The Graphical Sampling Method, introduced by Panahbehagh (2025), presents an innovative approach to finite population sampling based on a unique graphical framework. This method allows researchers to visually depict first-order inclusion probabilities (FIP) as bars on a two-dimensional graph. By adjusting the positions of these bars, users can explore a wide range of sampling designs while controlling second-order inclusion probabilities (SIP).

This package, graphical_sampling, provides tools for implementing the Graphical Sampling Method and is available on PyPI.

• Create various unequal probability sampling designs with a fixed FIP.
• Control and explore second-order inclusion probabilities (SIP) through visual manipulation.
• Incorporate search algorithms, such as A* and Genetic Algorithm, to optimize sampling designs for specific needs (e.g., well-spread or optimal sampling).

Install the package via pip:

pip install graphical_sampling

The package includes core classes and methods to facilitate sampling design creation and optimization. Below is a basic example demonstrating the API.

import graphical_sampling as gs
import numpy as np
# Set up random generator and sample data
rng = np.random.default_rng()
N = 50 # Population size
x = rng.random(size=N) # Auxiliary variable
n = 5 # Sample size
# Generate initial inclusion probabilities
inclusion = rng.random(N)
inclusion *= n / inclusion.sum()
# Define initial sampling design and evaluation criteria
initial_design = gs.Design(inclusion)
nht = gs.criteria.VarNHT(x, inclusion)
astar = gs.search.AStar(initial_design, nht, switch_coefficient=1)
# Display initial criteria and design
print("Initial criteria value:", astar.initial_criteria_value)
astar.initial_design.show()
# Run the A* search algorithm to optimize the design
astar.run(max_iterations=2000, num_new_nodes=10, max_open_set_size=10000, num_changes=1)
# Display results after optimization
print("Best criteria value:", astar.best_criteria_value)
astar.best_design.show()

• Bardia Panahbehagh - bardia.panah@gmail.com
• Mehdi Mohebbi - mehdi.mohebbi23@gmail.com
• AmirMohammad HosseiniNasab - awmirhn@gmail.com
• Mehdi Hosseini Moghadam - m.h.moghadam1996@gmail.com

For more details, consult the official paper: Panahbehagh, B. (2025). Graphical Sampling Method.