Prior

Definition

A prior is the probability assigned before observing new evidence.

In Bayes theorem:

P(H)

is the prior probability of hypothesis H.

Prior = starting probability before new evidence.

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Simple Example

Suppose:

H = a message is spam

Before reading the message, we may know:

P(spam) = 0.2

That is the prior.

It comes before inspecting specific words in the message.

The prior describes what we believe before seeing the current evidence.

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Prior Is Not Guessing Blindly

A prior can come from background information.

Examples:

historical frequency
domain knowledge
previous observations
base rate in data

If 20 percent of previous messages were spam, 0.2 may be a reasonable prior.

A prior can encode known background structure.

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Prior And Evidence

Evidence updates the prior.

Basic flow:

prior -> observe evidence -> posterior

Example:

P(spam) -> message contains suspicious phrase -> P(spam | phrase)

The prior is the starting point for an update.

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Strong Prior

A strong prior means the starting belief is hard to move.

Example:

P(H) is very close to 0 or 1

Evidence must be strong to change it substantially.

Strong priors resist weak evidence.

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Weak Prior

A weak prior means the starting belief is less committed.

Example:

several hypotheses start with similar probabilities

New evidence can shift the belief more easily.

Weak priors leave more room for evidence to decide.

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Why Priors Matter For Learning

Models often start with assumptions before seeing data.

Examples:

which labels are common
which patterns are likely
which solutions are simpler

These assumptions affect learning.

Learning never starts from nothing; some structure is already present.

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Final Summary

• A prior is probability before new evidence.
• It is written as P(H).
• Priors can come from background data or domain knowledge.
• Evidence updates priors into posteriors.
• Strong priors resist weak evidence.
• Weak priors are easier to shift.
• Priors matter because learning begins with assumptions.