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div(
withMathJax(),
h3(style = "color: #337ab7;", "What is posterior predictive checking?"),
p(
strong("The idea behind posterior predictive checking is simple:")
),
p(em("If our model is a good fit then we should be able to use it to generate")),
p(em("data that looks a lot like the data we observed.")),
br(),
p(
"To generate this 'replicated' data we use the",
em("posterior predictive distribution")
),
span(
style = "color: #337ab7; font-face: bold;",
withMathJax(
"$$ p(y^{rep} | y ) = \\int p(y^{rep} | \\theta) p(\\theta | y ) d \\theta,$$"
)
),
p(
"where \\(y\\) is the observed data and \\(\\theta\\) the parameters in our model."
),
br(),
p(
"For each draw of \\(\\theta\\) from the posterior \\(p(\\theta | y) \\)
we simulate data \\(y^{rep}\\) from the posterior predictive distribution \\(p(y^{rep} | y) \\)."
),
br(),
p(
"Using the simulations of \\(y^{rep}\\) we can make various
graphical displays comparing our observed data to the replications."
),
hr(),
helpText(
"For a more thorough discussion of posterior predictive checking see Chapter 6 of",
a("BDA3.", href = "http://www.stat.columbia.edu/~gelman/book/")
)
)
|
