1. having multiple parallel option helps founder distinguish between aleatoric and epistemic uncertainty, using hierarchical bayesian as a tool to keep expanding the region of reducible uncertainty.
2. probability comes from ratio (relative probability), so having multiple option sharpens the eye for success probability or quality evaluation.
[[🛝 Slide Deck eval(charlie-scott,angie)1]]
| Type | Risk (Measurable) 📊 | Uncertainty (Unknown) ❓ | Example | Strategy |
| ---------------------- | ----------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------- |
| **Demand** <br> 🎯 | - Market size for existing product <br> - Current customer acquisition cost <br> - Typical conversion rates | - Will new customers adopt? <br> - How will preferences change? <br> - What's the true market potential? | Tesla Model 3: <br> Known: EV market size <br> Unknown: Mass market adoption | Run parallel customer experiments with: <br> - Different segments <br> - Different value props <br> - Different price points |
| **Execution** <br> 🛠️ | - Team's track record <br> - Industry benchmarks <br> - Resource requirements | - Team dynamics <br> - Partner reliability <br> - Unforeseen challenges | Moderna's vaccine development: <br> Known: Lab capabilities <br> Unknown: Scale-up challenges | Keep parallel options for: <br> - Key hires <br> - Critical suppliers <br> - Core processes |
| **Financing** <br> 💰 | - Burn rate <br> - Industry funding norms <br> - Valuation multiples | - Future market conditions <br> - Investor sentiment <br> - Competitive funding | BYD's early days: <br> Known: Battery costs <br> Unknown: EV market timing | Maintain multiple: <br> - Funding sources <br> - Growth scenarios <br> - Cash runway plans |
| **Technology** <br> 💻 | - Technical feasibility <br> - Development timelines <br> - Known limitations | - Breakthrough potential <br> - Integration challenges <br> - Future tech landscape | SpaceX rockets: <br> Known: Physics constraints <br> Unknown: Reusability success | Focus on: <br> - Parallel prototypes <br> - Rapid iteration <br> - Fail-fast learning |
**Key Principles for Management:**
1. 🔄📊 **Uncertainty Decomposition**: Convert uncertainties to risks where possible through parallel experiments
2. ⚖️🎯 **Relative Assessment**: Use multiple parallel options to sharpen probability estimates
3. 🎲🔍 **Risk-Uncertainty Balance**: Match strategy to the dominant type (risk vs uncertainty)
| Document | Year | Primary Focus | Key Quote | Connection to Exchangeability & Hierarchical Bayes | Core Thesis on Uncertainty |
| ---------------------------------------------------------- | ---- | ---------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------ |
| Gelman06 Aleatory Epistemic Uncertainty | 2006 | Distinction between randomness and ignorance in Bayesian context | "In this larger, potentially hierarchical context, Bayesian inference can distinguish between aleatory uncertainty (randomness) and epistemic uncertainty (ignorance)" | Shows how hierarchical models provide framework for handling both types of uncertainty through exchangeable structures | Even seemingly "unknowable" uncertainties can be modeled through hierarchical Bayesian structures that acknowledge different levels of knowledge. |
| [[📜Gelman21_bayesholes]] | 2021 | Fundamental limitations of Bayesian methods | "The two-slit experiment demonstrates that quantum superposition violates basic rules of conditional probability. Standard Bayesian joint distributions cannot capture quantum behavior." | Reveals where exchangeability assumptions break down - particularly in quantum systems where joint distributions don't exist | While Bayesian methods are powerful, they have fundamental limitations in certain contexts where basic probability assumptions fail. |
| [[ten-great-ideas-about-chance]]<br>de-Finetti Unification | 2018 | de Finetti's theorem and exchangeability | "De Finetti proved that every such exchangeable sequence can be gotten in just this way. It is just as if you had independence in the chances and uncertainty about the bias." | Direct treatment of how exchangeability enables representation of uncertain sequences as mixtures of independent trials | Through exchangeability, complex uncertainties can be decomposed into simpler components that are more amenable to probabilistic reasoning. |
| O'Hagan04 Dicing with Unknown | 2004 | Types of uncertainty in statistical reasoning | "The distinction between aleatory and epistemic uncertainties is valuable in many areas where it is important to appreciate which uncertainties are potentially reducible by further investigation." | Shows how exchangeability connects to reducible (epistemic) vs irreducible (aleatory) uncertainty | Understanding the nature of uncertainty (whether reducible or irreducible) is crucial for choosing appropriate statistical methods and interpreting results. |
| Knightian Aleatoric Epistemic Discussion | 2022 | Synthesis of uncertainty concepts | "Distinction between brain and mind as hardware and software, sequential dependency in short term, but feedback in long term" | Links hierarchical structures to different forms of uncertainty through exchangeable sequences | Different types of uncertainty can be understood and managed through hierarchical structures that capture both short-term and long-term dependencies. |
**Key Synthesis:**
These works collectively suggest that while fundamental uncertainty (à la Knight) poses real challenges, hierarchical Bayesian methods with exchangeability provide a framework for quantifying and reasoning about uncertainties at different levels, even if some limitations remain in extreme cases like quantum systems.
| Document | Year | Primary Focus | Key Quote | Connection to Exchangeability & Hierarchical Bayes |
| ---------------------------------------- | ---- | ---------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------- |
| Gelman06 Aleatory Epistemic Uncertainty | 2006 | Distinction between randomness and ignorance in Bayesian context | "In this larger, potentially hierarchical context, Bayesian inference can distinguish between aleatory uncertainty (randomness) and epistemic uncertainty (ignorance)" | Shows how hierarchical models provide framework for handling both types of uncertainty through exchangeable structures |
| | 2021 | Fundamental limitations of Bayesian methods | "The two-slit experiment demonstrates that quantum superposition violates basic rules of conditional probability. Standard Bayesian joint distributions cannot capture quantum behavior." | Reveals where exchangeability assumptions break down - particularly in quantum systems where joint distributions don't exist |
| | 2018 | de Finetti's theorem and exchangeability | "De Finetti proved that every such exchangeable sequence can be gotten in just this way. It is just as if you had independence in the chances and uncertainty about the bias." | Direct treatment of how exchangeability enables representation of uncertain sequences as mixtures of independent trials |
| O'Hagan04 Dicing with Unknown | 2004 | Types of uncertainty in statistical reasoning | "The distinction between aleatory and epistemic uncertainties is valuable in many areas where it is important to appreciate which uncertainties are potentially reducible by further investigation." | Shows how exchangeability connects to reducible (epistemic) vs irreducible (aleatory) uncertainty |
| Knightian Aleatoric Epistemic Discussion | 2022 | Synthesis of uncertainty concepts | "Distinction between brain and mind as hardware and software, sequential dependency in short term, but feedback in long term" | Links hierarchical structures to different forms of uncertainty through exchangeable sequences |
**Key Overall Connection:**
These papers collectively show how exchangeability serves as a bridge between different types of uncertainty in Bayesian inference. The hierarchical Bayesian framework provides a natural way to represent this through:
1. Using exchangeable sequences to model aleatory uncertainty at lower levels
2. Using hierarchical structures to capture epistemic uncertainty at higher levels
3. Showing where this framework succeeds (most statistical applications) and fails (quantum systems)
The documents progress from foundational theory (de Finetti) through practical applications (O'Hagan) to fundamental limitations (Gelman), all connected by the concept of exchangeability in hierarchical structures.