[[Oct.23🌲tree]], [[Hierarchical prior]], [[Hierarchical model]] ![[Pasted image 20241215022302.png]] using [[966 Computational Cognitive Science]] w12. 1. **Marginal Likelihood of Data Given a Model:** $p(D∣M)=\underset{w}{∑}p(D∣w,M) p(w∣M)$ 2. **Model Learning (Posterior over Models):** $p(M \mid D, C) \propto p(D \mid M) \, p(M \mid C)$ 3. **Parameter Learning (Posterior over Parameters):** $p(w \mid D, M) = \frac{p(D \mid w, M) \, p(w \mid M)}{p(D \mid M)}$ This hierarchical learning framework positions inference as occurring at multiple levels. We start with a model class C, from which we select a particular model M. Given that model, we integrate over its parameter space w to determine how well it explains the data D. This integration yields the marginal likelihood $p(D \mid M)$, reflecting the model’s intrinsic fit without committing to a specific parameter setting. Using Bayes’ rule, we combine the marginal likelihood with the prior over models $p(M \mid C)$ to update our belief about which model M is appropriate, resulting in the posterior $p(M \mid D, C)$. Simultaneously, given a chosen model M, we update our belief about the parameters w to form the posterior $p(w \mid D, M)$. Thus, hierarchical learning involves two key inference steps: learning model structure and learning parameters within that model, each guided by Bayesian principles. --- **Applying the Hierarchical Bayes Template** In entrepreneurial learning, we begin with an **Opportunity Horizon (C)**—a strategic domain where new ventures can emerge. Within this horizon, we propose a **Value Creation & Capture Hypothesis (M)**, a model of how the venture will deliver and profit from value. The venture’s **Operational Variables (w)**—parameters like pricing, distribution channels, or partner agreements—are initially uncertain. As the entrepreneur runs pilots, prototypes, or market tests, they gather **Experimental Results (D)** serving as evidence. By integrating over these operational variables, the entrepreneur computes something akin to the marginal likelihood, assessing how well their hypothesis explains the observed outcomes. Leveraging Bayes’ rule, they refine their belief in the chosen hypothesis given the horizon, while also updating the operational parameters to best align with real-world feedback. This hierarchical Bayesian logic explains how entrepreneurs systematically navigate from broad strategic arenas to concrete, data-driven decisions that shape their venture’s evolving business model. using [🌲(🏎️)hier(tesla) cld](https://claude.ai/chat/9d18016f-bef7-44e3-a602-d7383ee6c056) | | Bayesians speak | Entrepreneurs speak | Example (Tesla) | | -------- | ------------------------------------------------------------------------------------------------------------------------ | ------------------------------------------------------------------------ | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | object | Hierarchical Level | | | | | C (Model Class) | Opportunity Horizon | Tesla’s initial broad domain: sustainable electric mobility. They researched the EV landscape, learned from failed attempts (e.g., GM’s EV1), and identified a strategic space where electric vehicles could be desirable and efficient compared to internal combustion engines. | | | M (Model) | Value Creation & Capture Hypothesis | Tesla’s chosen hypothesis: A premium electric sports car (the Roadster) would establish the brand, validate battery technology, and attract early adopters—funding subsequent mass-market models. This wasn’t the only option considered; mass-market EVs or hybrids were also on the table. | | | w (Parameters) | Operational Variables | Specific decisions like battery chemistry (lithium-ion vs. lead-acid), production approach (partnering with Lotus vs. building in-house), and pricing strategy ($109,000) that Tesla tested and refined based on early market signals and technical performance. | | | D (Data) | Market Data/Experimental Results | Early reservations from affluent tech entrepreneurs, feedback from a “beauty contest” of 30 employees evaluating design prototypes, performance tests (0-60 mph in ~4s, 250-mile range), and real production learnings on cost and quality. | | relation | | | | | | **Marginal Likelihood of Data Given a Model:** $p(D∣M)=\sum_{w}p(D∣w,M)p(w∣M)$ | “How well do our tests and feedback confirm this strategic bet?” | Tesla integrated feedback from test