An Essay Towards Solving a Problem in the Doctrine of Chances … in AI … from 1763

Beliefs change with evidence. When you hear a rumor about a colleague's promotion, you weigh it against what you already know about their recent performance, office politics, etc. before deciding how much to trust it. This process, Bayesian belief updating, treats beliefs as probabilities that shift with new information. The Fidelius memory architecture uses this approach, tracking confidence in opinions, updating them through reflection, and factoring in personality-like dispositions.

Bayes' Theorem and Cognitive Science

In 1763, Reverend Thomas Bayes published a theorem posthumously: Posterior Probability = (Likelihood of Evidence × Prior Probability) / Evidence Normalizer. Your updated belief (posterior) combines what you already thought (prior) with how well new data fits (likelihood).

Joshua Tenenbaum's lab at MIT has shown humans approximate Bayesian inference intuitively. We're not perfect calculators, but we update beliefs efficiently. A 2015 Neuron study framed confidence as Bayesian probability: when evidence aligns with priors, confidence rises; contradictions erode it. Herbert Simon's bounded rationality (1957) explains why we aren't purely rational: cognitive limits and biases skew updates. Confirmation bias, for instance, leads us to favor evidence matching our existing views.

In one experiment from the Journal of Personality and Social Psychology, participants estimated probabilities ("likelihood of rain tomorrow") then received new data. Those with strong priors updated slowly; open-minded participants shifted quickly. Overconfidence persists when evidence is noisy, contributing to polarization in debates about vaccines or climate change.

Real Life Examples

Weather Forecasting

You check the app: 30% chance of rain. Dark clouds appear. Your estimate jumps to 70%, and you grab an umbrella. If the app is consistently wrong, you downgrade its reliability over time.

Investment Decisions

A stock tip claims "TechCorp will soar." If you're skeptical due to market volatility, you assign low probability. Strong earnings reports push it upward. Optimistic investors overweight positives; cautious ones demand more proof.

Political Opinions

You start with 60% support for a policy based on ideology. Counterarguments might drop it to 40%. High-skepticism personalities resist change, which is how echo chambers reinforce priors and slow updates.

Relationship Trust

A partner arrives late. Your prior trust: 90%. Their explanation (traffic jam) fits past patterns, so your trust rises to 95%. Repeated incidents weaken it gradually as evidence accumulates.

Bayesian updating in Fidelius

Fidelius structures opinions as probabilistic beliefs in its Opinion Network, drawing from four memory stores: World (facts), Experience (events), Opinion (judgments), and Observation (patterns). Updates happen via the Reflect process, where new evidence from conversations refines confidence scores (0.0–1.0).

Prior beliefs are stored as confidence scores with history logs, such as "User prefers concise emails" at 0.6. The reflect operation assesses new experiences against priors using three operations: reinforce (confidence += alpha, capped at 1.0), weaken (-alpha, floored at 0.0), or contradict (-2alpha). Opinions evolve over time, with sleep cycles applying decay for unreinforced ones (e.g., -0.01 daily after a grace period).

Behavioral profiles (skepticism 1–5) weight evidence. High skepticism strengthens priors, slowing updates; low skepticism allows rapid shifts. Ontology classifies facts probabilistically and detects inconsistencies.

Handling uncertainty in LLMs

LLMs can hallucinate or contradict themselves without structure. Bayesian mechanics handle uncertainty by evolving opinions based on evidence rather than producing static outputs. This counters overconfidence in generation by flagging low-confidence posteriors and requesting clarification. In multi-turn interactions, responses adapt based on accumulated context rather than treating each exchange in isolation.

AI Examples

Project Management

User asks: "Is the deadline feasible?" Prior opinion: "Team often misses timelines" (confidence 0.7). New evidence: recent sprints succeeded. The system reinforces to 0.8 if skepticism is low, or holds at 0.7 for cautious profiles. Response: "Based on past delays, feasibility is medium, but recent wins are encouraging. Can you share more details?"

Health Advice

User shares symptoms. Prior: "User avoids meds" (0.5). Evidence: "Willing to try now." Prior weakens to 0.3. Response: "You've preferred natural remedies before, but you seem open to other options. Here's a balanced approach."

Product Recommendations

Query: "Suggest a laptop." Prior: "User favors Apple" (0.8). Evidence: "Budget concerns." Confidence drops to 0.6. Response: "You've preferred Apple, but given your budget, Dell and Lenovo offer comparable specs for less."

Debate Coaching

User: "Prep for AI regulation talk." Prior opinion: "Regulations stifle innovation" (0.9). Counter-evidence from stored facts: EU rules have improved ethics compliance. High-skepticism slows update to 0.8. Response: "Your view is that regulations hurt innovation, but EU data shows some benefits. You might address this counterargument directly."

Practical Benefits

Bayesian updating in Fidelius addresses several problems: evidence-based evolution prevents stale opinions; disposition traits personalize updates rather than applying uniform rules; confidence tracking highlights uncertainties and prompts user input; decay mechanisms prune outdated beliefs, similar to how humans forget irrelevant information.

Bayes' theorem, 260 years old, turns out to be useful for building AI that handles uncertainty. Fidelius applies it with structure: traceable updates, disposition-aware weighting, and confidence scores that flag when the system isn't sure. The goal is an agent that learns from interaction rather than one that pretends to know everything.