Problem $4\mathrm{.}1$ Match the following functions that play a role in Bayesian modeling with the

descriptions:

Functions:

$1.$Distribution of the posterior mean estimate

$2.$ Prior distribution

$3.$ Likelihood function

$4.$ Posterior distribution

$5.$ Measurement distribution

Descriptions:

a$)$ Result of inference on an individual trial

b$)$ Describes how potentially noisy observations are generated

c$)$ Can be directly compared to human responses in a psychophysical experiment

d$)$ Often modeled as a Gaussian function centered at the measurement

e$)$ May reflect statistics in the natural world