Run Stan's optimization algorithms

The $optimize() method of a CmdStanModel object runs Stan's optimizer to obtain a (penalized) maximum likelihood estimate or a maximum a posteriori estimate (if jacobian=TRUE). See the CmdStan User's Guide for more details.

Any argument left as NULL will default to the default value used by the installed version of CmdStan. See the CmdStan User’s Guide for more details on the default arguments. The default values can also be obtained by checking the metadata of an example model, e.g., cmdstanr_example(method="optimize")$metadata().

optimize(
  data = NULL,
  seed = NULL,
  refresh = NULL,
  init = NULL,
  save_latent_dynamics = FALSE,
  output_dir = getOption("cmdstanr_output_dir"),
  output_basename = NULL,
  sig_figs = NULL,
  threads = NULL,
  opencl_ids = NULL,
  algorithm = NULL,
  jacobian = FALSE,
  init_alpha = NULL,
  iter = NULL,
  tol_obj = NULL,
  tol_rel_obj = NULL,
  tol_grad = NULL,
  tol_rel_grad = NULL,
  tol_param = NULL,
  history_size = NULL,
  show_messages = TRUE,
  show_exceptions = TRUE,
  save_cmdstan_config = NULL
)

Arguments

data

(multiple options) The data to use for the variables specified in the data block of the Stan program. One of the following:

A named list of R objects with the names corresponding to variables declared in the data block of the Stan program. Internally this list is then written to JSON for CmdStan using write_stan_json(). See write_stan_json() for details on the conversions performed on R objects before they are passed to Stan.
A path to a data file compatible with CmdStan (JSON or R dump). See the appendices in the CmdStan guide for details on using these formats.
NULL or an empty list if the Stan program has no data block.

seed

(positive integer(s)) A seed for the (P)RNG to pass to CmdStan. In the case of multi-chain sampling the single seed will automatically be augmented by the the run (chain) ID so that each chain uses a different seed. The exception is the transformed data block, which defaults to using same seed for all chains so that the same data is generated for all chains if RNG functions are used. The only time seed should be specified as a vector (one element per chain) is if RNG functions are used in transformed data and the goal is to generate different data for each chain.

refresh

(non-negative integer) The number of iterations between printed screen updates. If refresh = 0, only error messages will be printed.

init

(multiple options) The initialization method to use for the variables declared in the parameters block of the Stan program. One of the following:

A real number x>0. This initializes all parameters randomly between [-x,x] on the unconstrained parameter space.;
The number 0. This initializes all parameters to 0;
A character vector of paths (one per chain) to JSON or Rdump files containing initial values for all or some parameters. See write_stan_json() to write R objects to JSON files compatible with CmdStan.
A list of lists containing initial values for all or some parameters. For MCMC the list should contain a sublist for each chain. For other model fitting methods there should be just one sublist. The sublists should have named elements corresponding to the parameters for which you are specifying initial values. See Examples.
A function that returns a single list with names corresponding to the parameters for which you are specifying initial values. The function can take no arguments or a single argument chain_id. For MCMC, if the function has argument chain_id it will be supplied with the chain id (from 1 to number of chains) when called to generate the initial values. See Examples.
A CmdStanMCMC, CmdStanMLE, CmdStanVB, CmdStanPathfinder, or CmdStanLaplace fit object. If the fit object's parameters are only a subset of the model parameters then the other parameters will be drawn by Stan's default initialization. The fit object must have at least some parameters that are the same name and dimensions as the current Stan model. For the sample and pathfinder method, if the fit object has fewer draws than the requested number of chains/paths then the inits will be drawn using sampling with replacement. Otherwise sampling without replacement will be used. When a CmdStanPathfinder fit object is used as the init, if . psis_resample was set to FALSE and calculate_lp was set to TRUE (default), then resampling without replacement with Pareto smoothed weights will be used. If psis_resample was set to TRUE or calculate_lp was set to FALSE then sampling without replacement with uniform weights will be used to select the draws. PSIS resampling is used to select the draws for CmdStanVB, and CmdStanLaplace fit objects.
A type inheriting from posterior::draws. If the draws object has less samples than the number of requested chains/paths then the inits will be drawn using sampling with replacement. Otherwise sampling without replacement will be used. If the draws object's parameters are only a subset of the model parameters then the other parameters will be drawn by Stan's default initialization. The fit object must have at least some parameters that are the same name and dimensions as the current Stan model.

