Prior knowledge and new evidence

Bayesian reasoning gives us a simple pattern:

PRIOR

↓

EVIDENCE

↓

POSTERIOR

But that immediately raises two deeper questions.

Where does the prior come from?

and:

How much should new evidence change what we already believe?

These questions sit at the heart of intelligent reasoning.

A system that ignores prior knowledge may overreact to weak evidence.

A system that clings too strongly to the past may fail to recognise that the world has changed.

Good reasoning requires a balance between:

what history tells us

and:

what is happening now.

Prior knowledge is not optional

Suppose a doctor sees a patient with a cough.

Before running any tests, the doctor already knows something.

They know:

which illnesses are common,
which are rare,
the patient's age,
the season,
the patient's medical history.

The doctor does not begin from zero.

Likewise, a robot estimating its position already has:

a previous position estimate,
a map,
knowledge of how quickly it can move.

A forecasting model has historical data.

A language model has learned statistical structure from previous training.

Intelligent systems almost always begin with prior information.

The prior is a starting point

A prior is not necessarily a final judgement.

It is the belief we hold before incorporating the current evidence.

Suppose:

P(machine failure tomorrow) = 2%

based on historical reliability.

That 2% is a starting point.

Now new evidence arrives:

vibration increases,
temperature rises.

The posterior may become:

20%

or:

80%

depending on how informative those observations are.

The prior matters.

But it is supposed to be updateable.

Priors can come from historical frequency

One obvious source of prior knowledge is historical data.

Suppose a type of component failed:

5 times in 10,000 operating days.

We may use that history to estimate a baseline failure probability.

Likewise:

average customer churn,
historical rainfall,
previous hospital admission rates,
past electricity demand

can all provide prior information.

The past gives us evidence about what has tended to happen before.

Priors can come from the current state

Not all prior information comes from long-run statistics.

Suppose a robot estimated its position one second ago.

It moved forward.

Its new prior position comes from:

previous state + known action + motion model.

So prior knowledge can be dynamic.

In a stateful system:

POSTERIOR AT TIME t

becomes:

PRIOR AT TIME t+1.

This is one of the most important recurring ideas in the course.

Priors can come from physical constraints

Suppose a battery state of charge must lie between:

0% and 100%.

We already know that values outside this range are impossible.

That is prior knowledge.

Suppose a vehicle cannot teleport 10 kilometres in one second.

That too is prior knowledge.

Physical laws constrain the set of plausible states before new observations arrive.

Priors can come from domain expertise

Sometimes we have relevant knowledge that is not captured fully in the dataset.

An engineer may know:

a component usually fails after a particular symptom,
a sensor becomes unreliable at high temperature.

A doctor may know:

certain symptoms are strongly associated with particular diseases.

This knowledge can inform prior beliefs.

The challenge is to incorporate it explicitly rather than pretend the model starts from no assumptions.

Priors can be broad or narrow

Suppose we are estimating an unknown quantity.

A broad prior says:

Many values are plausible.

A narrow prior says:

I already have strong evidence that the value is likely to lie near here.

For example:

Broad prior

Temperature could plausibly be anywhere between 0°C and 30°C.

Narrow prior

Temperature is almost certainly between 19°C and 21°C.

The width of the prior reflects how much certainty we begin with.

Strong priors change slowly

Suppose a machine has operated reliably for 20 years.

One slightly unusual sensor reading appears.

Should we immediately conclude:

The machine is about to fail?

Probably not.

The prior belief in normal operation may be strong.

A weak piece of evidence produces only a small update.

But if:

vibration rises sharply,
temperature rises,
pressure drops

then the evidence may become strong enough to overwhelm the prior.

Weak priors change quickly

Suppose we know almost nothing about a new machine.

Our prior is broad.

The first few measurements may substantially change what we believe.

This is reasonable.

When prior knowledge is weak, new evidence should have more influence.

Prior strength should reflect evidence

A dangerous system can arise when a prior is treated as stronger than the evidence justifies.

Suppose an organisation assumes:

This type of customer almost never defaults.

But that assumption is based on:

20 historical examples.

The prior may be far less certain than it appears.

Good probabilistic reasoning should represent uncertainty about prior knowledge too.

New evidence has different strength

Not all observations are equally informative.

Suppose a doctor receives:

Evidence A

Patient says they feel slightly tired.

Evidence B

Highly specific laboratory test is positive.

Both are evidence.

They should not cause the same update.

