Access Hessian from optimize method in CmdStanR

Is it possible to access the Hessian from the output when using cmdstan’s optimize method in R or to specify a draws argument so I can get estimates of standard errors on the constrained parameter space?

I was using the optimize function from rstan, but when I moved over to using my universities’ HPC I ran into issues with rstan. I’ve found a workaround with CmdstanR but I can’t seem to figure out where in the output object the Hessian might be stored, or how to return it, or how to get draws from the constrained parameter space.

Here’s how I would get what I want from rstan::optimizing():

    # Use example model from cmdstan
    file <- file.path(cmdstan_path(), "examples", "bernoulli", "bernoulli.stan")
    mod <- stan_model(file) <- list(N = 10, y = c(0,1,0,0,0,0,0,0,0,1))
    # Get optimization results
    stan_output <- optimizing(mod,
                              data =,
                              algorithm = "LBFGS",
                              hessian = TRUE,
                              draws = 50000)
    # Extract parameter names
    par_names <- names(stan_output$par)
    # Get parameter estimates
    par_values <- stan_output$par
    # By grabbing many draws of the parameters, we can take the square root
    # of the variances in the cov matrix for these draws to estimate SE
    par_se <- sqrt(diag(cov(stan_output$theta_tilde)))
    # Get our t-values
    t_val <- par_values / par_se
    output <- data.frame(parameters = par_names,
                         est = par_values,
                         se = par_se,
                         t_val = t_val,
                         row.names = NULL)

Tagging @mitzimorris, because I honestly don’t know…

tldr: not yet; we’re working on it.

this came up at a recent Gelman group Stan meeting - my recollection is that @bgoodri said that there were problems with what RStan is doing. we agreed that this should be done in core Stan. as soon as it happens, it can then be exposed via CmdStan and the CmdStanX wrappers.


Hello @mitzimorris, @bgoodri,

Is it possible to extract the Hessian from a cmdstanMLE object now?
Thanks in anticipation of the response.

thanks for checking, sorry to report, no progress.


Hi @mitzimorris ,
I was wondering whether there might have been any further process. Is it now possible to extract the Hessian from a cmdstanMLE object? From the manual, there is an option as follows so I had a hope that I might be able to access hessian when using L-BFGS. Is it correct?
history_size (positive integer) The size of the history used when approximating the Hessian. Only available for L-BFGS.
P.S. Hessian please (if not supported yet)? 😊

1 Like

+1 to that. I’ve been using RStan just because it gives me access to the Hessian and cmdstanr does not.

Just note that it’s not necessarily giving you the Hessian you would like to get, see e.g. Visual illustration of Jacobian of parameter transformation


This is very helpful. Thanks, Aki.