Sequential Bayesian Interference

What is an estimator?

A computed value used to estimate a population parameter.
Example: Sample mean estimates true average salary

Variance

Variability of estimator around its expectation (remember spread on each side of a mean)

Robustness

Resistance to outliers and bad data.

Sequential Bayesian inference

Use posterior from one update as the prior for the next.
Example: Weather apps updating forecast as new sensor data arrives.

Conjugate priors

Posterior has same form as prior

Why conjugates are useful

Enables fast/analytical Bayesian updates.
Example: Quality control line updating defect rate in real time.

Markov property

Next state depends only on current, not full history.
Analogy: Chess knight moves - only board position matters, not how it got there.

Transition matrix

Probability from state i → j
Web surfing model: probability of clicking links between pages.

Under what condition are two events, A and B, said to be 'conditionally independent' given a third event, C?

They are conditionally independent if P(A∣B∩C)=P(A∣C).

What is the practical advantage of using a conjugate prior in Bayesian calculations?

They are very useful for simplifying Bayesian calculations, as the form of the posterior distribution is known in advance.

What defines the 'stationary distribution' of a Markov chain?

It is a probability distribution that remains unchanged when the transition matrix is applied to it.

Key Process for Kalman Filter
Prediction - Estimation - Observation - Update