Bayesian Basics

Question 1

probability

Answer 1

a way to quantify uncertainty

Question 2

prior distribution

Answer 2

initial belief. can be any probability distribution that reflects your knowledge

Question 3

uniform prior

Answer 3

equal probability assigned to all values

Question 4

Bayes rule

Question 5

posterior

Answer 5

(likelihood x prior)/evidence

Question 6

convergence

Question 7

Markov Chain Monte Carlo (MCMC)

Answer 7

a way to approximate the posterior

Question 8

likelihood function

Answer 8

probability of observing data given a particular value of theta (parameter). is directly related to data. quantifies how well parameter values explain/predict collected data

Question 9

binomial coefficient

Question 10

conjugancy

Answer 10

A special relationship between probability distributions where if you start with a particular type of distribution (prior) and update it with observed data, you end up with the same type of distribution (posterior).

Question 11

conjugate priors

Answer 11

Specific prior probability distributions that, when combined with specific likelihood functions, lead to posterior distributions that have the same mathematical form as the prior distribution.

Like matching puzzle pieces for likelihood functions, making it easier to calculate updated probabilities.

Question 12

likelihood function

Question 13

probability density function (PDF)

Question 14

probability mass function (PMF)

Question 15

difference between probability mass function (PMF) and probability density function (PDF)

Answer 15

PFF = continuous random variables. must be integrated over an interval to yield probs.

PMF = discrete random variables. probs at specific points.

Question 16

y-axis of a probability density function (PDF)

Answer 16

probability density