🚀 decision_methods

A scientific Python library for computing decision thresholds and limits using numerical methods independent of the analytical expression.

Includes advanced implementations such as:

• UD — Decision Threshold
• LID — Decision Limit

---

✨ Key Features

• Numerical methods applicable to any analytical model
• Full uncertainty propagation
• Robust root-finding algorithms
• Scientific computation ready for real-world data
• Visualization tools for LID analysis

---

⚙️ Core Function

🔹 compute_F_ud_lid

Computes:

• Model value
• Associated uncertainty
• Decision Threshold (UD)
• Decision Limit (LID)

Parameters

• p (array-like) — Model parameter vector
• t_m (float) — Measurement time
• t_f (float) — Background time
• f (callable) — Multivariable function
• pderivative (callable) — Partial derivative function
• bisection (callable) — Root-finding method
• k (float, optional) — Coverage factor (default: 1.65)
• LID_a (float) — Lower bound for LID search
• LID_b (float) — Upper bound for LID search
• cpm_min(float) — Lower bound of the count rate (counts per unit time, e.g., minutes or seconds; CPM) used in the LID search
• cpm_max(float) — Upper bound of the count rate (counts per unit time, e.g., minutes or seconds; CPM) used in the LID search
• cpm_index(integer) — Index of the parameter corresponding to the count rate (CPM) used in the LID search
• sample_indices (tuple of int, optional) — Indices of parameters corresponding to sample measurements modeled as Poisson-distributed variables, with expected counts defined as the parameter value scaled by the measurement time t_m (default: (0,))
• background_indices (tuple of int, optional) — Indices of parameters corresponding to sample measurements modeled as Poisson-distributed variables, with expected counts defined as the parameter value scaled by the measurement time t_f (default: (1,))
• rel_map (tuple of (int, float), optional) — Relative uncertainty definitions as (index, relative_error) pairs
• frac_fondo (float, optional) — Relative uncertainty for background when t_f <= 0

Returns

• value (float) — Evaluated value of the model function
• u_value (float) — Combined uncertainty
• UD (float) — Decision threshold
• LID (float) — Decision limit

Returns

• value (float) — Evaluated value of the model function
• u_value (float) — Combined uncertainty
• UD (float) — Decision threshold
• LID (float) — Decision limit

---

📊 Visualization

🔹 plot_lid_function

Generates plots to analyze LID behavior.

Parameters

• LID_a (float) — Lower bound
• LID_b (float) — Upper bound
• p (array-like) — Parameters
• f (callable) — Function
• UD (float) — Decision threshold
• t_m (float) — Measurement time
• t_f (float) — Background time
• pderivative (callable) — Partial derivative function
• bisection (callable) — Root-finding method
• cpm_min(float) — Lower bound of the count rate (counts per unit time, e.g., minutes or seconds; CPM) used in the LID search
• cpm_max(float) — Upper bound of the count rate (counts per unit time, e.g., minutes or seconds; CPM) used in the LID search
• n(integer) — Number of samples or observations used in the LID search
• cpm_index(integer) — Index of the parameter corresponding to the count rate (CPM) used in the LID search
• k (float, optional) — Coverage factor (default: 1.65)
• rel_map (tuple of (int, float), optional) — Relative uncertainty definitions as (index, relative_error) pairs

---

🧪 Activity Functions

🔹 AT — Total Alpha

Computes total alpha activity.

$AT(Bq\cdot m^{3})= \frac{CPM_M-CPM_F}{60 \cdot ɛ \cdot V_{Alicuot}}$

Parameters

• CPM_m (float) — Sample counts
• CPM_f (float) — Background counts
• Eps (float) — Detection efficiency
• V_ali (float) — Aliquot volume

Returns

• (float) — Activity

---

🔹 BT — Total Beta

Computes total beta activity.

$BT(Bq\cdot m^{3})= \frac{CPM_{\beta-M}-CPM_{\beta-F} - γ \cdot(CPM_{α-M}-CPM_{α-F})}{60 \cdot Ef_{Sr} \cdot V_{Alicuot}⋅Fa}$

Parameters

• CPM_b_m (float) — Measured beta counts
• CPM_b_f (float) — Background beta counts
• CPM_a_m (float) — Measured alpha counts
• CPM_a_f (float) — Background alpha counts
• Spill (float) — Spillover correction factor
• EFSr (float) — Detection efficiency factor
• Fa (float) — Correction factor
• V_ali (float) — Aliquot volume

Returns

• (float) — Total beta activity

---

📦 Installation

pip install decision_methods