4.10. Relative Score Method — General

imselection.compute_rsm_general(demands, im1_values, im2_values, pdf_func_im1, pdf_func_im2)[source]

General Relative Sufficiency Measure using user-supplied PDF callables.

Implements Equation 1 of Ebrahimian & Jalayer (2021). Useful for custom demand models or non-lognormal formulations.

Parameters:

demands (array_like) – EDP value for each record, shape (N,).
im1_values (array_like) – IM₁ value for each record, shape (N,).
im2_values (array_like) – IM₂ value for each record, shape (N,).
pdf_func_im1 (callable) – f(d_k, im1_k) → float — probability density of demand d_k given IM₁ = im1_k.
pdf_func_im2 (callable) – f(d_k, im2_k) → float — same for IM₂.

Returns:

dict with keys
* 'rsm' — scalar RSM in bits
* 'rsm_per_record' — ndarray of per-record log₂ ratios
* 'n_records' — total records
* 'n_valid' — records with finite log₂ ratio
* 'method' — 'general'

Example

from openquake.vmtk.imselection import imselection

import numpy as np
from scipy.stats import lognorm

ims = imselection()

# f(d, im): density of the demand d given the IM, here a lognormal
# model ln(d) ~ N(ln(a) + b ln(im), sigma) with user-fitted (a, b, sigma)
def pdf_im1(d, im, a=0.01, b=1.0, sigma=0.4):
    return lognorm.pdf(d, s=sigma, scale=a * im**b)

def pdf_im2(d, im, a=0.012, b=0.9, sigma=0.6):
    return lognorm.pdf(d, s=sigma, scale=a * im**b)

# demands, im1_values, im2_values: 1-D arrays of equal length
result = ims.compute_rsm_general(
    demands, im1_values, im2_values, pdf_im1, pdf_im2
)
print(f"RSM = {result['rsm']:.4f} bits")