save_latent_dynamics

(logical) Should auxiliary diagnostic information about the latent dynamics be written to temporary diagnostic CSV files? This argument replaces CmdStan's diagnostic_file argument and the content written to CSV is controlled by the user's CmdStan installation and not CmdStanR (for some algorithms no content may be written). The default is FALSE, which is appropriate for almost every use case. To save the temporary files created when save_latent_dynamics=TRUE see the $save_latent_dynamics_files() method.

output_dir

(string) A path to a directory where CmdStan should write its output CSV files. For MCMC there will be one file per chain; for other methods there will be a single file. For interactive use this can typically be left at NULL (temporary directory) since CmdStanR makes the CmdStan output (posterior draws and diagnostics) available in R via methods of the fitted model objects. This can be set for an entire R session using options(cmdstanr_output_dir). The behavior of output_dir is as follows:

If NULL (the default), then the CSV files are written to a temporary directory and only saved permanently if the user calls one of the $save_* methods of the fitted model object (e.g., $save_output_files()). These temporary files are removed when the fitted model object is garbage collected (manually or automatically).
If a path, then the files are created in output_dir with names corresponding to the defaults used by $save_output_files().

output_basename

(string) A string to use as a prefix for the names of the output CSV files of CmdStan. If NULL (the default), the basename of the output CSV files will be comprised from the model name, timestamp, and 5 random characters.

sig_figs

(positive integer) The number of significant figures used when storing the output values. By default, CmdStan represent the output values with 6 significant figures. The upper limit for sig_figs is 18. Increasing this value will result in larger output CSV files and thus an increased usage of disk space.

threads

(positive integer) If the model was compiled with threading support, the number of threads to use in parallelized sections (e.g., when using the Stan functions reduce_sum() or map_rect()).

opencl_ids

(integer vector of length 2) The platform and device IDs of the OpenCL device to use for fitting. The model must be compiled with cpp_options = list(stan_opencl = TRUE) for this argument to have an effect.

algorithm

(string) The optimization algorithm. One of "lbfgs", "bfgs", or "newton". The control parameters below are only available for "lbfgs" and "bfgs. For their default values and more details see the CmdStan User's Guide. The default values can also be obtained by running cmdstanr_example(method="optimize")$metadata().

jacobian

(logical) Whether or not to use the Jacobian adjustment for constrained variables. For historical reasons, the default is FALSE, meaning optimization yields the (regularized) maximum likelihood estimate. Setting it to TRUE yields the maximum a posteriori estimate. See the Maximum Likelihood Estimation section of the CmdStan User's Guide for more details. For use later with $laplace() the jacobian argument should typically be set to TRUE.

init_alpha

(positive real) The initial step size parameter.

iter

(positive integer) The maximum number of iterations.

tol_obj

(positive real) Convergence tolerance on changes in objective function value.

tol_rel_obj

(positive real) Convergence tolerance on relative changes in objective function value.

tol_grad

(positive real) Convergence tolerance on the norm of the gradient.

tol_rel_grad

(positive real) Convergence tolerance on the relative norm of the gradient.

tol_param

(positive real) Convergence tolerance on changes in parameter value.

history_size

(positive integer) The size of the history used when approximating the Hessian. Only available for L-BFGS.

show_messages

(logical) When TRUE (the default), prints all output during the execution process, such as iteration numbers and elapsed times. If the output is silenced then the $output() method of the resulting fit object can be used to display the silenced messages.

show_exceptions

(logical) When TRUE (the default), prints all informational messages, for example rejection of the current proposal. Disable if you wish to silence these messages, but this is not usually recommended unless you are very confident that the model is correct up to numerical error. If the messages are silenced then the $output() method of the resulting fit object can be used to display the silenced messages.

save_cmdstan_config

(logical) When TRUE (the default), call CmdStan with argument "output save_config=1" to save a json file which contains the argument tree and extra information (equivalent to the output CSV file header). This option is only available in CmdStan 2.34.0 and later.

Value

A CmdStanMLE object.

