# 20 Stan CSV File Format

The output from all CmdStan methods is in CSV format. A Stan CSV file is a data table where the columns are the method and model parameters and quantities of interest. Each row contains one record’s worth of data in plain-text format using the comma character (‘,’) as the field delimiter (hence the name).

For the Stan CSV files, data is strictly numerical, however, possible values include both positive and negative infinity and “Not-a-Number” which are represented as the strings NaN, inf, +inf, -inf. All other values are written in decimal notation with at most 6 digits of precision.

Stan CSV files have a header row containing the column names. They also make extensive use of CSV comments, i.e., lines which begin with the # character. In addition to initial and final comment rows, some methods also put comment rows in the middle of the data table, which makes it difficult to use many of the commonly used CSV parser packages.

## 20.1 CSV column names and order

The data table is laid out with zero or more method-specific columns followed by the Stan program variables declared in the parameter block, then the variables in the transformed parameters block, finally variables declared in the generated quantities, in declaration order.

Stan provides three types of container objects: arrays, vectors, and matrices. In order to output all elements of a container object, it is necessary to choose an indexing notation and a serialization order. The Stan CSV file indexing notation is

• The column name consists of the variable name followed by the element indices.
• Indices are delimited by periods (‘.’).
• Indexing is 1-based, i.e., given a dimension of size $$N$$, the first element index is $$1$$ and the last element index is $$N$$.

Container variables are serialized in column major order, a.k.a. “Fortran” order. In column major-order, all elements of column 1 are listed in ascending order, followed by all elements of column 2, thus the first index changes the slowest and the last index changes the fastest.

To see how this works, consider a 3-dimensional variable with dimension sizes 2, 3, and 4, e.g., an array of matrices, a 2-D array of vectors or row_vectors, or a 3-D array of scalars. Given a Stan program with model parameter variable:

 array[2, 3, 4] real foo;

The Stan CSV file will require 24 columns to output the elements of foo. The first 6 columns will be labeled:

foo.1.1.1, foo.1.1.2, foo.1.1.3, foo.1.1.4, foo.1.2.1, foo.1.2.2

The final 6 columns will be labeled:

foo.2.2.3, foo.2.2.4, foo.2.3.1, foo.2.3.2, foo.2.3.3, foo.2.3.4

## 20.2 MCMC sampler CSV output

The sample method produces both a Stan CSV output file and a diagnostic file which contains the sampler parameters together with the gradients on the unconstrained scale and log probabilities for all parameters in the model.

To see how this works, we show snippets of the output file resulting from the following command:

./bernoulli sample save_warmup=1 num_warmup=200 num_samples=100 \
data file=bernoulli.data.json \
output file=bernoulli_samples.csv

### 20.2.1 Sampler Stan CSV output file

The sampler output file contains the following:

• Initial comment rows listing full CmdStan argument configuration.
• Data rows containing warmup draws, if run with option save_warmup=1
• Comment rows for adaptation listing step size and metric used for sampling
• Sampling draws
• Comment rows giving timing information

All configuration arguments are listed, one per line, indented according to CmdStan’s hierarchy of arguments and sub-arguments. Arguments not overtly specified on the command line are annotated as (Default).

In the above example the num_samples, num_warmup, and save_warmup arguments were specified, whereas subargument thin is left at its default value, as seen in the initial comment rows:

# stan_version_major = 2
# stan_version_minor = 24
# stan_version_patch = 0
# model = bernoulli_model
# method = sample (Default)
#   sample
#     num_samples = 100
#     num_warmup = 200
#     save_warmup = 1
#     thin = 1 (Default)
#       engaged = 1 (Default)
#       gamma = 0.050000000000000003 (Default)
#       delta = 0.80000000000000004 (Default)
#       kappa = 0.75 (Default)
#       t0 = 10 (Default)
#       init_buffer = 75 (Default)
#       term_buffer = 50 (Default)
#       window = 25 (Default)
#     algorithm = hmc (Default)
#       hmc
#         engine = nuts (Default)
#           nuts
#             max_depth = 10 (Default)
#         metric = diag_e (Default)
#         metric_file =  (Default)
#         stepsize = 1 (Default)
#         stepsize_jitter = 0 (Default)
# id = 0 (Default)
# data
#   file = bernoulli.data.json
# init = 2 (Default)
# random
#   seed = 2991989946 (Default)
# output
#   file = bernoulli_samples.csv
#   diagnostic_file = bernoulli_diagnostics.csv
#   refresh = 100 (Default)

Note that when running multi-threaded programs which use reduce_sum for high-level parallelization, the number of threads used will also be included in this initial comment header.

The CSV header row lists all sampler parameters, model parameters, transformed parameters, and quantities of interest. The sampler parameters are described in detail in the output file section of the Quickstart Guide chapter on MCMC Sampling. The example model bernoulli.stan only contains one parameter theta, therefore the CSV file data table consists of 7 sampler parameter columns and one column for the model parameter:

lp__,accept_stat__,stepsize__,treedepth__,n_leapfrog__,divergent__,energy__,theta

As a second example, we show the output of the eight_schools.stan model on run on example dataset. This model has 3 parameters: mu, theta a vector whose length is dependent on the input data, here N = 8, and tau. The initial columns are for the 7 sampler parameters, as before. The column headers for the model parameters are:

mu,theta.1,theta.2,theta.3,theta.4,theta.5,theta.6,theta.7,theta.8,tau

Data rows containing warmup draws

When run with option save_warmup=1, the thinned warmup draws are written to the CSV output file directly after the CSV header line. Since the default option is save_warmup=0, this section is usually not present in the output file.

