Bayes’ rule used as an analogy

Read the equation

The posterior is proportional to the likelihood times the prior, with the evidence providing normalization. This formula updates a distribution over hypotheses using observed data. The neighboring scalar clamp expression does not supply the probability distributions needed to implement it.

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Original context

## 3.5 Family 4: Bayesian Inference

```
f₄(x) = clamp₀₁((x + utility) / (1 + |utility|))
```

**Equation Type**: Posterior update: P(θ|D) ∝ P(D|θ)P(θ)

**Explanation**: Implements belief updating where the current state serves as prior and utility as likelihood. Division by (1 + |utility|) normalizes the posterior. Used for probabilistic reasoning.

## 3.6 Family 5: Learning / Weight Update

```
f₅(x) = x + 0.1 · dx_norm
```

**Equation Type**: Delta rule: W_{t+1} = W_t + ΔW

Posterior update: P(θ|D) ∝ P(D|θ)P(θ)

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