Examples

# \dontrun{
library(cmdstanr)
library(posterior)
library(bayesplot)
color_scheme_set("brightblue")

# Set path to CmdStan
# (Note: if you installed CmdStan via install_cmdstan() with default settings
# then setting the path is unnecessary but the default below should still work.
# Otherwise use the `path` argument to specify the location of your
# CmdStan installation.)
set_cmdstan_path(path = NULL)
#> CmdStan path set to: /Users/jgabry/.cmdstan/cmdstan-2.35.0

# Create a CmdStanModel object from a Stan program,
# here using the example model that comes with CmdStan
file <- file.path(cmdstan_path(), "examples/bernoulli/bernoulli.stan")
mod <- cmdstan_model(file)
mod$print()
#> data {
#>   int<lower=0> N;
#>   array[N] int<lower=0, upper=1> y;
#> }
#> parameters {
#>   real<lower=0, upper=1> theta;
#> }
#> model {
#>   theta ~ beta(1, 1); // uniform prior on interval 0,1
#>   y ~ bernoulli(theta);
#> }
# Print with line numbers. This can be set globally using the
# `cmdstanr_print_line_numbers` option.
mod$print(line_numbers = TRUE)
#>  1: data {
#>  2:   int<lower=0> N;
#>  3:   array[N] int<lower=0, upper=1> y;
#>  4: }
#>  5: parameters {
#>  6:   real<lower=0, upper=1> theta;
#>  7: }
#>  8: model {
#>  9:   theta ~ beta(1, 1); // uniform prior on interval 0,1
#> 10:   y ~ bernoulli(theta);
#> 11: }

# Data as a named list (like RStan)
stan_data <- list(N = 10, y = c(0,1,0,0,0,0,0,0,0,1))

# Run MCMC using the 'sample' method
fit_mcmc <- mod$sample(
  data = stan_data,
  seed = 123,
  chains = 2,
  parallel_chains = 2
)
#> Running MCMC with 2 parallel chains...
#> 
#> Chain 1 Iteration:    1 / 2000 [  0%]  (Warmup) 
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#> Chain 1 finished in 0.0 seconds.
#> Chain 2 finished in 0.0 seconds.
#> 
#> Both chains finished successfully.
#> Mean chain execution time: 0.0 seconds.
#> Total execution time: 0.2 seconds.
#> 

# Use 'posterior' package for summaries
fit_mcmc$summary()
#> # A tibble: 2 × 10
#>   variable   mean median    sd   mad      q5    q95  rhat ess_bulk ess_tail
#>   <chr>     <dbl>  <dbl> <dbl> <dbl>   <dbl>  <dbl> <dbl>    <dbl>    <dbl>
#> 1 lp__     -7.30  -7.00  0.811 0.344 -8.83   -6.75   1.00     702.     776.
#> 2 theta     0.254  0.238 0.125 0.124  0.0807  0.483  1.00     634.     580.

# Check sampling diagnostics
fit_mcmc$diagnostic_summary()
#> $num_divergent
#> [1] 0 0
#> 
#> $num_max_treedepth
#> [1] 0 0
#> 
#> $ebfmi
#> [1] 1.1148699 0.8012192
#> 

# Get posterior draws
draws <- fit_mcmc$draws()
print(draws)
#> # A draws_array: 1000 iterations, 2 chains, and 2 variables
#> , , variable = lp__
#> 
#>          chain
#> iteration    1     2
#>         1 -7.0  -6.8
#>         2 -7.9  -6.9
#>         3 -7.4  -6.8
#>         4 -6.7  -6.8
#>         5 -6.9 -10.2
#> 
#> , , variable = theta
#> 
#>          chain
#> iteration    1    2
#>         1 0.17 0.23
#>         2 0.46 0.18
#>         3 0.41 0.28
#>         4 0.25 0.23
#>         5 0.18 0.62
#> 
#> # ... with 995 more iterations

# Convert to data frame using posterior::as_draws_df
as_draws_df(draws)
#> # A draws_df: 1000 iterations, 2 chains, and 2 variables
#>    lp__ theta
#> 1  -7.0  0.17
#> 2  -7.9  0.46
#> 3  -7.4  0.41
#> 4  -6.7  0.25
#> 5  -6.9  0.18
#> 6  -6.9  0.33
#> 7  -7.2  0.15
#> 8  -6.8  0.29
#> 9  -6.8  0.24
#> 10 -6.8  0.24
#> # ... with 1990 more draws
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}

# Plot posterior using bayesplot (ggplot2)
mcmc_hist(fit_mcmc$draws("theta"))
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


# For models fit using MCMC, if you like working with RStan's stanfit objects
# then you can create one with rstan::read_stan_csv()
# stanfit <- rstan::read_stan_csv(fit_mcmc$output_files())


