"Just like you would not want to assume a Normal distribution for the likelihood in every problem, you would not want to use a flat prior in every problem."
"Analytical expressions for the posterior distribution tenstend to require a so-called conjugate prior distribution, which means that the prior distribution is in the same class of distributions as the posterior distribution."
"Conversely, the posterior probability will be lower than
thanthe prior probability when the normalised likelihood is smaller than 1.""One way to view a Bayesian model is as a hierarchical model, similar to how linear mixed-effects models can be viewed as hierarchical models."
"Figure 15.3 shows 1000
samplessampled parameter values (prior samples), [...]""If the chain is reducible, it is not possible to arrive at a state from some other states."
"Just like you would not want to assume a Normal distribution for the likelihood in every problem, you would not want to use a flat prior in every problem."
"In all cases, it is a good idea to check the
sensibiltysensibility of the prior distribution by inspecting the prior predictive distribution.""Analytical expressions for the posterior distribution
tenstend to require a so-called conjugate prior distribution, which means that the prior distribution is in the same class of distributions as the posterior distribution."Minor hyperlink rendering issue: "This section contains some material adapted from (https://bookdown.org/kevin_davisross/bayesian-reasoning-and-methods/)[“An Introduction to Bayesian Reasoning and Methods”] by Kevin Ross"