When decisions matter—allocating capital, managing risk, setting strategy—point estimates and dashboards aren’t enough. You need to understand uncertainty honestly, propagate it through your decision chains, and optimize for expected outcomes under genuine ambiguity.

1761 is a specialist consultancy focused on Bayesian methods for economic decision making. We work with organizations who recognize that rigorous uncertainty quantification is essential for high-stakes choices, and who need deep expertise in modern probabilistic modeling.

Our Approach

We build principled Bayesian models using modern probabilistic programming frameworks—PyMC, Stan, JAX, NumPyro, GPJax. Our work is grounded in:

• Honest uncertainty quantification - Full posterior distributions that reflect what you actually know, with credible intervals calibrated to your evidence
• Transparent methodology - Every modeling assumption is explicit and interrogable; we don’t build black boxes
• Decision-theoretic rigor - Expected utility optimization, value of information analysis, and principled sequential decision frameworks
• Production-ready deployment - Models that integrate into your operations with robust engineering practices
• Comprehensive knowledge transfer - You own the work and understand how to extend and maintain it

What We Do

Our engagements center on economic decisions where uncertainty is unavoidable and consequential:

Portfolio and Resource Allocation

We build models for capital budgeting, asset allocation, and project prioritization that account for parameter uncertainty, model uncertainty, and correlations. You get optimal allocations under your risk preferences with honest uncertainty bounds.

Pricing and Revenue Optimization

We develop demand models, price elasticity estimates, and revenue management frameworks with full posterior distributions. This lets you optimize pricing strategies while understanding the credible range of outcomes.

Risk Assessment and Management

We quantify tail risks, build stress testing frameworks, and develop uncertainty-aware scenario analyses. Our models propagate uncertainty through complex risk chains to give you calibrated risk estimates.

Causal Inference for Intervention Planning

We use Bayesian causal inference to understand what will happen if you change policy, pricing, product, or operations. This includes difference-in-differences, synthetic controls, and structural causal models with uncertainty quantification.

Value of Information Analysis

Before you commit to expensive data collection or lengthy experiments, we can quantify how much that information would be worth in expectation. This prevents wasteful spending on data that won’t change your decision.

Bayesian Experimentation

We design sequential experiments with proper uncertainty quantification and early stopping criteria. This includes A/B testing, bandit algorithms, and optimal experimental design that balances exploration and exploitation.

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Why Bayesian Methods?

Traditional approaches to business analytics often rely on point estimates, frequentist hypothesis tests, or pure machine learning prediction. These methods have their place, but for high-stakes economic decisions, Bayesian approaches offer distinct advantages:

Principled uncertainty propagation - Understand how uncertainty compounds through decision chains, from input assumptions to final recommendations.

Small data rigor - Valid inference even when you don’t have millions of observations. Bayesian methods work with the data you have.

Prior knowledge integration - Incorporate expert judgment, physical constraints, and domain knowledge formally rather than ignoring available information.

Sequential learning - Update beliefs continuously as evidence arrives. No need to wait for arbitrary sample sizes or pre-specified stopping rules.

Model comparison and averaging - Evaluate competing hypotheses rigorously and account for model uncertainty in your predictions.

Decision-theoretic optimization - Optimize decisions for expected utility under your actual objectives and risk preferences, not arbitrary metrics.

Our Expertise

We bring deep technical expertise in:

• MCMC methods - Hamiltonian Monte Carlo (NUTS), Metropolis-Hastings, Gibbs sampling, and advanced sampling techniques
• Variational inference - Stochastic variational inference, automatic differentiation VI, and black-box VI
• Gaussian processes - Sparse GPs, deep GPs, multi-output GPs, and GP-based surrogate modeling
• Hierarchical models - Multilevel models, random effects, and partial pooling for structured data
• Causal inference - Potential outcomes framework, graphical causal models, and identification strategies
• Decision theory - Expected utility maximization, value of information, and optimal experimental design
• Simulation-based inference - Approximate Bayesian computation and likelihood-free inference for complex generative models
• Production deployment - MLOps for probabilistic models, posterior storage, diagnostics monitoring, and uncertainty calibration

We work primarily in Python with PyMC, Stan, JAX-based frameworks (NumPyro, BlackJAX), and specialized tools like GPJax and GPyTorch. All code is version-controlled, documented, and delivered with reproducible workflows.

Who We Serve

We work with organizations across sectors:

• Investment and asset management - Portfolio optimization, risk modeling, and quantitative strategy development
• Corporate strategy and finance - Capital allocation, M&A valuation, and strategic planning under uncertainty
• Operations and supply chain - Inventory optimization, demand forecasting, and resource allocation
• Pricing and revenue management - Dynamic pricing, demand modeling, and revenue optimization
• Product development - Bayesian testing, preference elicitation, and market sizing
• Policy and public sector - Cost-benefit analysis, program evaluation, and policy simulation

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How We Work

Discovery - We start by understanding your decision problem, constraints, data, and existing analytical capability. This shapes the engagement scope and technical approach.

Model Development - We build Bayesian models iteratively, validating assumptions with domain experts and checking diagnostics rigorously. You see the work as it develops.

Deployment - We integrate models into your operations with proper engineering: version control, testing, monitoring, and documentation. No orphaned notebooks.

Knowledge Transfer - We ensure your team understands the models and can maintain them. This includes documentation, training, and hands-on collaboration.

Flexible Engagements - We work on retainer, project basis, or integrated with your team. The structure adapts to your needs.

Get Started

Whether you’re facing a one-off strategic decision or building ongoing analytical capability, we can help you apply rigorous Bayesian methods to make better choices.

Get in touch to discuss your challenge.