The strength of evidence depends on how differently we would expect to see it under competing possibilities.

Evidence that is common under every hypothesis tells us little

Suppose:

Hypothesis A: machine healthy

Hypothesis B: machine failing

Observation:

machine is making some noise.

If both healthy and failing machines commonly make noise, this observation provides little information.

Now observe:

a very specific vibration pattern occurs almost only before failure.

That evidence is much more informative.

Evidence changes beliefs when it discriminates

Good evidence helps distinguish between hypotheses.

Suppose:

P(Evidence | Hypothesis A) = 0.9

and:

P(Evidence | Hypothesis B) = 0.1.

The evidence strongly favours A.

But if:

P(Evidence | A) = 0.51

and:

P(Evidence | B) = 0.49,

it tells us very little.

The observation matters only relative to what each explanation predicts.

Repeated evidence accumulates

Suppose one weak signal suggests a machine might fail.

Our probability moves from:

2% to 3%.

Then another independent signal appears.

It rises to:

8%.

Then another.

It rises to:

30%.

Evidence can accumulate gradually.

This is how beliefs should evolve in a stateful system.

But repeated evidence may not be independent

Suppose three alarm systems all rely on the same underlying temperature sensor.

They all trigger.

It may appear as though we have:

three pieces of evidence.

In reality, we may have:

one measurement reported three ways.

If we treat them as independent, we will become too confident.

This is called double-counting evidence.

Shared data sources create correlated evidence

Modern AI systems frequently combine:

websites,
articles,
databases,
reports.

But many of those sources may copy from one another.

Suppose ten websites repeat the same incorrect claim from one original source.

That is not necessarily ten independent pieces of evidence.

It may be:

one claim replicated ten times.

Source dependence matters.

Consensus is not always independent evidence

Suppose many models agree on a prediction.

That may increase confidence.

But perhaps every model was trained on:

the same dataset,
similar architectures,
the same assumptions.

Their errors may be correlated.

Agreement is more informative when the evidence sources are genuinely diverse.

New evidence should sometimes overturn history

Historical patterns can be powerful.

But they should not become destiny.

Suppose a company's demand historically follows a stable pattern.

Then a major new competitor enters the market.

Recent observations begin falling sharply.

A system that puts too much weight on the historical prior may keep predicting the old world.

Eventually, new evidence should dominate.

Recency matters in changing systems

Suppose electricity demand from:

2010–2020

followed one pattern.

Then:

electric vehicles grow,
heat pumps grow,
industrial demand changes.

Recent observations may provide more information about the current system than older observations.

Historical data is still valuable.

But its relevance may decay.

Not all old data should have equal weight

A simple model might treat:

an observation from yesterday

and:

an observation from 20 years ago

equally.

But in a changing system, this may be inappropriate.

We may want:

recent evidence → more weight

and:

old evidence → less weight.

This introduces the idea of forgetting or discounting old evidence.

Stateful systems need memory and forgetting

An intelligent system needs memory.

Without memory, it cannot learn from the past.

But unlimited memory with equal weight forever can also be harmful.

If the world changes, very old evidence may become misleading.

So a useful system may need both:

memory

and:

forgetting.

This is a recurring issue in adaptive systems.

Too little memory creates instability

Suppose an electricity controller responds only to the most recent measurement.

Demand rises slightly.

The controller reacts strongly.

Demand falls slightly.

The controller reacts strongly again.

The system may become unstable.

Some memory of recent history can smooth noisy observations.

Too much memory creates inertia

Now suppose the controller averages the previous:

10 years

of data equally.

A major structural change occurs today.

The controller may react extremely slowly because the huge historical dataset overwhelms the new evidence.

So there is a trade-off:

too little memory → overreaction

too much memory → underreaction

Learning rates encode this trade-off

Many adaptive algorithms contain something resembling a learning rate.

A high learning rate means:

New evidence changes the model quickly.

A low learning rate means:

Existing beliefs change slowly.

Neither is automatically correct.

The appropriate rate depends on:

measurement noise,
how quickly the world changes,
consequences of reacting incorrectly.

Stable worlds favour stronger history

Suppose a physical constant is being estimated.

We do not expect it to change every day.

Historical evidence should remain highly relevant.

A strong prior can be sensible.

Now consider:

social-media trends.

Preferences can change quickly.

Very old data may be much less useful.

The appropriate balance between prior and evidence depends on system dynamics.

Time scale matters

Different parts of the same system may change at different speeds.

