Hierarchical Bayesian Inference (Continuous Method)

Introduction

It is recommended to read Introduction and Model Specification sections of Generating Mock Posterior Estimates tutorial to get familiar with the model and the data used in this tutorial, and Hierarchical Bayesian Inference (Discrete Method) tutorial to understand the discrete method.

MCMC Sampler Configurations

Hierarchical Bayesian Inference with continuous method can only be performed on flowMC at the moment. The configuration for FlowMC is also provided through a json file and saved in flowMC_config.json. We will talk about the various configurations in detail in another tutorial.

{
    "data_dump": {
        "n_samples": 10000
    },
    "bundle_config": {
        "chain_batch_size": 0,
        "n_chains": 100,
        "batch_size": 10000,
        "n_epochs": 4,
        "n_max_examples": 200000,
        "history_window": 2000,
        "n_NFproposal_batch_size": 50,
        "n_global_steps": 100,
        "n_local_steps": 100,
        "n_production_loops": 10,
        "n_training_loops": 10,
        "global_thinning": 4,
        "local_thinning": 4,
        "local_sampler_name": "hmc",
        "step_size": 0.01,
        "condition_matrix": 1.0,
        "n_leapfrog": 5,
        "rq_spline_hidden_units": [64, 64],
        "rq_spline_n_bins": 10,
        "rq_spline_n_layers": 8,
        "rq_spline_range": [-10.0, 10.0],
        "learning_rate": 0.001,
        "verbose": false
    }
}

Then you can run the following command to perform Hierarchical Bayesian Inference using FlowMC sampler.

f_monk_n_pls_m_gs \
    --seed 37 \
    --n-pl 1 \
    --n-g 0 \
    --data-filename "../generating_mock_posterior_estimates/data/realization_0/means_covs.hdf5" \
    --n-samples 100 \
    --minimum-mc-error 0.01 \
    --n-checkpoints 10 \
    --n-max-steps 3 \
    --pmean-cfg pmean.json \
    --prior-cfg prior.json \
    --sampler-cfg flowMC_config.json

Analysis of Results

Mon Nov  3 03:38:17 2025
+-----------------------------------------------------------------------------------------+
| NVIDIA-SMI 575.57.08              Driver Version: 575.57.08      CUDA Version: 12.9     |
|-----------------------------------------+------------------------+----------------------+
| GPU  Name                 Persistence-M | Bus-Id          Disp.A | Volatile Uncorr. ECC |
| Fan  Temp   Perf          Pwr:Usage/Cap |           Memory-Usage | GPU-Util  Compute M. |
|                                         |                        |               MIG M. |
|=========================================+========================+======================|
|   0  NVIDIA GeForce RTX 4090        On  |   00000000:01:00.0 Off |                  Off |
|  0%   39C    P8             34W /  450W |      40MiB /  24564MiB |      0%      Default |
|                                         |                        |                  N/A |
+-----------------------------------------+------------------------+----------------------+

+-----------------------------------------------------------------------------------------+
| Processes:                                                                              |
|  GPU   GI   CI              PID   Type   Process name                        GPU Memory |
|        ID   ID                                                               Usage      |
|=========================================================================================|
|    0   N/A  N/A            1326      G   /usr/lib/xorg/Xorg                        9MiB |
|    0   N/A  N/A            1501      G   /usr/bin/gnome-shell                     10MiB |
+-----------------------------------------------------------------------------------------+

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All the code and files used in this tutorial can be found in hello-gwkokab/hbi_continuous_method.