# Run 'optimize' method to get a point estimate (default is Stan's LBFGS algorithm)
# and also demonstrate specifying data as a path to a file instead of a list
my_data_file <- file.path(cmdstan_path(), "examples/bernoulli/bernoulli.data.json")
fit_optim <- mod$optimize(data = my_data_file, seed = 123)
#> Initial log joint probability = -16.144 
#>     Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes  
#>        6      -5.00402   0.000246518   8.73164e-07           1           1        9    
#> Optimization terminated normally:  
#>   Convergence detected: relative gradient magnitude is below tolerance 
#> Finished in  0.1 seconds.
fit_optim$summary()
#> # A tibble: 2 × 2
#>   variable estimate
#>   <chr>       <dbl>
#> 1 lp__        -5.00
#> 2 theta        0.2 

# Run 'optimize' again with 'jacobian=TRUE' and then draw from Laplace approximation
# to the posterior
fit_optim <- mod$optimize(data = my_data_file, jacobian = TRUE)
#> Initial log joint probability = -11.9711 
#>     Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes  
#>        5      -6.74802    0.00123686   2.20415e-05           1           1        8    
#> Optimization terminated normally:  
#>   Convergence detected: relative gradient magnitude is below tolerance 
#> Finished in  0.2 seconds.
fit_laplace <- mod$laplace(data = my_data_file, mode = fit_optim, draws = 2000)
#> Calculating Hessian 
#> Calculating inverse of Cholesky factor 
#> Generating draws 
#> iteration: 0 
#> iteration: 100 
#> iteration: 200 
#> iteration: 300 
#> iteration: 400 
#> iteration: 500 
#> iteration: 600 
#> iteration: 700 
#> iteration: 800 
#> iteration: 900 
#> iteration: 1000 
#> iteration: 1100 
#> iteration: 1200 
#> iteration: 1300 
#> iteration: 1400 
#> iteration: 1500 
#> iteration: 1600 
#> iteration: 1700 
#> iteration: 1800 
#> iteration: 1900 
#> Finished in  0.2 seconds.
fit_laplace$summary()
#> # A tibble: 3 × 7
#>   variable      mean median    sd   mad     q5      q95
#>   <chr>        <dbl>  <dbl> <dbl> <dbl>  <dbl>    <dbl>
#> 1 lp__        -7.23  -6.96  0.697 0.297 -8.63  -6.75   
#> 2 lp_approx__ -0.491 -0.213 0.686 0.296 -1.89  -0.00171
#> 3 theta        0.268  0.249 0.123 0.118  0.102  0.507  

# Run 'variational' method to use ADVI to approximate posterior
fit_vb <- mod$variational(data = stan_data, seed = 123)
#> ------------------------------------------------------------ 
#> EXPERIMENTAL ALGORITHM: 
#>   This procedure has not been thoroughly tested and may be unstable 
#>   or buggy. The interface is subject to change. 
#> ------------------------------------------------------------ 
#> Gradient evaluation took 1.2e-05 seconds 
#> 1000 transitions using 10 leapfrog steps per transition would take 0.12 seconds. 
#> Adjust your expectations accordingly! 
#> Begin eta adaptation. 
#> Iteration:   1 / 250 [  0%]  (Adaptation) 
#> Iteration:  50 / 250 [ 20%]  (Adaptation) 
#> Iteration: 100 / 250 [ 40%]  (Adaptation) 
#> Iteration: 150 / 250 [ 60%]  (Adaptation) 
#> Iteration: 200 / 250 [ 80%]  (Adaptation) 
#> Success! Found best value [eta = 1] earlier than expected. 
#> Begin stochastic gradient ascent. 
#>   iter             ELBO   delta_ELBO_mean   delta_ELBO_med   notes  
#>    100           -6.164             1.000            1.000 
#>    200           -6.225             0.505            1.000 
#>    300           -6.186             0.339            0.010   MEDIAN ELBO CONVERGED 
#> Drawing a sample of size 1000 from the approximate posterior...  
#> COMPLETED. 
#> Finished in  0.1 seconds.
fit_vb$summary()
#> # A tibble: 3 × 7
#>   variable      mean median    sd   mad     q5      q95
#>   <chr>        <dbl>  <dbl> <dbl> <dbl>  <dbl>    <dbl>
#> 1 lp__        -7.14  -6.93  0.528 0.247 -8.21  -6.75   
#> 2 lp_approx__ -0.520 -0.244 0.740 0.326 -1.90  -0.00227
#> 3 theta        0.251  0.236 0.107 0.108  0.100  0.446  
mcmc_hist(fit_vb$draws("theta"))
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


