log_prob and grad_log_prob functions

Using model's log_prob and grad_log_prob take values from the unconstrained space of model parameters and (by default) return values in the same space. Sometimes we need to convert the values of parameters from their support defined in the parameters block (which might be constrained, and for simplicity, we call it the constrained space) to the unconstrained space and vice versa. The constrain_pars and unconstrain_pars functions are used for this purpose.

<!-- %% log_prob(object, upars, adjust_transform = TRUE, gradient = FALSE)  -->
  # S4 method for stanfit
log_prob(object, upars, adjust_transform = TRUE, gradient = FALSE)
  <!-- %% grad_log_prob(object, upars, adjust_transform = TRUE)  -->
  # S4 method for stanfit
grad_log_prob(object, upars, adjust_transform = TRUE)
  <!-- %% get_num_upars(object) -->
  # S4 method for stanfit
get_num_upars(object)
  <!-- %% constrain_pars(object, upars) -->
  # S4 method for stanfit
constrain_pars(object, upars)
  <!-- %% unconstrain_pars(object, pars) -->
  # S4 method for stanfit
unconstrain_pars(object, pars)

Methods

log_prob

signature(object = "stanfit")

Compute lp__, the log posterior (up to an additive constant) for the model represented by a stanfit object. Note that, by default, log_prob returns the log posterior in the unconstrained space Stan works in internally. set adjust_transform = FALSE to make the values match Stan's output.

grad_log_prob

signature(object = "stanfit")

Compute the gradients for log_prob as well as the log posterior. The latter is returned as an attribute.

get_num_upars

signature(object = "stanfit")

Get the number of unconstrained parameters.

constrain_pars

signature(object = "stanfit")

Convert values of the parameter from unconstrained space (given as a vector) to their constrained space (returned as a named list).

unconstrain_pars

signature(object = "stanfit")

Contrary to constrained, conert values of the parameters from constrained to unconstrained space.

Arguments

object

An object of class stanfit.

pars

An list specifying the values for all parameters on the constrained space.

upars

A numeric vector for specifying the values for all parameters on the unconstrained space.

adjust_transform

Logical to indicate whether to adjust the log density since Stan transforms parameters to unconstrained space if it is in constrained space. Set to FALSE to make the function return the same values as Stan's lp__ output.

gradient

Logical to indicate whether gradients are also computed as well as the log density.

Details

Stan requires that parameters be defined along with their support. For example, for a variance parameter, we must define it on the positive real line. But inside Stan's samplers all parameters defined on the constrained space are transformed to an unconstrained space amenable to Hamiltonian Monte Carlo. Because of this, Stan adjusts the log density function by adding the log absolute value of the Jacobian determinant. Once a new iteration is drawn, Stan transforms the parameters back to the original constrained space without requiring interference from the user. However, when using the log density function for a model exposed to R, we need to be careful. For example, if we are interested in finding the mode of parameters on the constrained space, we then do not need the adjustment. For this reason, the log_prob and grad_log_prob functions accept an adjust_transform argument.

Value

log_prob returns a value (up to an additive constant) the log posterior. If gradient is TRUE, the gradients are also returned as an attribute with name gradient.

grad_log_prob returns a vector of the gradients. Additionally, the vector has an attribute named log_prob being the value the same as log_prob

is called for the input parameters.

get_num_upars returns the number of parameters on the unconstrained space.

constrain_pars returns a list and unconstrain_pars returns a vector.

References

The Stan Development Team Stan Modeling Language User's Guide and Reference Manual. https://mc-stan.org.

See also

stanfit

Examples

if (FALSE) {
# see the examples in the help for stanfit as well
# do a simple optimization problem 
opcode <- "
parameters {
  real y;
}
model {
  target += log(square(y - 5) + 1);
}
"
opfit <- stan(model_code = opcode, chains = 0)
tfun <- function(y) log_prob(opfit, y)
tgrfun <- function(y) grad_log_prob(opfit, y)
or <- optim(1, tfun, tgrfun, method = 'BFGS')
print(or)

# return the gradient as an attribute
tfun2 <- function(y) { 
  g <- grad_log_prob(opfit, y) 
  lp <- attr(g, "log_prob")
  attr(lp, "gradient") <- g
  lp
} 

or2 <- nlm(tfun2, 10)
or2 
}