Priors and Likelihoods in Plain Language
Two distributions do most of the work inside a Bayesian agent: a prior and a likelihood. The vocabulary sounds heavier than the ideas actually are. Here is a slower pass through both, with just enough math to be honest and just enough plain language to be usable.
The prior: what the agent expected before it looked.
A prior is a probability distribution the agent carries before any new observation arrives. In an active-inference agent it is often written P(s), a distribution over hidden states s of the world Class E. If the agent is a controller for a service cell, s might be a joint setting of latency, error rate, and queue depth. If the agent is walking a maze, s might be its position and orientation. The prior says: without new evidence, these settings are more plausible than those.
Priors are not guesses pulled out of the air. They are summaries of everything the agent has already learned or been told about how the world tends to be arranged. A useful mental picture: the prior is a landscape of expectation, higher where the world is thought to sit, lower elsewhere. When a new observation arrives, it does not overwrite that landscape. It reshapes it.
The likelihood: how observations depend on states.
A likelihood is the other half of the pair. It is written P(o | s), the probability of seeing observation o given that the hidden state is s (Parr, Pezzulo and Friston, 2022) Class E. Read it out loud: if the true state were s, how surprised would I be to see o? Small numbers mean the state and the observation disagree. Larger numbers mean they fit.
Likelihoods live inside the generative model. In a POMDP, the likelihood matrix (often called A) encodes which observations each hidden state tends to produce. In the UNI Precision Lab, the sensory precision dial sharpens or blurs this matrix directly: at high precision the agent trusts the sensor to name the true state cleanly, at low precision the same observation is compatible with many states, and the agent stays cautious Class C. The dial is the likelihood, made steerable.
Combining them: the posterior.
Bayes' rule combines the two into a posterior P(s | o), the belief the agent holds after the observation:
P(s | o) is proportional to P(o | s) times P(s).
In words: take the prior landscape, multiply it pointwise by the likelihood of the new observation under each state, and renormalize. States that were plausible and that also fit the new observation come out on top. States that were plausible but that fit poorly get pushed down. States that fit the observation but were implausible to begin with rise, but not as much as if the prior had already favored them Class E.
That is the whole content of the update, and it is why priors and likelihoods matter equally. A very confident prior can drown out a weak observation. A very sharp likelihood on a strong observation can dominate a mild prior. The posterior is neither, it is the balance.
Why this framing pays off later.
Once priors and likelihoods are clear, most of the rest of active inference becomes readable. Free energy is a way of scoring how badly a candidate belief fits the joint (prior times likelihood). Variational inference is the trick of finding a tractable belief that scores well. Prior preferences over observations, the pragmatic term inside expected free energy, are a second, distinct use of the word "prior", not the same object as P(s). Keeping the two priors separate in your head is worth the effort. One says what the agent expects to be true. The other says what it wants to see.
In our voice, from a Themesis resource map that catalogs entry points into active inference (Where to Start with Active Inference, A Resource Map for 2026): a helpful survey of how newcomers enter the field, with SWU listed as one of several pathways. Factual, not endorsement.
UNI is a working hypothesis on an attainable path toward General Natural Intelligence: a natural, active-inference approach whose evidence is growing, evidence-classed, and tested in the open. Do not take the claim on faith. Test the build, inspect the gates, and help us find where it fails.
Foundations. Parr, T., Pezzulo, G., and Friston, K. (2022). Active Inference: The Free Energy Principle in Mind, Brain, and Behavior. MIT Press. The prior over hidden states, the likelihood matrix, and Bayesian belief updating are treated in chapters 2 and 4. Cited, not hosted.