# Run 'pathfinder' method, a new alternative to the variational method
fit_pf <- mod$pathfinder(data = stan_data, seed = 123)
#> Path [1] :Initial log joint density = -18.273334 
#> Path [1] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               5      -6.748e+00      7.082e-04   1.432e-05    1.000e+00  1.000e+00       126 -6.145e+00 -6.145e+00                   
#> Path [1] :Best Iter: [5] ELBO (-6.145070) evaluations: (126) 
#> Path [2] :Initial log joint density = -19.192715 
#> Path [2] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               5      -6.748e+00      2.015e-04   2.228e-06    1.000e+00  1.000e+00       126 -6.223e+00 -6.223e+00                   
#> Path [2] :Best Iter: [2] ELBO (-6.170358) evaluations: (126) 
#> Path [3] :Initial log joint density = -6.774820 
#> Path [3] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               4      -6.748e+00      1.137e-04   2.596e-07    1.000e+00  1.000e+00       101 -6.178e+00 -6.178e+00                   
#> Path [3] :Best Iter: [4] ELBO (-6.177909) evaluations: (101) 
#> Path [4] :Initial log joint density = -7.949193 
#> Path [4] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               5      -6.748e+00      2.145e-04   1.301e-06    1.000e+00  1.000e+00       126 -6.197e+00 -6.197e+00                   
#> Path [4] :Best Iter: [5] ELBO (-6.197118) evaluations: (126) 
#> Total log probability function evaluations:4379 
#> Finished in  0.1 seconds.
fit_pf$summary()
#> # A tibble: 3 × 7
#>   variable      mean median    sd   mad      q5    q95
#>   <chr>        <dbl>  <dbl> <dbl> <dbl>   <dbl>  <dbl>
#> 1 lp_approx__ -1.07  -0.727 0.945 0.311 -2.91   -0.450
#> 2 lp__        -7.25  -6.97  0.753 0.308 -8.78   -6.75 
#> 3 theta        0.256  0.245 0.119 0.123  0.0824  0.462
mcmc_hist(fit_pf$draws("theta"))
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


# Run 'pathfinder' again with more paths, fewer draws per path,
# better covariance approximation, and fewer LBFGSs iterations
fit_pf <- mod$pathfinder(data = stan_data, num_paths=10, single_path_draws=40,
                         history_size=50, max_lbfgs_iters=100)
#> Warning: Number of PSIS draws is larger than the total number of draws returned by the single Pathfinders. This is likely unintentional and leads to re-sampling from the same draws. 
#> Path [1] :Initial log joint density = -14.241761 
#> Path [1] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               5      -6.748e+00      2.000e-03   5.597e-05    1.000e+00  1.000e+00       126 -6.236e+00 -6.236e+00                   
#> Path [1] :Best Iter: [5] ELBO (-6.235525) evaluations: (126) 
#> Path [2] :Initial log joint density = -13.402374 
#> Path [2] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               5      -6.748e+00      1.810e-03   4.511e-05    1.000e+00  1.000e+00       126 -6.208e+00 -6.208e+00                   
#> Path [2] :Best Iter: [2] ELBO (-6.203915) evaluations: (126) 
#> Path [3] :Initial log joint density = -12.050800 
#> Path [3] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               5      -6.748e+00      1.274e-03   2.325e-05    1.000e+00  1.000e+00       126 -6.196e+00 -6.196e+00                   
#> Path [3] :Best Iter: [3] ELBO (-6.168581) evaluations: (126) 
#> Path [4] :Initial log joint density = -11.907691 
#> Path [4] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               5      -6.748e+00      1.208e-03   2.110e-05    1.000e+00  1.000e+00       126 -6.195e+00 -6.195e+00                   
#> Path [4] :Best Iter: [3] ELBO (-6.184266) evaluations: (126) 
#> Path [5] :Initial log joint density = -17.062583 
#> Path [5] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               5      -6.748e+00      1.424e-03   3.915e-05    1.000e+00  1.000e+00       126 -6.229e+00 -6.229e+00                   
#> Path [5] :Best Iter: [4] ELBO (-6.180989) evaluations: (126) 
#> Path [6] :Initial log joint density = -7.950926 
#> Path [6] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               5      -6.748e+00      2.149e-04   1.305e-06    1.000e+00  1.000e+00       126 -6.210e+00 -6.210e+00                   
#> Path [6] :Best Iter: [4] ELBO (-6.193547) evaluations: (126) 
#> Path [7] :Initial log joint density = -13.337353 
#> Path [7] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               5      -6.748e+00      1.789e-03   4.411e-05    1.000e+00  1.000e+00       126 -6.275e+00 -6.275e+00                   
#> Path [7] :Best Iter: [4] ELBO (-6.264759) evaluations: (126) 
#> Path [8] :Initial log joint density = -6.856154 
#> Path [8] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               4      -6.748e+00      7.559e-04   6.106e-06    1.000e+00  1.000e+00       101 -6.237e+00 -6.237e+00                   
#> Path [8] :Best Iter: [2] ELBO (-6.233924) evaluations: (101) 
#> Path [9] :Initial log joint density = -19.158821 
#> Path [9] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               5      -6.748e+00      2.167e-04   2.482e-06    1.000e+00  1.000e+00       126 -6.251e+00 -6.251e+00                   
#> Path [9] :Best Iter: [3] ELBO (-6.196829) evaluations: (126) 
#> Path [10] :Initial log joint density = -6.894545 
#> Path [10] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
#>               4      -6.748e+00      1.811e-04   2.981e-05    9.341e-01  9.341e-01       101 -6.227e+00 -6.227e+00                   
#> Path [10] :Best Iter: [2] ELBO (-6.144040) evaluations: (101) 
#> Total log probability function evaluations:1360 
#> Pareto k value (0.73) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. 
#> Finished in  0.1 seconds.

