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diff --git a/docs/source/guides/up.md b/docs/source/guides/up.md
index 7f6c9e4a..351d1c5a 100644
--- a/docs/source/guides/up.md
+++ b/docs/source/guides/up.md
@@ -4,9 +4,9 @@
 Methods to efficiently propagate different types of uncertainty through computational models are of vital interests.
 `PyUncertainNumber` includes strategies for black box uncertainty propagation (i.e.non-intrusive) as well as a library of functions for PBA ([Probability Bounds Analysis](https://en.wikipedia.org/wiki/Probability_bounds_analysis)) if the code can be accessed (i.e. intrusive). `PyUncertainNumber` provides a series of uncertainty propagation methods.
 
-It is suggested to use [interval analysis](../interval_analysis.md) for propagating ignorance and the methods of probability theory for propagating variability. But realistic engineering problems or risk analyses will most likely involve a mixture of both types and as such probability bounds analysis provides means to rigourously propagate the uncertainty.
+It is suggested to use [interval analysis](../interval_analysis.md) for propagating ignorance and the methods of probability theory for propagating variability. But realistic engineering problems or risk analyses will most likely involve a mixture of both types and as such probability bounds analysis provides means to rigorously propagate the uncertainty.
 
-For aleatory uncertainty, probability theory already provides some established approaches, such as Taylor expansion or sampling methods, etc. This guide will mostly focuses on the propagation of intervals due to the close relations with propagation of p-boxes. A detailed review can be found in this [report](https://sites.google.com/view/dawsreports/up/report). Importantly, see {ref}`up` for a hands-on tutorial.
+For aleatory uncertainty, probability theory already provides some established approaches, such as Taylor expansion or sampling methods, etc. This guide will mostly focus on the propagation of intervals due to the close relations with propagation of p-boxes. A detailed review can be found in this [report](https://sites.google.com/view/dawsreports/up/report). Importantly, see {ref}`up` for a hands-on tutorial.
 
 ## Vertex method
 
diff --git a/docs/source/guides/vvuq.md b/docs/source/guides/vvuq.md
new file mode 100644
index 00000000..61f33761
--- /dev/null
+++ b/docs/source/guides/vvuq.md
@@ -0,0 +1,85 @@
+(vvuq_guide)=
+# VV&UQ framework
+
+Numerical simulations plan an ever-growing role in simulating the behaviour of natural and engineered systems. Various sources uncertainties existing in the computational pipeline shadow the credibility the mathematical model or the numerical implementation {cite:p}`roy2011comprehensive`. 
+
+```{note}
+The VV&UQ framework is one comprehensive framework, composed by the elements of *validation*, *verification* and *uncertainty quantification*, that estimates the predictive uncertainty of computing applications.
+```
+
+## Validation, verification, and uncertainty quantification 
+
+The uncertainty about the discrepancy between the model and reality is called *model form* uncertainty {cite:p}`cary2026summary`. This type of uncertainty is most commonly assessed during validation campaigns, which collect experimental data about the phenomena of interest and compare this data to model predictions of conditions nominally identical to those in the tests. Although reflecting the best state of knowledge of the engineer, experimental data is affected, among other things, by *measurement uncertainty*, which must be accounted for during validation.
+
+Moreover, models are generally built to reflect a family of physical processes and are given tunable parameters which allow the engineer to set the model for use in specific scenarios. The values of these parameters which represent the true physical process, to be compared against in validation, are not precisely known, because of the presence of *parametric input uncertainty*. Models that compute numerical solutions to partial differential equations are also subject to *numerical uncertainty* due to finite spatial and/or temporal resolution, iterative convergence error, and the use of finite precision arithmetic in computer codes. 