For example:

Electricity system

Network topology may change slowly.

Electricity demand may change every second.

Consumer technology may change over years.

Weather changes over hours.

A good model may therefore need different memory timescales for different variables.

State helps distinguish persistent from temporary change

Suppose demand suddenly increases.

Is it:

a short-lived random fluctuation,
a persistent new regime?

One observation may not tell us.

Repeated observations can update our belief.

A stateful model can distinguish:

temporary disturbance

from:

structural change.

This is one reason memory matters.

Regime changes

Suppose financial markets usually behave one way during:

normal conditions

and another during:

crises.

We may model a hidden state:

Normal regime

or:

Crisis regime.

New evidence changes:

P(Regime | observations).

Once the posterior shifts strongly toward Crisis, predictions should change too.

This is another form of Bayesian state estimation.

Structural breaks

Sometimes relationships change abruptly.

For example:

new regulation,
war,
pandemic,
technological breakthrough.

Historical data before the change may no longer describe the system well.

This is a structural break.

A learning system must recognise when the prior world has stopped being a good guide.

Distribution shift is a prior-evidence problem

Machine learning often assumes:

The future will resemble the training data.

That assumption acts like a powerful prior.

When deployment data begins to differ, the system faces new evidence.

The challenge is recognising:

The distribution has shifted.

A robust system should reduce confidence when evidence no longer fits historical expectations.

Surprise can indicate that the prior is wrong

Suppose observations repeatedly occur that had:

very low probability under the existing model.

Perhaps we are experiencing extraordinary bad luck.

Or perhaps:

the model is no longer appropriate.

Repeated surprise should trigger reconsideration.

This is a crucial property for adaptive AI.

Models should be able to doubt themselves

Suppose a model says:

This observation was extremely unlikely according to me.

A weak system may still continue confidently.

A stronger system might ask:

Is my model wrong?

This is model uncertainty.

Evidence should sometimes update not only:

belief about the state

but also:

belief about the model itself.

Hierarchies of uncertainty

Imagine an AI predicting electricity demand.

It may be uncertain about:

the current temperature,
the relationship between temperature and demand,
whether that relationship has changed,
whether the model architecture is appropriate.

These are different layers.

So updating may occur at multiple levels:

STATE

PARAMETERS

MODEL

The deeper the uncertainty, the harder the inference problem becomes.

Prior knowledge can accelerate learning

Suppose two robots enter a new building.

Robot A knows nothing about buildings.

Robot B already knows that buildings often contain:

rooms,
doors,
corridors,
walls.

Robot B can interpret observations much more efficiently.

Prior knowledge makes learning faster.

This is one reason pre-trained AI models can adapt quickly to new tasks.

Pre-training creates prior knowledge

Modern foundation models are trained on huge datasets before being used for a particular task.

That training creates a vast amount of prior statistical knowledge.

When a user provides a prompt, the model does not learn language from scratch.

It combines:

pre-trained structure

with:

current context.

Conceptually:

PRIOR KNOWLEDGE FROM TRAINING

NEW CONTEXT

↓

CURRENT PREDICTION

Fine-tuning changes the prior

Suppose a general language model is fine-tuned on:

medical text,
legal documents,
engineering data.

The model's prior behaviour changes.

Certain patterns become more probable.

It has incorporated new evidence from a specialised domain.

Fine-tuning can therefore be understood partly as changing the model's prior knowledge.

Retrieval adds fresh evidence

Suppose a language model was trained last year.

A user asks about something that happened today.

The model's pre-trained knowledge may be outdated.

A retrieval system can provide:

new documents

as fresh evidence.

Then:

OLD PRIOR KNOWLEDGE

CURRENT RETRIEVED EVIDENCE

↓

UPDATED ANSWER

This is an important design pattern in modern AI.

Memory adds personal evidence

An AI agent may also retain information from previous interactions.

That memory becomes prior context for the next interaction.

So:

PREVIOUS INTERACTION

↓

MEMORY

↓

PRIOR FOR NEXT DECISION

But memory must be managed carefully.

Old information may become:

outdated,
irrelevant,
incorrect.

Again, memory and forgetting matter.

Prior knowledge can create bias

Priors are useful.

But they can also encode historical bias.

Suppose an organisation has historically hired mostly from:

Group A.

A model trained on that history may begin with a strong prior association:

Group A-like profile → success.

New candidates from other backgrounds may need stronger evidence to overcome that prior.