# Specifying initial values as a function
fit_mcmc_w_init_fun <- mod$sample(
  data = stan_data,
  seed = 123,
  chains = 2,
  refresh = 0,
  init = function() list(theta = runif(1))
)
#> Running MCMC with 2 sequential chains...
#> 
#> Chain 1 finished in 0.0 seconds.
#> Chain 2 finished in 0.0 seconds.
#> 
#> Both chains finished successfully.
#> Mean chain execution time: 0.0 seconds.
#> Total execution time: 0.3 seconds.
#> 
fit_mcmc_w_init_fun_2 <- mod$sample(
  data = stan_data,
  seed = 123,
  chains = 2,
  refresh = 0,
  init = function(chain_id) {
    # silly but demonstrates optional use of chain_id
    list(theta = 1 / (chain_id + 1))
  }
)
#> Running MCMC with 2 sequential chains...
#> 
#> Chain 1 finished in 0.0 seconds.
#> Chain 2 finished in 0.0 seconds.
#> 
#> Both chains finished successfully.
#> Mean chain execution time: 0.0 seconds.
#> Total execution time: 0.3 seconds.
#> 
fit_mcmc_w_init_fun_2$init()
#> [[1]]
#> [[1]]$theta
#> [1] 0.5
#> 
#> 
#> [[2]]
#> [[2]]$theta
#> [1] 0.3333333
#> 
#> 

# Specifying initial values as a list of lists
fit_mcmc_w_init_list <- mod$sample(
  data = stan_data,
  seed = 123,
  chains = 2,
  refresh = 0,
  init = list(
    list(theta = 0.75), # chain 1
    list(theta = 0.25)  # chain 2
  )
)
#> Running MCMC with 2 sequential chains...
#> 
#> Chain 1 finished in 0.0 seconds.
#> Chain 2 finished in 0.0 seconds.
#> 
#> Both chains finished successfully.
#> Mean chain execution time: 0.0 seconds.
#> Total execution time: 0.3 seconds.
#> 
fit_optim_w_init_list <- mod$optimize(
  data = stan_data,
  seed = 123,
  init = list(
    list(theta = 0.75)
  )
)
#> Initial log joint probability = -11.6657 
#>     Iter      log prob        ||dx||      ||grad||       alpha      alpha0  # evals  Notes  
#>        6      -5.00402   0.000237915   9.55309e-07           1           1        9    
#> Optimization terminated normally:  
#>   Convergence detected: relative gradient magnitude is below tolerance 
#> Finished in  0.2 seconds.
fit_optim_w_init_list$init()
#> [[1]]
#> [[1]]$theta
#> [1] 0.75
#> 
#> 
# }

Arguments

Value

See also

Examples