Distributions that can be described by the same set of parameters make
up a family of distributions. For example the normal/Gaussian family
includes all of the possible distributions that can be described by the
two parameters \(\mu\) and \(\sigma\) alone.

In brms you set the family of the probability distribution of the
outcome variable with the argument family. For example,
family = gaussian(), family = bernoulli().

In practice, you can think of the family as the prior probability
distribution of the outcome variable.

Likelihood

This is the probability distribution of the outcome variable conditional
on the prior(s).

Notation: \(p(d|\theta)\).

Outcome/response/dependent variables

These are the variables that appear on the left-hand side of a model
formula. For example, f0 in f0 ~ attitude;
F1 and F2 in c(F1, F2) ~ stress.

Parameter

A parameter in a statistical model (for example intercept/mean, standard
deviation, slope/\(\beta\), etc).

A parameter used to describe a probability distribution (for example
\(\mu\) and \(\sigma\) for normal/Gaussian
distributions).

Predictors, independent variables

These are the variable that appear on the right-hand side of a model
formula. For example, novel_word in
reaction_t ~ novel_word;
s(longitude, latitude) in
temperature ~ s(longitude, latitude).

Prior probability distribution or simply prior

This is the probability distribution of the values a parameter can take,
based on prior knowledge/belief, domain expertise, previous research,
pilot data.