+
+Furthermore, the main purpose of any model is to be used where experiments are impractical or impossible to be conducted and the engineer must reason about the performance of the model from the evidence obtained during validation. This results in *extrapolation uncertainty*. The individual contributions of each uncertainty source interact to determine the ultimate measure of model reliability in its application domain, termed *predictive capability*. To quantify the effect of these process-dependent sources of uncertainty, the model must, typically, be run many times. Many models however are complex enough to only allow a single or a handful of runs at any particular setting, necessitating the need for reduced-order models. These approximations of the full model, also called *surrogates*, come with their own surrogate modeling uncertainty. Together, these uncertainties are referred to here as *total uncertainty*. 
+
+
+## The discrepancy between non-determinstic simulations and experiments
+
+```{tip}
+Validation is a process of determining the degree to which a (non-deterministic) model simulation is an accurate representation of the corresponding (imperfect) physical experiment.
+```
+
+- Both model predictions and empirical data may contain both aleatory and epistemic uncertainty.
+
+- Effectively the discrepancy measure is between two uncertain data generating processes.
+
+- The discrepancy measure indicated the model-form uncertainty
+
+```{image} ../_static/area_metric_illustration_3.png
+:alt: Illustration of the stochastic area metric
+:class: bg-primary
+:width: 400px
+:align: center
+
+Illustration of the stochastic area metric
+```
+
+```python
+from pyuncertainnumber import area_metric
+
+dist = pba.normal(4, 1) data_sample = dist.sample(5)
+ecdf_ = pba.ECDF(data_sample)
+area_metric(dist, ecdf_) 
+0.33125451465728933
+```
+
+## Predictive capability
+
+Predictive capability suggests the prediction, along with its uncertainty estimation, with respect to a scenario in the application domain that is likely to be beyond the validation domain. Such predictive uncertainty shall comprise all the possible sources of uncertainties during the computational pipeline, as mentioned above. Notably, some uncertainties are of aleatory nature while others are of epistemic nature. The mechanism of probability bounding is employed to aggregate the effects of all these uncertainties to produce a reliable prediction.
+
+```{image} ../_static/pbox_layers_static.png
+:alt: Predictive capability
+:class: bg-primary
+:width: 400px
+:align: center
+
+Predictive capability
+```
+
+
+
+## An open challenge for VVUQ on aerodynamics
+
+An open challenge has been proposed to focuses on estimating the predictive capability of an aerodynamic analysis tool (XFOIL) given a set of synthetic experimental data in AIAA Sci-Tech Forum 2026 {cite:p}`cary2026summary`.
+
+```{image} ../_static/aiaa_challenge_statement.png
+:alt: Problem statement 
+:class: bg-primary
+:width: 600px
+:align: center
+
+Problem statement of the AIAA Second Uncertainty Quantification Challenge Problem for Aerodynamics
+```
+
+In response to this challenge, The UQ team at UoL presents a methodological framework {cite:p}`chen2026efficient` for tackling the Second Uncertainty Quantification Challenge Problem for Aerodynamics. The challenge requires assessments of validation and predictive capability for an aerodynamic tool given imperfect experimental measurements that are scarce and imprecise. We propose an efficient interval-based integrated approach that comprehensively accounts for multiple sources of uncertainties including experimental data uncertainties, inputs incertitude, model-form discrepancy, numerical approximation, surrogate model prediction, and, importantly, uncertainties related to extrapolated application domains. These uncertainties are tackled by efficient meta-modelling techniques involving interval predictor models, Bayesian optimization on the basis of Gaussian processes, and stochastic neural network models. Our results underscore the effectiveness and efficiency of the approach in achieving a practical balance between comprehensive uncertainty quantification and computational cost, demonstrating broad applicability for uncertainty-driven validation and assessment of predictive capability in engineering applications.
