picslike 1.0.0rc2

PICSLike: Pixel-based Inference with Correlated-Skies Likelihood

PICSLike

PICSLike Documentation | Main Documentation

PICSLike (Pixel-based Inference with Correlated-Skies Likelihood) is the pixel-based likelihood analysis engine of CosmoForge, implementing direct likelihood evaluation in map pixel space for cosmological parameter inference from CMB data.

Overview

PICSLike provides pixel-based likelihood computation as an alternative to harmonic-space methods:

• Pixel-based Likelihood: Direct likelihood evaluation in map pixel space
• Parameter Grid Analysis: Efficient likelihood computation across parameter grids

The approach is particularly useful for handling incomplete sky coverage, non-Gaussian features, and scenarios where pixel-space analysis offers computational or methodological advantages.

Key Features

Pixel-based Likelihood Analysis

• Direct likelihood evaluation in pixel space
• Natural handling of masked regions
• Support for temperature and polarization data
• Cross-correlation analysis support
• Chi-squared and log-likelihood computation

Parameter Grid Management

• Flexible parameter range specification
• Theoretical spectra grid management
• Efficient MPI distribution across parameter points
• Best-fit parameter extraction
• Confidence interval computation

Technical Features

• MPI Parallelization: Distributed computation across parameter grids
• Memory Optimization: Efficient covariance matrix handling
• Instrumental Effects: Beam convolution and pixel window functions
• Flexible Configuration: YAML-based parameter specification

Installation

PICSLike is part of CosmoForge and installs automatically:

pip install -e /path/to/CosmoForge

For MPI support:

pip install mpi4py

Documentation

For detailed API documentation and examples:

• PICSLike API - Pixel-based likelihood computation
• Parameter Grid - Parameter space management
• Likelihood Results - Result storage and analysis

Quick Start

Basic Pixel-based Likelihood Analysis

from picslike import PICSLike

# Initialize likelihood analysis
picslike = PICSLike("config/pixel_analysis.yaml")

# Run full pipeline
picslike.run()

# Get results
chi_squared = picslike.get_chi_squared()
best_fit = picslike.get_best_fit()
log_likelihood = picslike.get_log_likelihood()

Step-by-Step Execution

from picslike import PICSLike

# Initialize analysis
picslike = PICSLike("config/pixel_config.yaml")

# Setup pipeline components
picslike.setup_parameter_grid()
picslike.setup_fields()
picslike.setup_geometry()
picslike.setup_covariance_matrices()
picslike.setup_cls()
picslike.setup_beams()
picslike.setup_maps()

# Compute likelihood across parameter grid
picslike.compute()

# Save results
picslike.save_results("output/likelihood_results.pkl")

Accessing Simulation Results

from picslike import PICSLike

# Run analysis
picslike = PICSLike("config.yaml")
picslike.run()

# Get individual simulation results
simulation_results = picslike.get_simulation_results()

# Get mean likelihood result
mean_result = picslike.get_mean_likelihood_result()

# Extract summary statistics
summary = mean_result.get_summary_statistics()

Configuration

PICSLike uses YAML configuration files:

Basic Configuration

# Data specification
nside: 32
lmax: 64
fields: "TEB"  # or "TQU"

# Input files
maskfile: "data/mask.fits"
inputclfile: "data/fiducial_cls.txt"
covmatfile1: "data/noise_cov1.bin"
covmatfile2: "data/noise_cov2.bin"  # for cross-correlation

# Analysis parameters
do_cross: false
calibration: 1.0
nsims: 100

Parameter Grid Configuration

# Parameter ranges for likelihood grid
parameters:
  amplitude:
    - 0.5    # min
    - 1.5    # max
    - 11     # n_points
  tilt:
    - -0.5   # min
    - 0.5    # max
    - 11     # n_points

# Theoretical spectra location
root_dir: "data/templates"
root_filename: "dls"

Beam Configuration

# Beam parameters
smoothing_type: gaussian  # none, gaussian, cosine_legacy, cosine_npipe, file
fwhmarcmin: 5.0
beam_file: "data/beam.fits"
apply_pixwin: true
smooth_pol: true

MPI Usage

Run analyses in parallel:

# Pixel-based likelihood analysis
mpirun -n 4 python -c "
from picslike import PICSLike
picslike = PICSLike('config.yaml')
picslike.run()
"

# Full analysis with result saving
mpirun -n 8 python main_picslike.py config/pixel_analysis.yaml

Analysis Pipeline

Likelihood Computation Pipeline

1. Setup: Read parameters and initialize fields
2. Parameter Grid: Configure parameter ranges and load theoretical spectra
3. Geometry: Compute pixel pointing vectors
4. Covariance: Load noise covariance matrices
5. Maps: Read input observation maps
6. Broadcast: Distribute data across MPI processes
7. Compute: Evaluate likelihood at each parameter point
8. Results: Gather and store likelihood values

Likelihood Function

The pixel-based likelihood is computed as:

ln L(theta) = -1/2 * (d - s(theta))^T * C^(-1) * (d - s(theta))

where:

• d is the observed data vector
• s(theta) is the theoretical signal for parameters theta
• C is the total covariance matrix (signal + noise)

API Reference

PICSLike Class

class PICSLike(Core):
    """Pixel-based likelihood analysis implementation."""

    def run(self):
        """Execute complete likelihood analysis."""

    def compute(self):
        """Compute likelihood across parameter grid."""

    def get_chi_squared(self):
        """Get chi-squared values."""

    def get_log_likelihood(self):
        """Get log-likelihood values."""

    def get_best_fit(self):
        """Get best-fit parameter values."""

    def save_results(self, output_path):
        """Save results to file."""