This can reproduce historical inequality.

Historical patterns are not automatically legitimate priors

Suppose historical data shows:

lower lending rates in Region B.

Why?

Perhaps because of:

genuine credit risk,
historical underinvestment,
discrimination,
lack of access.

Using the historical pattern as a prior may accurately reproduce history while perpetuating its causes.

So we must ask:

Should this historical relationship influence future decisions?

That is not purely a statistical question.

A prior can encode policy

Suppose a service deliberately says:

Every new user begins with the same priority.

That is effectively a prior assumption.

Another system might use:

Previous usage determines starting priority.

Different prior rules create different services.

Priors are therefore not only statistical choices.

They can be design choices.

Equal priors are not always neutral

Imagine two groups with very different historical evidence.

Giving them identical priors may ignore relevant information.

Using different priors may reproduce historical inequality.

There is no universally neutral choice.

The correct design depends on:

objective,
legitimacy of the evidence,
fairness principles.

This is why AI fairness cannot be reduced to one mathematical formula.

Evidence quality matters

Suppose new evidence comes from:

Sensor A: high accuracy

and:

Sensor B: poor accuracy.

The two observations should not necessarily influence belief equally.

Likewise:

peer-reviewed study,
anonymous rumour,
verified database,
low-quality web page

should not necessarily carry equal evidential weight.

Intelligent reasoning requires some model of source reliability.

Provenance affects belief

Recall our earlier discussion of provenance.

A value may come from:

direct measurement,
interpolation,
human entry,
another model.

These sources have different uncertainty.

So new evidence should ideally carry information about:

where it came from

and:

how reliable it is.

Age of evidence matters too

Suppose a customer said:

I live in Dublin.

Five years ago.

Is that still reliable?

Perhaps.

Perhaps not.

Evidence can become stale.

A stateful system may need to represent not only:

what was observed

but:

when it was observed.

Time turns evidence into history

At the moment an observation arrives, it is new evidence.

Later, it becomes prior knowledge.

Conceptually:

NEW EVIDENCE TODAY

↓

POSTERIOR TODAY

↓

PRIOR TOMORROW

This is the connection between:

past

present

and:

future.

Historical evidence should decay when appropriate

Suppose a user's preferred commute changes after moving house.

Their old behaviour may become less relevant.

A model that never forgets may continue making poor predictions.

A useful system may assign older observations decreasing weight.

This is sometimes called temporal decay.

But forgetting can destroy important long-term patterns

Suppose a machine fails only after a slow degradation process lasting years.

If the model forgets old measurements too quickly, it may miss the trend.

So forgetting must match the timescale of the process.

The system needs to remember what remains causally relevant.

Multi-timescale memory

Complex intelligent systems may need several forms of memory.

For example:

short-term memory

for rapidly changing conditions.

medium-term memory

for behavioural patterns.

long-term memory

for stable knowledge.

This resembles human reasoning.

We remember:

what happened seconds ago,
recurring experiences,
long-term facts

differently.

Prior knowledge can reduce data requirements

Suppose we want a robot to recognise chairs.

A system with no prior visual knowledge may require enormous amounts of training.

A pre-trained vision model already understands:

shapes,
edges,
objects.

It may need relatively few examples to learn the new task.

Prior knowledge makes learning more data-efficient.

Transfer learning

This is one reason transfer learning is powerful.

Knowledge learned in one setting is reused in another.

For example:

GENERAL IMAGE KNOWLEDGE

↓

SMALL SPECIALISED DATASET

↓

SPECIALISED MODEL

The system does not start again from zero.

It carries prior structure forward.

But transfer can fail

Suppose a model trained on urban roads is deployed in:

remote Arctic conditions.

Its prior representations may not transfer well.

Prior knowledge helps when the new environment is sufficiently related to the old one.

If not, it can become misleading.

This is sometimes called negative transfer.

New evidence should be able to challenge the prior

A good intelligent system should have a mechanism for saying:

My previous assumptions no longer fit what I am seeing.

This may require:

anomaly detection,
uncertainty estimation,
distribution-shift detection,
model retraining.

Otherwise, the past becomes a prison.

Catastrophic forgetting

There is also an opposite problem in machine learning.

A model learns a new task and loses performance on older tasks.

This is known as catastrophic forgetting.

So continual learning has two competing goals:

adapt to new evidence

while:

preserving useful old knowledge.

This is a difficult problem in modern AI.