+
+
+
+## References
+
+```{bibliography}
+:filter: docname in docnames
+```
\ No newline at end of file
diff --git a/docs/source/index.md b/docs/source/index.md
index 019fd239..7a802dc5 100755
--- a/docs/source/index.md
+++ b/docs/source/index.md
@@ -14,6 +14,7 @@ guides/up
 pbox
 cbox
 interval_analysis
+guides/vvuq
 ```
 
 ```{toctree}
diff --git a/docs/source/refs.bib b/docs/source/refs.bib
index 6db1003b..78791e99 100644
--- a/docs/source/refs.bib
+++ b/docs/source/refs.bib
@@ -37,4 +37,32 @@ @article{de2023robust
   pages={109877},
   year={2023},
   publisher={Elsevier}
+}
+
+@article{roy2011comprehensive,
+  title={A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing},
+  author={Roy, Christopher J and Oberkampf, William L},
+  journal={Computer methods in applied mechanics and engineering},
+  volume={200},
+  number={25-28},
+  pages={2131--2144},
+  year={2011},
+  publisher={Elsevier}
+}
+
+
+@inproceedings{cary2026summary,
+  title={Summary of the Second AIAA Uncertainty Quantification Challenge Problem for Aerodynamics},
+  author={Cary, Andrew W and Rumpfkeil, Markus and Hristov, Peter O and Schaefer, John A},
+  booktitle={AIAA SCITECH 2026 Forum},
+  pages={0091},
+  year={2026}
+}
+
+@inproceedings{chen2026efficient,
+  title={Efficient Interval-Based Uncertainty Quantification for Model Validation and Predictive Capability},
+  author={Chen, Yu and Ioannou, Ioanna and Ferson, Scott},
+  booktitle={AIAA SCITECH 2026 Forum},
+  pages={0296},
+  year={2026}
 }
\ No newline at end of file
diff --git a/docs/source/tutorials/index.md b/docs/source/tutorials/index.md
index 7afd81bf..e5b7de40 100644
--- a/docs/source/tutorials/index.md
+++ b/docs/source/tutorials/index.md
@@ -11,6 +11,7 @@ what_is_un
 uncertainty_characterisation
 uncertainty_aggregation
 uncertainty_propagation
+validation_assessment
 ```
 
 ::::{grid} 1 2 2 3
@@ -51,4 +52,12 @@ Techniques for combining multiple sources of uncertainty.
 Propagate uncertainty through computational models and functions.
 :::
 
+
+:::{card} Discrepancy assessment by validation 
+:link: validation_assessment
+:link-type: doc
+:img-top: ../_static/pbox_layers_static.png
+Validation of imprecise probability models.
+:::
+
 ::::
diff --git a/docs/source/tutorials/uncertainty_propagation.ipynb b/docs/source/tutorials/uncertainty_propagation.ipynb
index f0ee4165..8b3b21b7 100644
--- a/docs/source/tutorials/uncertainty_propagation.ipynb
+++ b/docs/source/tutorials/uncertainty_propagation.ipynb
@@ -49,9 +49,9 @@
     "jp-MarkdownHeadingCollapsed": true
    },
    "source": [
-    "## arithmetic of uncertain number\n",
+    "## Arithmetic of uncertain numbers\n",
     "\n",
-    "[Probability bounds anlaysis](https://en.wikipedia.org/wiki/Probability_bounds_analysis) combines both interval analysis and probability theory, allowing\n",
+    "[Probability bounds analysis](https://en.wikipedia.org/wiki/Probability_bounds_analysis) combines both interval analysis and probability theory, allowing\n",
     "rigorous bounds of (arithmetic) functions of random variables to be computed even with partial information."
