Distributional parameters can be added to the list of parameters that are fit
during calibration. By default, distributional parameters in priors and
likelihoods are not fit. Use mp_nofit to exclude distributional parameters
from being fit and mp_fit to fit them.
Arguments
- x
numeric starting value of the distributional parameter to fit, or character name of an existing variable in the model with a default starting value to use.
- trans
transformation to apply to the distributional parameter. By default, distributional parameters inherit a default transformation from the associated distribution. For example, the standard deviation parameter
sdin themp_normaldistributions has a default log transformation specified usingmp_log.
Examples
# First we call the SIR model spec, and generate some data for calibration.
spec = mp_tmb_library("starter_models", "sir", package = "macpan2")
data = mp_simulator(spec, 50, "infection") |> mp_trajectory()
# Suppose we want to specify a Normal prior on the transmission parameter
# beta, and we are interested in estimating the prior standard deviation.
# Here we use `mp_fit` to estimate the standard deviation, `sd`, and we
# provide a numeric starting value for `sd` in the optimization.
cal = mp_tmb_calibrator(
spec
, data
, traj = "infection"
, par = list(beta = mp_normal(location = 0.35, sd = mp_fit(0.1)))
, default = list(beta = 0.25)
)
# When viewing the calibration objective function we can see the additional
# prior density term added for beta. The standard deviation parameter has
# been automatically named 'distr_params_log_sd_beta'.
cal$simulator$tmb_model$obj_fn$obj_fn_expr
#> ~-sum(dpois(obs_infection, clamp(sim_infection))) - sum(dnorm(beta,
#> 0.35, exp(distr_params_log_sd_beta)))
#> <environment: 0x55c0fbdb67d0>
# Next we optimize and view the fitted parameters. We can see the
# distributional parameter in the coefficient table with a default value
# equal to the numeric value we provided to `mp_fit` above.
mp_optimize(cal)
#> outer mgc: 379.7835
#> outer mgc: 253.0639
#> outer mgc: 40.08291
#> outer mgc: 1.60249
#> outer mgc: 0.002833777
#> outer mgc: 8.986787e-09
#> $par
#> params params
#> 0.2005665 -1.9009040
#>
#> $objective
#> [1] 49.2679
#>
#> $convergence
#> [1] 0
#>
#> $iterations
#> [1] 5
#>
#> $evaluations
#> function gradient
#> 6 6
#>
#> $message
#> [1] "relative convergence (4)"
#>
mp_tmb_coef(cal)
#> outer mgc: 8.986787e-09
#> outer mgc: 11.62005
#> outer mgc: 11.92421
#> outer mgc: 0.0133705
#> outer mgc: 0.01339728
#> outer mgc: 31.09242
#> term mat row col default type estimate std.error
#> 1 params beta 0 0 0.25 fixed 0.2005665 0.009251899
#> 2 params.1 distr_params_sd_beta 0 0 0.10 fixed 0.1494335 0.106069656
# If instead we want control over the name of the new fitted distributional
# parameter, we can add a new variable to our model specification with the
# default value set to the desired optimization starting value.
updated_spec = spec |> mp_tmb_insert(default = list(sd_var = 0.1))
# In the calibrator, we use the name of this newly added variable, "sd_var",
# as input to `mp_fit`.
cal = mp_tmb_calibrator(
updated_spec
, data
, traj = "infection"
, par = list(beta = mp_normal(location = 0.35, sd = mp_fit("sd_var")))
, default = list(beta = 0.25)
)
# We can see this distributional parameter get propogated to the objective
# function and the fitted parameter table.
cal$simulator$tmb_model$obj_fn$obj_fn_expr
#> ~-sum(dpois(obs_infection, clamp(sim_infection))) - sum(dnorm(beta,
#> 0.35, exp(sd_var)))
#> <environment: 0x55c0fb9bfd58>
mp_optimize(cal)
#> outer mgc: 389.7016
#> outer mgc: 258.9379
#> outer mgc: 42.94112
#> outer mgc: 2.418362
#> outer mgc: 0.01416442
#> outer mgc: 7.421077e-06
#> outer mgc: 3.974682e-12
#> $par
#> params params
#> 0.2005665 -1.9009040
#>
#> $objective
#> [1] 49.2679
#>
#> $convergence
#> [1] 0
#>
#> $iterations
#> [1] 6
#>
#> $evaluations
#> function gradient
#> 7 7
#>
#> $message
#> [1] "relative convergence (4)"
#>
mp_tmb_coef(cal)
#> outer mgc: 3.974682e-12
#> outer mgc: 11.62005
#> outer mgc: 11.92421
#> outer mgc: 0.01337051
#> outer mgc: 0.01339727
#> outer mgc: 31.09242
#> term mat row col default type estimate std.error
#> 1 params beta 0 0 0.25 fixed 0.2005665 0.009251899
#> 2 params.1 sd_var 0 0 0.10 fixed -1.9009040 0.709811879