getLogModelPrior: Get the log prior probability for a model
In hypergsplines: Bayesian model selection with penalised splines and hyper-g prior

Description Usage Arguments Details Value Author(s) Examples

The “exponential” prior assumes f(d) ~ exp(-2 * sum(d_j)) which penalizes models with many degrees of freedom regardless of linear (d_j = 1) or smooth (d_j > 1) inclusion of covariates.

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  getLogModelPrior(config,
    type = c("flat", "exponential", "independent", "dependent", "dep.linear"),
    modelData)

`config`	the model configuration vector, or a matrix of model configurations in rows. There may be additional elements to the right, e.g. the log marginal likelihood column/value, if `modelData` is provided. These are then ignored internally.
`type`	either “flat” (default), “exponential”, “independent” or “dependent”. See the details.
`modelData`	the model setup from `modelData`

The “independent” prior (as the exponential prior) that the different covariates are independent, f(d) = prod(f(d_j)), where f(d_j) is built hierarchically: The prior probability for exclusion is 0.5, thus f(0)=0.5. Given inclusion, the other half is split up uniformly between all possible degrees of freedom larger than 0.

The “dependent” prior imposes a uniform distribution for the number of included variables. The “position” of the included variables, i.e. which of the variables are included, is uniformly distributed on all possible configurations. The degrees of freedoms are then conditionally independent and uniformly distributed on the respective possible values.

The “dep.linear” prior is similar, but imposes a uniform distribution for the number of smoothly included variables conditional on inclusion. The “position” of the (smoothly) included variables, i.e. which of the (linearly included) variables are included (as splines), is uniformly distributed on the possible configurations at both steps. The spline variance parameters are then conditionally independent and uniformly distributed on the respective possible values. This leads to a fixed prior probability of linear inclusion of 1/4.

the (unnormalized) log prior probability

Daniel Sabanes Bove daniel.sabanesbove@ifspm.uzh.ch

## artificial configuration:
config <- c(a=0L, b=1L, c=3L, d=0L)

## get log prior probs:
getLogModelPrior(config=config,
                 type="flat")

getLogModelPrior(config=config,
                 type="exponential")