    ]
   },
@@ -137,7 +137,7 @@
    "id": "299a3953-1a37-4e59-ab02-a769e1b54467",
    "metadata": {},
    "source": [
-    "## generic propagation of uncertain numbers"
+    "## Generic propagation of uncertain numbers"
    ]
   },
   {
diff --git a/docs/source/tutorials/validation_assessment.ipynb b/docs/source/tutorials/validation_assessment.ipynb
new file mode 100644
index 00000000..95938a23
--- /dev/null
+++ b/docs/source/tutorials/validation_assessment.ipynb
@@ -0,0 +1,294 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "8e8cd960-d712-4d80-a578-b23876a85e9c",
+   "metadata": {},
+   "source": [
+    "(up)=\n",
+    "# Validation: discrepancy assessment\n",
+    "\n",
+    "\n",
+    "\n",
+    "A general measure of validation assessment is demonstrated herein to characterise the discrepancy between the quantitative predictions from a model, and relevant empirical data when predictions and data may both contain aleatory and epistemic uncertainty. This measure has a specific focus on imprecise probability. \n",
+    "\n",
+    "\n",
+    "This extends beyond the deterministic world when the predicted quantity is a scalar (real) value. In fact, we recognise the case when predictions or data contain epistemic uncertainty that cannot be well characterised with any single probability distribution.\n",
+    "\n",
+    "In this tutorial, we will explore the different cases of uncertainty representation in either the prediction or observation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fe75b385-30b7-4670-9924-198479c09281",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pyuncertainnumber import pba, area_metric\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "plt.rcParams.update({\n",
+    "        \"font.size\": 11,\n",
+    "        \"text.usetex\": True,\n",
+    "        \"font.family\": \"serif\",\n",
+    "        \"figure.figsize\": (6, 4.5),\n",
+    "        \"legend.fontsize\": 'small',\n",
+    "        })"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "20f719a3-1f00-4559-8c4f-c8667112595c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def verify_area_metric(a, b, ax=None):\n",
+    "    am = area_metric(a, b)\n",
+    "\n",
+    "    if ax is None:\n",
+    "        fig, ax = plt.subplots()\n",
+    "    a.plot(ax=ax, fill_color='salmon', bound_colors=['salmon', 'salmon'], label='a', nuance='curve')\n",
+    "    b.plot(ax=ax, label='b', nuance='curve')\n",
+    "    ax.set_title(f\"area metric: {am:.5f}\")\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1919dc93-32b8-49b4-b1a5-33cb59e19af2",
+   "metadata": {
+    "jp-MarkdownHeadingCollapsed": true
+   },
+   "source": [
+    "### Example case 1: two distributions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "29e33e1c-dde2-47d8-b841-46814211f4b4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "\u001b[1m<\u001b[0m\u001b[1;95mFigure\u001b[0m\u001b[39m size 60\u001b[0m\u001b[1;36m0x450\u001b[0m\u001b[39m with \u001b[0m\u001b[1;36m1\u001b[0m\u001b[39m Axes\u001b[0m\u001b[1m>\u001b[0m"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "a = pba.normal(5, 1)\n",
+    "b = pba.uniform(2, 9)\n",
+    "verify_area_metric(a, b)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e6803024-24f0-4e0f-ae91-8382b0f7312c",
+   "metadata": {
+    "jp-MarkdownHeadingCollapsed": true
+   },
+   "source": [
+    "### Example case 2: a distribution and a scalar value"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "8de0d826-5094-490f-9b46-3607f323816c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "\u001b[1m<\u001b[0m\u001b[1;95mFigure\u001b[0m\u001b[39m size 60\u001b[0m\u001b[1;36m0x450\u001b[0m\u001b[39m with \u001b[0m\u001b[1;36m1\u001b[0m\u001b[39m Axes\u001b[0m\u001b[1m>\u001b[0m"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "NUMBER = 5.0\n",
+    "a = pba.normal(5, 1)\n",
+    "b = pba.I(NUMBER).to_pbox()\n",
+    "verify_area_metric(a, b)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "91992fdf-d6f7-45c4-b603-9a583bdd625a",
+   "metadata": {
+    "jp-MarkdownHeadingCollapsed": true
+   },