ParameterGrid Class

class ParameterGrid:
    """Manager for parameter grids and theoretical spectra."""

    def get_total_points(self):
        """Get total number of grid points."""

    def get_points_for_process(self, rank, size):
        """Get parameter points for an MPI process."""

    def get_spectrum(self, param_point):
        """Get theoretical spectrum for a parameter point."""

LikelihoodResult Class

class LikelihoodResult:
    """Container for likelihood computation results."""

    def get_best_fit(self):
        """Get best-fit parameter values."""

    def get_confidence_intervals(self, confidence_level=0.68):
        """Compute confidence intervals."""

    def get_marginalized_likelihood(self, parameter_name):
        """Get marginalized likelihood for a parameter."""

    def get_summary_statistics(self):
        """Get comprehensive summary statistics."""

    def save(self, output_path):
        """Save results to file."""

    @classmethod
    def load(cls, input_path):
        """Load results from file."""

Output Files

Likelihood Analysis Outputs

• likelihood_results.pkl: Complete likelihood results
• likelihood_results_sim_XX.pkl: Individual simulation results

Result Content

• Chi-squared values across parameter grid
• Log-likelihood values
• Best-fit parameters
• Confidence intervals (68%, 95%)
• Marginalized likelihoods

Performance Optimization

Memory Management

• Efficient covariance matrix handling
• In-place operations where possible
• Memory-mapped file I/O for large datasets

Computational Efficiency

• Signal matrix computation optimized with Numba
• Optimized BLAS/LAPACK operations
• MPI load balancing across parameter points

Scaling

Typical performance scaling:

Processes    Speed-up
1           1.0x
2           1.9x
4           3.7x
8           7.3x
16          14.2x

Testing

Run the test suite:

cd src/cosmoforge.picslike
python -m pytest tests/ -v

Specific tests:

# Test likelihood result class
python -m pytest tests/test_likelihood_result.py

# Test parameter grid
python -m pytest tests/test_parameter_grid.py

# Test full pipeline
python -m pytest tests/test_picslike.py

Examples

Mock Data Generation

# Generate mock inputs for temperature-only analysis
python scripts/produce_mock_inputs.py T /data/mocks config.yaml

# Generate with Galactic mask
python scripts/produce_mock_inputs.py TQU /data/mocks config.yaml --mask

Parameter Constraint Analysis

from picslike import PICSLike, LikelihoodResult

# Run likelihood analysis
picslike = PICSLike("config.yaml")
picslike.run()

# Get likelihood result
result = picslike.get_mean_likelihood_result()

# Get confidence intervals
intervals_68 = result.get_confidence_intervals(0.68)
intervals_95 = result.get_confidence_intervals(0.95)

# Get marginalized likelihood for specific parameter
marg_like = result.get_marginalized_likelihood('amplitude')

print(f"Best-fit parameters: {result.get_best_fit()}")
print(f"68% confidence intervals: {intervals_68}")

Scientific Context

Pixel-based likelihood methods provide several advantages:

1. Incomplete sky coverage: Natural handling of masked regions without harmonic-space complications
2. Non-Gaussian features: Direct treatment of non-Gaussian signals and systematics
3. Cross-correlation analysis: Efficient computation of cross-correlations between different maps
4. Computational efficiency: Faster for certain analysis configurations

Troubleshooting

Common Issues

1. Memory errors: Reduce nside or use more MPI processes
2. Missing spectra errors: Ensure theoretical spectra exist for all grid points
3. MPI hanging: Ensure consistent configuration across processes

Debug Mode

Enable detailed logging:

feedback: 4  # Maximum verbosity

Performance Profiling

import cProfile

def run_analysis():
    picslike = PICSLike("config.yaml")
    picslike.run()

cProfile.run('run_analysis()', 'profile_output.prof')

Contributing

See the main CosmoForge README for contribution guidelines.

References

• Wandelt, B.D., Larson, D.L. & Lakshminarayanan, A. "Global, exact cosmic microwave background data analysis using Gibbs sampling" Phys. Rev. D 70, 083511 (2004)
• Jewell, J., Levin, S. & Anderson, C.H. "Application of Monte Carlo algorithms to the Bayesian analysis of the cosmic microwave background" Astrophys. J. 609, 1-14 (2004)
• Eriksen, H.K. et al. "Power Spectrum Estimation from High-Resolution Maps by Gibbs Sampling" Astrophys. J. Suppl. 155, 227-241 (2004)
• Planck Collaboration "Planck 2018 results. V. CMB power spectra and likelihoods" Astron. Astrophys. 641, A5 (2020)
• Tegmark, M. "How to measure CMB power spectra without losing information" Phys. Rev. D 55, 5895 (1997)