Bayesian Functional Time Series Modeling

This repository provides a runnable example of Bayesian latent time series modeling for high dimensional data. The workflow produces posterior diagnostics and a latent signal recovery figure saved to results/latent_recovery.png.

Why this matters

Many real world datasets are high dimensional, noisy, and evolve over time, while the true driving structure is latent. This project demonstrates a Bayesian approach for recovering interpretable temporal signals with uncertainty quantification.

Model at a glance

• Latent time series modeled with a Gaussian random walk prior
• Dimension specific loadings with shrinkage priors
• Observation model with shared noise
• Bayesian inference via MCMC using PyMC
• Outputs include posterior diagnostics and latent recovery plots

Repository structure

• src/: core modeling code
• notebooks/: exploratory analysis and examples
• scripts/: runnable analysis pipelines
• data/: simulated or small example datasets
• results/: figures and output summaries

python -m venv .venv source .venv/bin/activate # macOS or Linux

.venv\Scripts\activate # Windows PowerShell

pip install -r requirements.txt python scripts/run_simulation.py

Example output

Running the script generates the following latent signal recovery plot with posterior uncertainty.

How to run

Create a virtual environment, install dependencies, and run the simulation script.