+   "source": [
+    "### Example case 3: p-boxes that overlap"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "d9934192-179b-42c9-8c9c-745aa3060dc0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "\u001b[1m<\u001b[0m\u001b[1;95mFigure\u001b[0m\u001b[39m size 60\u001b[0m\u001b[1;36m0x450\u001b[0m\u001b[39m with \u001b[0m\u001b[1;36m1\u001b[0m\u001b[39m Axes\u001b[0m\u001b[1m>\u001b[0m"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "a = pba.normal([2, 5], 1)\n",
+    "b = pba.uniform([2, 4], [7,9])\n",
+    "verify_area_metric(a, b)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b4e2ad4a-0d8a-4703-8a26-8cefdec5b846",
+   "metadata": {},
+   "source": [
+    "### Example case 4: p-boxes that have imposition"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "e598c730-6b19-437f-b5db-e768a8693600",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "\u001b[1m<\u001b[0m\u001b[1;95mFigure\u001b[0m\u001b[39m size 60\u001b[0m\u001b[1;36m0x450\u001b[0m\u001b[39m with \u001b[0m\u001b[1;36m1\u001b[0m\u001b[39m Axes\u001b[0m\u001b[1m>\u001b[0m"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "a = pba.normal([2, 5], 1)\n",
+    "b = pba.uniform([1, 4], [5,9])\n",
+    "verify_area_metric(a, b)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f27b7a73-e17f-4c03-9aa4-8b0769c894e5",
+   "metadata": {
+    "jp-MarkdownHeadingCollapsed": true
+   },
+   "source": [
+    "### Example case 5: a p-box and a scalar value"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "d1ddf24d-35f1-4ea0-ab6a-6bc6873a0ba6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "\u001b[1m<\u001b[0m\u001b[1;95mFigure\u001b[0m\u001b[39m size 60\u001b[0m\u001b[1;36m0x450\u001b[0m\u001b[39m with \u001b[0m\u001b[1;36m1\u001b[0m\u001b[39m Axes\u001b[0m\u001b[1m>\u001b[0m"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "a = pba.normal([2, 5], 1)\n",
+    "b = pba.I(5).to_pbox()\n",
+    "verify_area_metric(a, b)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "pbox_nn",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/pyproject.toml b/pyproject.toml
index c3deee3e..19293023 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -38,7 +38,7 @@ maintainers = [
 name = "pyuncertainnumber"
 readme = "README.md"
 requires-python = ">= 3.11"
-version = "0.1.4"
+version = "0.1.15"
 
 [project.optional-dependencies]
 test = [
diff --git a/requirements.txt b/requirements.txt
index 1d364c80..b6c3cea1 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,7 +1,6 @@
 matplotlib==3.9.2
 numpy==2.1.3
 pandas==2.2.3
-pillow==11.0.0
 Pint==0.24.4
 Pygments==2.18.0
 pymongo==4.10.1
diff --git a/src/pyuncertainnumber/__init__.py b/src/pyuncertainnumber/__init__.py
index c3b94052..7df98331 100644
--- a/src/pyuncertainnumber/__init__.py
+++ b/src/pyuncertainnumber/__init__.py
@@ -60,7 +60,7 @@
 
 
 # * --------------------- validation ---------------------*#
-from .pba.core import area_metric
+from pyuncertainnumber.validation.area_metric import area_metric
 
 # * ---------------------  utils ---------------------*#
 from pyuncertainnumber.gutils import inspect_un
diff --git a/src/pyuncertainnumber/calibration/tmcmc.py b/src/pyuncertainnumber/calibration/tmcmc.py
index ed0f9ae6..afaa0c97 100644
--- a/src/pyuncertainnumber/calibration/tmcmc.py
+++ b/src/pyuncertainnumber/calibration/tmcmc.py
@@ -1203,6 +1203,23 @@ def get_hdi_bounds(
     return pd.DataFrame(out).rename_axis("column").reset_index()
 
 
+def filter_hdi_bounds(df, level: int = 95) -> pd.DataFrame:
+    """Extract HDI bounds for a given credibility level.
+
+    args:
+        df (pd.DataFrame): HDI dataframe containing columns like `hdi_95_low`, `hdi_95_high`
+
+        level (int | str): significance level (e.g. 95, 90, 20)
+
+    returns:
+        (pd.DataFrame): DataFrame with columns [hdi_<level>_low, hdi_<level>_high]
+
+    """
+    level = str(level)
+    cols = [f"hdi_{level}_low", f"hdi_{level}_high"]
+    return df.loc[:, cols]
+
+
 def transform_old_trace_to_new(trace: list[list]) -> list[Stage]:
     """Transform old trace format to new Stage class format.