Stability versus plasticity

This trade-off is sometimes described as:

stability

versus:

plasticity.

Stability means:

Retain what has already been learned.

Plasticity means:

Adapt to new information.

Too much stability:

cannot learn.

Too much plasticity:

forgets everything.

An intelligent learning system needs both.

Human societies face the same problem

Institutions also rely on priors.

Policies may be based on:

historical experience,
established rules,
previous crises.

That memory can make systems robust.

But institutions can also become slow to respond when circumstances change.

So the tension between:

history

and:

new evidence

is not unique to AI.

It is a general problem of adaptive systems.

The past is evidence, not destiny

This brings us back to the philosophical foundation of the course.

We learn from the past because it is the evidence we have.

But:

The future is not obliged to repeat it.

The past provides a prior.

The present provides new evidence.

Intelligence consists partly in deciding how much each should matter.

A forecast is continuously revisable

Suppose at midnight:

expected wind generation tomorrow = 10 GW.

At 06:00:

new weather observations arrive.

Forecast becomes:

12 GW.

At 10:00:

the weather system changes unexpectedly.

Forecast becomes:

8 GW.

None of the previous forecasts was necessarily irrational.

Each reflected the evidence available at the time.

A good forecast evolves.

Judging a prediction requires knowing what was known then

This is important when evaluating historical decisions.

Suppose a forecast made yesterday looks obviously wrong today.

But today's information was not available yesterday.

A fair evaluation should ask:

Was the prediction reasonable given the information available at the time?

Not:

Could someone with knowledge of the future have done better?

This distinction is fundamental to good forecasting evaluation.

Hindsight bias

Humans often suffer from hindsight bias.

After an event occurs, it can feel as though the outcome was obvious.

We forget how uncertain the future actually was beforehand.

Bayesian reasoning helps preserve the distinction between:

what was known before

and:

what became known later.

Historical outcomes do not erase historical uncertainty

Suppose an event with:

10% probability

occurs.

Afterward, it is:

100% known to have happened.

But before it occurred, it was still a 10% event according to the model.

We should not rewrite the past as though the realised outcome had always been certain.

One future became real.

The alternatives were still plausible beforehand.

Prior knowledge and innovation

There is another interesting tension.

Models learn from historical patterns.

But innovation often involves something genuinely new.

Suppose a model predicts technology adoption based on previous technologies.

A breakthrough product behaves differently.

Historical priors may systematically underestimate transformative change.

Novelty is difficult precisely because there is little directly comparable historical evidence.

AI faces the frontier problem

AI systems are often strongest in situations resembling their training data.

But many important decisions occur at the frontier:

new technologies,
new diseases,
new geopolitical events,
new market structures.

Here, prior knowledge may be less reliable.

A good system should increase uncertainty rather than project historical confidence into unfamiliar territory.

Prior knowledge should affect confidence

Suppose a model has seen:

one million highly similar examples.

It may reasonably be confident.

Now it encounters something far outside the training distribution.

Confidence should fall.

The prior is less informative there.

This is the connection between:

prior knowledge

and:

out-of-distribution uncertainty.

New evidence has value when it changes decisions

Suppose we already have overwhelming evidence that:

Action A is best.

Another measurement may add little value.

But if two actions are nearly tied and uncertainty is high, another observation may change the decision.

This is the value of information.

Evidence matters most when it can change what we should do.

Active learning chooses evidence deliberately

An intelligent system can sometimes choose which evidence to obtain.

Suppose a robot is uncertain between:

State A

and:

State B.

It can perform an action that produces different observations depending on which state is true.

That action is valuable because it distinguishes the hypotheses.

So:

CURRENT BELIEF

↓

WHAT OBSERVATION WOULD BE MOST INFORMATIVE?

↓

COLLECT EVIDENCE

↓

UPDATE BELIEF

This is active information gathering.

Experiments create evidence

Science does the same thing.

Instead of waiting passively for observations, researchers design experiments that distinguish between hypotheses.

A good experiment asks:

What outcome would we expect if Theory A were true?

versus:

What outcome would we expect if Theory B were true?

Then observations update belief.

Experimental design is therefore closely related to Bayesian reasoning.

Decisions can also reveal information

Suppose a recommendation system is uncertain whether a user likes documentaries.

Showing a documentary is:

a service decision,
an experiment.

The user's response provides evidence.

So actions can serve two purposes:

produce immediate value

and:

generate information for future decisions.

This is the exploration-exploitation trade-off again.

