Enhanced Bayesian GP State-Space Model for Paleoclimate Reconstruction

This project implements a sophisticated Bayesian Gaussian Process State-Space Model specifically designed for paleoclimate reconstruction, with enhanced capabilities for handling abrupt climate transitions, multiple proxies, and data irregularities.

Key Features

• Adaptive Kernel Lengthscales: Automatically adjusts model flexibility based on climate rate of change
• Multi-proxy Integration: Balanced weighting mechanism for combining δ18O, UK37, Mg/Ca proxies
• Multi-scale Orbital Components: Models Milankovitch cycles (100kyr, 41kyr, 23kyr)
• Heteroscedastic Noise Model: Handles observation-specific uncertainty
• Advanced MCMC Sampling: Robust uncertainty quantification with GPyTorch compatibility
• Temperature-Dependent Calibration: Improved proxy-temperature relationships
• Flexible Data Import: Support for irregular/sparse data from various formats

Installation

# Clone the repository
git clone https://github.com/yourusername/paleoclimate-gp-model.git
cd paleoclimate-gp-model

# Set up virtual environment
python -m venv venv
source venv/bin/activate  # On Windows: venv\Scripts\activate

# Install dependencies
pip install torch gpytorch numpy scipy matplotlib pandas pywt tqdm

Quick Start

Run the quick demonstration:

python quick_start.py

This will generate synthetic multi-proxy data, fit the model, detect transitions, and create visualizations.

Using with Custom Data

Import data from various formats:

from utils.data_loader import load_paleoclimate_data

# Load data from CSV/Excel
proxy_data = load_paleoclimate_data(
    "your_data.csv",
    proxy_columns={
        'd18O': 'delta18O_column',
        'UK37': 'alkenone_column',
        'Mg_Ca': 'MgCa_column'
    },
    age_column='age_kyr'
)

# Or use auto-detection
proxy_data = load_paleoclimate_data("your_data.csv")

Run the model:

from models.bayesian_gp_state_space import BayesianGPStateSpaceModel

# Configure and initialize model
model = BayesianGPStateSpaceModel(
    proxy_types=['d18O', 'UK37', 'Mg_Ca'],
    weighting_method='balanced',
    kernel_config={
        'base_kernel_type': 'matern',
        'base_lengthscale': 5.0,
        'adaptation_strength': 1.5
    }
)

# Fit model to data
model.fit(proxy_data, training_iterations=500)

# Predict and detect transitions
test_ages = np.linspace(0, 500, 1000)
mean, lower_ci, upper_ci = model.predict(test_ages)
transitions = model.detect_abrupt_transitions(test_ages)

# Visualize results
model.plot_reconstruction(test_ages, proxy_data_dict=proxy_data, detected_transitions=transitions)

Advanced Usage

Temperature-Dependent Calibration

from utils.temperature_dependent_calibration import temperature_to_d18o, d18o_to_temperature

# Define calibration parameters
params = {
    'a': -0.22,      # Linear coefficient
    'b': 3.0,        # Intercept
    'c': 0.02,       # Nonlinearity coefficient
    'threshold': 10.0  # Temperature threshold
}

# Convert temperature to proxy values
d18o_values = temperature_to_d18o(temperatures, params)

# Convert proxy values to temperature
reconstructed_temps = d18o_to_temperature(d18o_values, params)

Advanced Transition Detection

from models.improved_transition_detection import ensemble_transition_detector

# Detect transitions using ensemble approach
transitions = ensemble_transition_detector(
    ages, temperatures,
    detectors=['derivative', 'wavelet', 'bayesian'],
    min_separation=20.0,
    min_magnitude=1.5
)

# Visualize detected transitions
from models.improved_transition_detection import plot_detected_transitions
plot_detected_transitions(ages, temperatures, transitions)

Enhanced MCMC Sampling

from mcmc.enhanced_sampler import EnhancedMCMCSampler

# Configure MCMC
mcmc_sampler = EnhancedMCMCSampler(
    model, likelihood,
    n_samples=1000,
    burn_in=200,
    step_size=0.01
)

# Run sampler
mcmc_sampler.run_hmc(progress_bar=True)

# Visualize posterior distributions
mcmc_sampler.plot_trace(figure_path="posterior_trace.png")

# Make predictions with uncertainty
pred_dict = mcmc_sampler.sample_posterior_predictive(test_ages, n_samples=100)

Non-Stationary Covariance Functions

from kernels.non_stationary_kernel import TemperatureDependentKernel

# Configure kernel
kernel = TemperatureDependentKernel(
    base_kernel_type='matern',
    cold_lengthscale=4.0,
    warm_lengthscale=8.0,
    transition_midpoint=10.0
)

# Update with temperature values
kernel.update_temperature_values(temperatures)

Directory Structure

• kernels/: Kernel implementations (adaptive, non-stationary)
• mcmc/: MCMC sampling implementations
• models/: Main model and transition detection implementations
• utils/: Data loading, proxy calibration, and utility functions
• docs/: Detailed documentation
• quick_start.py: Demonstration script
• main.py: Command-line interface

Documentation

For detailed documentation, see the docs/ directory:

• Mathematical Details
• Data Import Guide
• Transition Detection
• MCMC Sampling
• API Reference

Citation

If you use this model in your research, please cite:

Author, A. (2025). Enhanced Bayesian Gaussian Process State-Space Model 
for Paleoclimate Reconstruction. GitHub repository: 
https://github.com/yourusername/paleoclimate-gp-model

License

This project is licensed under the MIT License - see the LICENSE file for details.