https://github.com/piras-s/tuningcurvesnestedbayesianinference

Bayesian inference of neural tuning curves using nested sampling (PyMultiNest), with theory, simulation, and diagnostic visualizations.
https://github.com/piras-s/tuningcurvesnestedbayesianinference

bayesian-inference data-visualization machine-learning model-evaluation nested-sampling neuroscience pymultinest python3 simulation

Last synced: 3 months ago
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Bayesian inference of neural tuning curves using nested sampling (PyMultiNest), with theory, simulation, and diagnostic visualizations.

• Host: GitHub
• URL: https://github.com/piras-s/tuningcurvesnestedbayesianinference
• Owner: Piras-S
• License: gpl-3.0
• Created: 2025-03-27T08:45:57.000Z (9 months ago)
• Default Branch: main
• Last Pushed: 2025-03-27T09:14:17.000Z (9 months ago)
• Last Synced: 2025-09-05T13:57:31.572Z (4 months ago)
• Topics: bayesian-inference, data-visualization, machine-learning, model-evaluation, nested-sampling, neuroscience, pymultinest, python3, simulation
• Language: Jupyter Notebook
• Homepage:
• Size: 729 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
#  Bayesian Inference of Neural Tuning Curves with Nested Sampling

This project demonstrates how to simulate and analyze neural tuning curve data using **Bayesian inference** via **nested sampling**. It combines theory, code, and visual intuition to explain how posterior distributions are obtained, and why they should be interpreted with care.

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## Project Overview

I simulate the firing response of a neuron to different stimulus angles (e.g., orientation of a visual stimulus), assuming a Gaussian-shaped tuning curve. Using synthetic data, I then perform **Bayesian parameter estimation** with PyMultiNest to recover the model parameters:

- $r_{\text{max}}$: maximum firing rate,

- $s_{\text{max}}$: preferred stimulus orientation,

- $\sigma_f$: tuning width.

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## Concepts Covered

- Bayesian inference: likelihood, priors, posteriors, evidence

- Nested sampling algorithm (with theory + toy implementation)

- Parameter estimation in a neural tuning model

- Posterior uncertainty, model mismatch, and identifiability

- Practical diagnostics for PyMultiNest fits

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## Visual Highlights

### Toy Nested Sampling Animation

A minimal 2D implementation of nested sampling illustrates the algorithm’s core idea: removing low-likelihood regions and progressively zooming in on high-probability space.



  



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**Dependencies**:

   numpy matplotlib pandas pymultinest corner imageio

   

   

**References**

Dayan, P., & Abbott, L. F. (2001). Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. MIT Press.

Feroz, F., Hobson, M. P., & Bridges, M. (2009). MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics.

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## Project Structure

```bash

├── simulation.ipynb # Generate and visualize synthetic data 

├── fitting.ipynb # Educational toy example of nested sampling  + Run and analyze full model fitting 

├── run_pymultinest_fit.py # Script to perform inference with PyMultiNest 

├── tuning_data.csv # Simulated dataset 

├── figures/

├── chains/

└── nested_sampling.gif # Animation of toy nested sampling