Here we specified num_warmup=200 and left thin at the default value $$1$$, therefore the next 200 lines are data rows containing the sampler and model parameter values for each warmup draw.

-6.74827,1,1,1,1,0,6.75348,0.247195
-6.74827,4.1311e-103,14.3855,1,1,0,6.95087,0.247195
-6.74827,1.74545e-21,2.43117,1,1,0,7.67546,0.247195
-6.77655,0.99873,0.239791,2,7,0,6.81982,0.280619
-6.7552,0.999392,0.323158,1,3,0,6.79175,0.26517

During warmup, the sampler adjusts the stepsize and the metric. At the end warmup, the sampler outputs this information as comments.

# Adaptation terminated
# Step size = 0.813694
# Diagonal elements of inverse mass matrix:
# 0.592879

As the example bernoulli model only contains a single parameter, and as the default metric is diag_e, the inverse mass matrix is a $$1 \times 1$$ matrix, and the length of the diagonal vector is also $$1$$.

In contrast, if we run the eight schools example model with metric dense_e, the adaptation comments section lists both the stepsize and the full $$10 \times 10$$ inverse mass matrix:

# Adaptation terminated
# Step size = 0.211252
# Elements of inverse mass matrix:
# 25.6389, 17.3379, 13.9455, 15.9036, 15.1953, 8.73729, 16.9486, 14.4231, 17.4969, 0.518757
# 17.3379, 79.8719, 12.2989, -1.28006, 9.92895, -3.51622, 10.073, 22.0196, 19.8151, 4.71028
# 13.9455, 12.2989, 36.1572, 12.8734, 11.9446, 9.09582, 9.74519, 10.9539, 12.1204, 0.211353
# 15.9036, -1.28006, 12.8734, 59.9998, 10.245, 8.03461, 16.9754, 3.13443, 9.68292, -1.36097
# 15.1953, 9.92895, 11.9446, 10.245, 43.548, 15.3403, 13.0537, 7.69818, 10.1093, 0.155245
# 8.73729, -3.51622, 9.09582, 8.03461, 15.3403, 39.981, 12.7695, 1.16248, 6.13749, -2.08507
# 16.9486, 10.073, 9.74519, 16.9754, 13.0537, 12.7695, 45.8884, 11.6074, 8.96413, -1.15946
# 14.4231, 22.0196, 10.9539, 3.13443, 7.69818, 1.16248, 11.6074, 49.4083, 18.9169, 3.15661
# 17.4969, 19.8151, 12.1204, 9.68292, 10.1093, 6.13749, 8.96413, 18.9169, 68.0228, 1.74104
# 0.518757, 4.71028, 0.211353, -1.36097, 0.155245, -2.08507, -1.15946, 3.15661, 1.74104, 1.50433

Note that when the sampler is run with arguments algorithm=fixed_param, this section will be missing.

Data rows containing sampling draws

The output file contains the values for the thinned set draws during sampling. Here we specified num_sampling=100 and left thin at the default value $$1$$, therefore the next 100 lines are data rows containing the sampler and model parameter values for each sampling iteration.

-8.76921,0.796814,0.813694,1,1,0,9.75854,0.535093
-6.79143,0.979604,0.813694,1,3,0,9.13092,0.214431
-6.79451,0.955359,0.813694,2,3,0,7.19149,0.289341

Timing information

Upon successful completion, the sampler writes timing information to the output CSV file as a series of final comment lines:

#
#  Elapsed Time: 0.005 seconds (Warm-up)
#                0.002 seconds (Sampling)
#                0.007 seconds (Total)
#

### 20.2.2 Diagnostic CSV output file

The diagnostic file contains the following:

• Initial comment rows listing full CmdStan argument configuration.
• Data rows containing warmup draws, if run with option save_warmup=1
• Sampling draws
• Comment rows giving timing information

The columns in this file contain, in order:

• all sampler parameters
• all model parameter estimates (on the unconstrained scale)
• the latent Hamiltonian for each parameter
• the gradient for each parameters

The labels for the latent Hamiltonian columns are the parameter column label with prefix p_ and the labels for the gradient columns are the parameter column label with prefix g_.

These are the column labels from the file bernoulli_diagnostic.csv:

lp__,accept_stat__,stepsize__,treedepth__,n_leapfrog__,divergent__,energy__,theta,p_theta,g_theta

### 20.2.3 Profiling CSV output file

The profiling information is stored in a plain CSV format with no meta information in the comments.

Each row represents timing information collected in a profile statement for a given thread. It is possible that some profile statements have only one entry (if they were only executed by one thread) and others have multiple entries (if they were executed by multiple threads).

The columns are as follows:

• name, The name of the profile statement that is being timed
• thread_id, The thread that executed the profile statement
• total_time, The combined time spent executing statements inside the profile which includes calculation with and without automatic differentiation
• forward_time, The time spent in the profile statement during the forward pass of a reverse mode automatic differentiation calculation or during a cauculation without automatic differentiation
• reverse_time, The time spent in the profile statement during the reverse (backward) pass of reverse mode automatic differentiation
• chain_stack, The number of objects allocated on the chaining automatic differentiation stack. There is a function call for each of these objects in the reverse pass
• no_chain_stack, The number of objects allocated on the non-chaining automatic differentiation stack
• autodiff_calls, The total number of times the profile statement was executed with automatic differentiation
• no_autodiff_calls - The total number of times the profile statement was executed without automatic differentiation

## 20.3 Optimization output

• Penalized maximum likelihood estimate