Prior knowledge and intelligent agents

An autonomous agent continuously combines:

memory

with:

new observation.

Its internal loop might be:

MEMORY / PRIOR STATE

↓

NEW OBSERVATION

↓

UPDATED STATE

↓

PREDICTION

↓

ACTION

↓

NEW OBSERVATION

Memory gives continuity.

Evidence gives adaptability.

Both are required for intelligent behaviour.

An agent without prior knowledge

Imagine a robot that forgets everything after every second.

At every moment it asks:

Where am I?

with no memory of where it was previously.

This would be extremely inefficient.

The previous state contains valuable prior information.

An agent that ignores evidence

Now imagine the opposite.

The robot believes:

I am at Position A.

Its sensors repeatedly indicate Position B.

But it refuses to update.

Memory has become rigidity.

Intelligence requires:

Remember enough to learn efficiently, but remain updateable when evidence changes.

Prior and evidence in service design

Suppose a hospital expects:

100 patients tomorrow

based on historical data.

That is prior knowledge.

By 08:00, actual arrivals are much higher than expected.

The service should update.

It may:

add staff,
open capacity,
reschedule non-urgent activity.

A stateful service should respond to current evidence rather than blindly follow the historical plan.

Forecasting and real-time control are different timescales

Historical data may provide a day-ahead forecast.

Real-time measurements update the state.

The system therefore uses both:

longer-term prior expectations

and:

short-term evidence.

This pattern occurs in:

electricity,
transport,
logistics,
healthcare,
computing.

The intelligent service is continuously updating

A useful service does not calculate:

one prediction

and stop.

Instead:

FORECAST

↓

OBSERVE ACTUAL SYSTEM

↓

UPDATE

↓

REALLOCATE

↓

OBSERVE AGAIN

This makes intelligence an ongoing process rather than a one-time computation.

Prior knowledge and fairness

Historical information can improve prediction.

But historical information can also encode:

unequal opportunity,
discriminatory decisions,
structural disadvantage.

So before treating history as a legitimate prior, we should ask:

Why did the historical pattern exist?

Prediction quality alone does not answer whether using it is fair.

New evidence can counter stereotypes

Suppose a group-level prior suggests:

average risk = high.

But an individual provides strong evidence of:

low risk.

A system that updates properly should respond to the individual evidence.

A system that overweights the group prior may become unfairly rigid.

This is one reason personalised evidence can matter.

But evidence itself may be unequal

Suppose some people have:

long financial histories,
detailed records,
abundant data.

Others have:

sparse histories,
missing data.

The first group can provide more evidence to overcome a prior.

The second cannot.

Unequal data availability can therefore create unequal posterior certainty.

This is another route through which data inequality can become service inequality.

We should separate prior probability from moral judgement

A model may estimate that an outcome is historically more likely for a particular group.

That is a probabilistic statement.

Whether society should:

act differently,
allocate differently,
impose different burdens

is a separate decision.

Probability describes belief.

Policy determines action.

The two should not be confused.

Ask where the prior came from

Whenever you encounter a prediction, ask:

What prior knowledge is being used?
Does it come from history?
How old is that history?
Is the current system still comparable?
How strong is the prior?
How uncertain is it?
What new evidence has arrived?
How reliable is that evidence?
Is the evidence independent?
Is old evidence being double-counted?
Should recent information receive more weight?
Is the system adapting too quickly?
Is it adapting too slowly?
Could historical bias be embedded in the prior?
Is the new situation outside the model's previous experience?

These questions reveal how a system balances memory and learning.

The central idea

Intelligence depends on both:

memory

and:

adaptation.

Prior knowledge allows us to use what the past has taught us.

New evidence allows us to recognise when the present differs from the past.

A good learning system therefore follows:

PAST EXPERIENCE

↓

PRIOR BELIEF

NEW EVIDENCE

↓

UPDATED BELIEF

↓

NEW DECISION

↓

NEW EXPERIENCE

The updated belief becomes part of future prior knowledge.

The loop continues.

The past should inform the future without imprisoning it.

Too little weight on prior knowledge creates unstable systems that overreact to noise.

Too much weight creates rigid systems that cannot adapt when reality changes.

The task is not to choose between:

history

and:

new evidence.

It is to combine them intelligently.

In the next lesson, we will ask how we know whether the probabilities produced by this process deserve to be trusted.

That leads to confidence and calibration: whether a model that says "80% confident" is actually right about 80% of the time.