 
diff --git a/src/pyuncertainnumber/pba/__init__.py b/src/pyuncertainnumber/pba/__init__.py
index ba3bb43b..c075dd45 100644
--- a/src/pyuncertainnumber/pba/__init__.py
+++ b/src/pyuncertainnumber/pba/__init__.py
@@ -15,4 +15,3 @@
 from .operation import convert
 from .aggregation import *
 from .pbox_free import KS_bounds
-from .core import area_metric
diff --git a/src/pyuncertainnumber/pba/aggregation.py b/src/pyuncertainnumber/pba/aggregation.py
index 7a49edaa..b7c5655c 100644
--- a/src/pyuncertainnumber/pba/aggregation.py
+++ b/src/pyuncertainnumber/pba/aggregation.py
@@ -135,6 +135,7 @@ def stochastic_mixture(
         return mixture_pbox(*converted_constructs, weights)
 
 
+# TODO. weights cannot be None for intervals with same weights
 def stacking(
     vec_interval: Interval | list[Interval],
     *,
diff --git a/src/pyuncertainnumber/pba/core.py b/src/pyuncertainnumber/pba/core.py
index e85c93cc..03f6252b 100644
--- a/src/pyuncertainnumber/pba/core.py
+++ b/src/pyuncertainnumber/pba/core.py
@@ -2,12 +2,14 @@
 from typing import TYPE_CHECKING
 
 from abc import ABC, abstractmethod
-import numpy as np
 from numpy.typing import ArrayLike
 import scipy.stats as sps
 from numbers import Number
 from pyuncertainnumber.pba.pbox_abc import Pbox, Staircase
+from pyuncertainnumber.pba.intervals import Interval
 from bisect import bisect_left
+import numpy as np
+import matplotlib.pyplot as plt
 
 
 class Joint(ABC):
@@ -78,267 +80,6 @@ def endpoint_distance(A, B):
     return distances
 
 
-def am_distance_counter(A, B):
-    """Compute the distance between two sets of intervals as used in the area metric.
-
-    notes:
-        It is essentially doing:
-
-        def f(a, b, c, d):
-            return np.maximum.reduce([c - b, a - d, 0])
-
-    """
-    a, b = A[:, 0], A[:, 1]
-    c, d = B[:, 0], B[:, 1]
-    return np.maximum.reduce([c - b, a - d, np.zeros_like(a)])
-
-
-def function_succeeds(f, *args, **kwargs):
-    try:
-        f(*args, **kwargs)
-        return True
-    except Exception:
-        return False
-
-
-def area_metric_pbox(a: Pbox, b: Pbox):
-    """when a and b are both Pboxes"""
-    # diff = endpoint_distance(a.to_numpy(), b.to_numpy())  # old version busted by Scott
-    diff = am_distance_counter(a.to_numpy(), b.to_numpy())
-    return np.trapz(y=diff, x=a.p_values)
-
-
-def area_metric_pbox_diff(a: Pbox, b: Pbox):
-    """when a and b are both Pboxes"""
-    # diff = endpoint_distance(a.to_numpy(), b.to_numpy())  # old version busted by Scott
-    diff = am_distance_counter(a.to_numpy(), b.to_numpy())
-    return diff
-
-
-def area_metric_sample(a: ArrayLike, b: ArrayLike):
-    return sps.wasserstein_distance(a, b)
-
-
-def area_metric_number(a: Pbox | Number, b: Pbox | Number) -> float:
-    """if any of a or b is a number, compute area metric accordingly"""
-    from pyuncertainnumber import pba
-
-    if isinstance(a, Number) and isinstance(b, Number):
-        return abs(a - b)
-    if isinstance(a, Number):
-        a, b = b, a  # swap so b is the number
-    if isinstance(a, Pbox) and a.degenerate:
-        return area_metric_ecdf(a.left, b, a.p_values)
-    if isinstance(a, Pbox) and (not a.degenerate):
-        # make b a Pbox
-        b = pba.I(b).to_pbox()
-        return area_metric_pbox(a, b)
-
-
-def area_metric(a: Number | Pbox | ArrayLike, b: Number | Pbox | ArrayLike) -> float:
-    """Compute the area metric between two objects.
