DSSM HMC Examples

This package provides the compete replication for "Differentiable State-Space Models and Hamiltonian Monte Carlo Estimation" by David Childers, Jesus Fernandez-Villaverde, Jesse Perla, Christopher Rackauckas, and Peifan Wu.

The algorithms are mostly implemented in:

1. DifferentiableStateSpaceModels.jl for the differentiable perturbation method solver
2. DifferenceEquations.jl for the differentiable solver for the Kalman filter, simulations of state space models, and likelihoods.

With Julia 1.9 and this repository cloned to your local machine, execute julia --project -e "using Pkg; Pkg.instantiate()"

To use with default options, and specifying a directory

julia --project bin/fit_rbc_1_kalman.jl --results_path ./.results/rbc_1_kalman --overwrite_results true --num_samples 100
julia --project bin/fit_rbc_1_joint.jl --results_path ./.results/rbc_1_joint --overwrite_results true --num_samples 100

(although the --threads auto may or may not be useful in this example.)

Or with options such as multiple chains

julia --project --threads auto bin/fit_rbc_1_kalman.jl --results_path ./.results/rbc_1_kalman --overwrite_results true --num_samples 1000 --num_chains 8

A few features for sampling and output:

• --target_acceptance_rate 0.65 set the target acceptance for NUTS
• --max_depth 5 set the max_depth for NUTS
• --init_params_file data/my_file.csv uses that file as the initial condition for sampling

In all cases, for long-burnins you can find the final draw of the chain as the last_draw.csv file, which can be used with the init_params_file argument after moving/renaming

Warning PackageCompiler.jl can be finicky and may not be always functional. If the process below stalls and doesn't complete after 30ish minutes, you might be between working versions.

Given the slow startup speed, it can be helpful to compile a custom sysimage. This would be used by both vscode and the commandline. To do this, execute the following in a commandline

julia --threads auto -e 'using Pkg; Pkg.add(\"PackageCompiler\")'
julia --project --threads auto ./deps/create_sysimage.jl

Grab coffee. This will take at least 15-30 minutes to run. It will help startup latency (maybe 2-3 minutes less to start sampling), but not as much as you would hope. Zygote.jl is not amenable to caching compilation when used with Turing.

After: when you use vscode it will also load this custom sysimage as long as you have the Julia: Use custom sysimage option enabled.

On the commandline you will need to provide the image manually. For example,

julia --project --sysimage JuliaSysimage.dll --threads auto bin/fit_rbc_1_kalman.jl --results_path ./.results/rbc_1_kalman --overwrite_results true --num_samples 1000

To replicate all of the results in the paper, see the README.md in the scripts directory.