`log_prob`

and `grad_log_prob`

functions`stanfit-method-logprob.Rd`

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)
```

- log_prob
`signature(object = "stanfit")`

Compute - grad_log_prob
`signature(object = "stanfit")`

Compute the gradients
for - 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

`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
`adjust_transform = FALSE`

to make the values match Stan's output.
`log_prob`

as well as the log posterior. The latter is returned as
an attribute.
`constrained`

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

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.

`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.

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

```
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
}
```