Job Description: Statistician — Multi-Input Score Fusion & Confidence Modeling
Summary
We are seeking a Statistician to design and validate the statistical framework behind a scoring and data-fusion system. The system converts a set of input measurements — each modeled as a Gaussian (Normal) distribution with an associated confidence level — into a set of output scores via a weighted conversion matrix, and then combines ("fuses") outputs from multiple input vectors into a single, statistically defensible result with its own confidence estimate. This role is responsible for the mathematical rigor, validation, and documentation of that framework, working closely with data engineers and software developers who will implement it in production.
Key Responsibilities
Statistical Modeling of Inputs and Outputs
• Define and validate the distributional assumptions for input measurements X = {x₁, x₂, ... xₙ}, each modeled as Normal(μ=100, σ=10), including an associated confidence score (e.g., p95, p99).
• Define and validate the same distributional assumptions for output scores Y = {y₁, y₂, ... yₘ}.
• Perform goodness-of-fit and normality testing to confirm (or flag violations of) the Gaussian assumption in real data.
Conversion Matrix Design
• Design the N×M conversion matrix K that maps each input xᵢ to each output yⱼ, consisting of:
o A spread factor fsⱼ (fraction of xᵢ''s contribution allocated to yⱼ, constrained so Σ fsⱼ = 1.0)
o A weight factor fwⱼ (relative importance of xᵢ to yⱼ, constrained so Σ fwⱼ = 1.0)
o A confidence score associated with each matrix element
• Define the mathematical basis for how spread and weight factors are derived, calibrated, and updated over time.
• Establish validation checks to ensure matrix normalization constraints hold and remain stable under recalibration.
Score Computation
• Derive and document the formula(s) for computing output scores Y from a single input vector X via matrix K, including how mean, variance, and confidence propagate through the transformation.
• Derive and document the fusion methodology for combining outputs from multiple input vectors into a single fused output score per yⱼ, including:
o Uncertainty/error propagation across combined inputs (e.g., variance combination, weighted averaging, Bayesian updating, or Kalman-filter-style fusion, as appropriate)
o Correlation or independence assumptions between input vectors
o How the fused confidence score (e.g., resulting p95/p99) is derived from the individual input and matrix confidence scores
Validation & Documentation
• Build test cases and simulations (e.g., Monte Carlo) to verify computed outputs and fused outputs behave as expected under known inputs.
• Produce clear technical documentation of all formulas, assumptions, and edge cases (e.g., missing inputs, degenerate matrix rows/columns, low-confidence inputs) for use by engineering teams.
• Partner with software/data engineers to review implementation for statistical correctness.
• Recommend recalibration cadence and monitoring approach to detect drift from the assumed Normal(100, 10) distributions over time.
Required Qualifications
• Bachelor''s or Master''s degree in Statistics, Applied Mathematics, Data Science, or a related quantitative field (Master''s or PhD preferred).
• Strong foundation in probability theory, particularly the Normal/Gaussian distribution, confidence intervals, and percentile-based confidence scoring (e.g., p95, p99).
• Working knowledge of linear algebra, including matrix transformations and weighted linear combinations.
• Experience with uncertainty quantification and error/variance propagation techniques.
• Familiarity with multi-source data fusion methods (e.g., weighted fusion, Bayesian fusion, Kalman filtering, or ensemble methods).
• Proficiency in a statistical/technical computing language such as Python, R, or MATLAB.
• Ability to translate statistical methodology into clear specifications that engineers can implement.
Preferred Qualifications
• Experience in domains that rely on sensor fusion, risk scoring, or multi-signal aggregation (e.g., aerospace/defense, fraud/risk scoring, quality scoring systems, ML model ensembling).
• Experience with Monte Carlo simulation for model validation.
• Familiarity with normalization/constraint-based systems (e.g., matrices where row or column sums must equal 1.0).
• Experience presenting statistical methodology to non-statistician stakeholders and reviewing implementation code for correctness.
Deliverables This Role Owns
• Formal specification of the single-input-vector scoring computation.
• Formal specification of the multi-input-vector fusion computation, including confidence propagation.
• Validation test suite / simulation results demonstrating correctness of both computations.
• Documentation package (assumptions, formulas, edge cases, recalibration guidance) for engineering handoff.
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