshold treatment into operational and financial tail risk.

ReliabilityTail risk
  • Peaks over threshold
  • Surrogate models
  • Python

Precursor and detection analytics for safety-critical operations

Extending the detection-pathway framework beyond aviation to industrial and supply-chain incident reporting: which hazards are detected, by whom, and how late.

Aviation safetySupply chain
  • NLP
  • Topic modelling
  • Python

Generative AI for decision support under data scarcity

Generative models that synthesise plausible rare-event scenarios for regimes where direct observation is impossible, with human-in-the-loop safeguards governing what synthetic evidence may license.

Decision supportRare events
  • Generative models
  • GAN
  • Python

Robust and multi-objective decision making in operations

Distribution-independent formulations for demand planning, inventory policy and maintenance scheduling, with trade-offs priced in the decision's own units rather than in model metrics.

OperationsMaintenance
  • Multi-objective optimisation
  • Pareto frontier
Predict, explain, prescribe A fitted model passes through an explanation gate. Where a variable's attribution is resolved it is released to the optimiser; where it is unresolved it is constrained in the search. Outcome data predict Fitted model the learned objective Explanation gate is the attribution resolved? yes no Released to the optimiser Constrained in the search Prescribed decision every released variable accounted for
Predictive accuracy alone cannot establish that a model's explanations are actionable — which is why the gate sits between the model and the search, not after it. Nothing reaches the decision that the gate has not either released or constrained.

The simulation for this thread is closed. Click here to open it, or use Inference and model selection from scarce samples containing extremes above.

See the publication record →

Methods against domains

The same grid as on the home page, read here from the method side: each row is something built for one problem, and the columns are where it has since been carried.

Sixteen of twenty-five cells are filled — the point being how few rows stay inside one column.

Three of these, drawn

Three of the threads above have a mechanism worth watching rather than reading. Click a thread card — tail-risk estimation, precursor and detection analytics, or generative AI under data scarcity — and its figure opens here and starts moving. Click it again to close.

Click here to jump to the threads, then pick one — or open a figure directly: , , .

One outlier, two estimators

Twelve measurements. Drag the last one out into the tail and watch the two ways of describing the sample's shape come apart. This is the premise the whole research programme rests on.

This one is closed too. Click here to open it, or use Uncertainty quantification for scarce data with extremes in the doctoral contribution above.

Sample skewness cannot exceed a ceiling fixed by the sample size — at twelve observations, 3.02. Push the extreme far enough and it presses against that ceiling and stops discriminating: on this sample, moving the last value from 20 to 24 changes it by 0.03, while L-skewness keeps responding. The conventional statistic runs out of range exactly where the tail becomes interesting, which is why practitioners discard extremes as outliers and lose the information the analysis existed to capture. L-moments are bounded by construction and stay informative.