drives, initial reservations, and prototype performance across various operational setups (different battery packs, production methods). By considering all configurations (w), Tesla assessed how strongly the premium sports EV hypothesis (M) explained the observed interest (D). | | | **Model Learning (Posterior over Models):** $p(M \mid D, C) \propto p(D \mid M) \, p(M \mid C)$ | “Which strategic direction should we commit to based on what we’ve learned?” | Starting with multiple potential EV strategies (mass-market, hybrid, premium), Tesla used initial data (reservations, test feedback) to confirm the Roadster model was viable within the chosen opportunity horizon. Encouraging early signals boosted confidence in the premium sports car approach. | | | **Parameter Learning (Posterior over Parameters):** $p(w \mid D, M) = \frac{p(D \mid w, M) \, p(w \mid M)}{p(D \mid M)}$ | “Given we’re going with the Roadster, what’s the optimal mix of tech, production, and pricing?” | With the Roadster model locked in, Tesla refined operational variables. They discovered that outsourcing too much (Lotus in the UK, parts from Thailand) created complexity. Adjusting production methods, perfecting battery technology, and honing the pricing strategy were informed by the data, leading to a more optimized operational setup. | | | Bayesians speak | Entrepreneurs speak | Example (Tesla) | | -------- | ------------------------------------------------------------------------------------------------------------------------ | ----------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | object | Hierarchical Level | | | | | C (Model Class) | Opportunity Horizon | Tesla’s initial broad domain: sustainable electric mobility. They researched the EV landscape, learned from failed attempts (e.g., GM’s EV1), and identified a strategic space where electric vehicles could be desirable and efficient compared to internal combustion engines. | | | M (Model) | Value Creation & Capture Hypothesis | Tesla’s chosen hypothesis: A premium electric sports car (the Roadster) would establish the brand, validate battery technology, and attract early adopters—funding subsequent mass-market models. This wasn’t the only option considered; mass-market EVs or hybrids were also on the table. | | | w (Parameters) | Operational Variables | Specific decisions like battery chemistry (lithium-ion vs. lead-acid), production approach (partnering with Lotus vs. building in-house), and pricing strategy ($109,000) that Tesla tested and refined based on early market signals and technical performance. | | | D (Data) | Market Data/Experimental Results | Early reservations from affluent tech entrepreneurs, feedback from a “beauty contest” of 30 employees evaluating design prototypes, performance tests (0-60 mph in ~4s, 250-mile range), and real production learnings on cost and quality. | | relation | | | | | | **Marginal Likelihood of Data Given a Model:** $p(D∣M)=\sum_{w}p(D∣w,M)p(w∣M)$ | “How well do our tests and feedback confirm this strategic bet?” | Tesla integrated feedback from test drives, initial reservations, and prototype performance across various operational setups (different battery packs, production methods). By considering all configurations (w), Tesla assessed how strongly the premium sports EV hypothesis (M) explained the observed interest (D). | | | **Model Learning (Posterior over Models):** $p(M \mid D, C) \propto p(D \mid M) \, p(M \mid C)$ | “Which strategic direction should we commit to based on what we’ve learned?” | Starting with multiple potential EV strategies (mass-market, hybrid, premium), Tesla used initial data (reservations, test feedback) to confirm the Roadster model was viable within the chosen opportunity horizon. Encouraging early signals boosted confidence in the premium sports car approach. | | | **Parameter Learning (Posterior over Parameters):** $p(w \mid D, M) = \frac{p(D \mid w, M) \, p(w \mid M)}{p(D \mid M)}$ | “Given we’re going with the Roadster, what’s the optimal mix of tech, production, and pricing?” | With the Roadster model locked in, Tesla refined operational variables. They discovered that outsourcing too much (Lotus in the UK, parts from Thailand) created complexity. Adjusting production methods, perfecting battery technology, and honing the pricing strategy were informed by the data, leading to a more optimized operational setup. | [[📜Felin23_disrupt_evol]]