-
-    note:
-        top-level function to compute area metric between any two objects
-    """
-    if isinstance(a, Number) or isinstance(b, Number):
-        return area_metric_number(a, b)
-    if isinstance(a, Pbox) and isinstance(b, Pbox):
-        if a.degenerate and b.degenerate:
-            return area_metric_ecdf(a.left, b.left, a.p_values)
-        elif function_succeeds(a.imp, b):
-            return 0.0
-        else:
-            return area_metric_pbox(a, b)
-    if isinstance(a, (np.ndarray, list)) and isinstance(b, (np.ndarray, list)):
-        return area_metric_sample(a, b)
-    elif (isinstance(a, Pbox) and isinstance(b, np.ndarray)) or (
-        isinstance(a, np.ndarray) and isinstance(b, Pbox)
-    ):
-        # make a a Pbox and b a sample anyway
-        if not isinstance(a, Pbox):
-            a, b = b, a
-
-        # b has to be a scalar sample
-        b = np.squeeze(b).item()
-        return area_metric_number(a, b)
-    else:
-        raise NotImplementedError("Area metric not implemented for these types.")
-
-
-# * --------------------------- area metric hints plot
-
-
-def am_diff_register(A, B, debug=False):
-    """Register the distance and return a structured array with fields:
-
-    returns:
-        In each tuple of the output array:
-        - distance: float (max of c-b, a-d, 0)
-        - x1: first endpoint (c or a, or 0 if 0 wins)
-        - x2: second endpoint (b or d, or 0 if 0 wins)
-    """
-    A = np.asarray(A)
-    B = np.asarray(B)
-
-    # Expect shape (N, 2): [:,0]=start=a/c, [:,1]=end=b/d
-    a, b = A[:, 0], A[:, 1]
-    c, d = B[:, 0], B[:, 1]
-
-    c_minus_b = c - b
-    a_minus_d = a - d
-    zeros = np.zeros_like(a, dtype=np.result_type(a, b, c, d, float))
-
-    # Stack and argmax exactly mirrors "max(c-b, a-d, 0)" with deterministic tie-breaking.
-    stacked = np.stack([c_minus_b, a_minus_d, zeros], axis=1)
-    max_indices = np.argmax(stacked, axis=1)
-    distances = stacked[np.arange(len(a)), max_indices]
-
-    # Structured result
-    result = np.zeros(len(a), dtype=[("distance", "f8"), ("x1", "f8"), ("x2", "f8")])
-    result["distance"] = distances
-
-    mask_cb = max_indices == 0
-    mask_ad = max_indices == 1
-    mask_0 = max_indices == 2
-
-    result["x1"][mask_cb] = c[mask_cb]
-    result["x2"][mask_cb] = b[mask_cb]
-
-    result["x1"][mask_ad] = a[mask_ad]
-    result["x2"][mask_ad] = d[mask_ad]
-
-    result["x1"][mask_0] = 0.0
-    result["x2"][mask_0] = 0.0
-
-    if debug:
-        print("a:", a)
-        print("b:", b)
-        print("c:", c)
-        print("d:", d)
-        print("c-b:", c_minus_b)
-        print("a-d:", a_minus_d)
-        print("stacked:\n", stacked)
-        print("argmax:", max_indices)
-        print("distances:", distances)
-        print("result:", result)
-
-    return result
-
-
-import numpy as np
-import matplotlib.pyplot as plt
-
-
-def intervals_from_res(res):
-    """
-    From a structured array `res` with fields: 'distance', 'x1', 'x2',
-    return:
-      - mask: boolean mask where distance != 0
-      - intervals: (N, 2) array of sorted [lo, hi] endpoints for rows where mask is True
-    """
-    mask = res["distance"] != 0
-    x1 = res["x1"][mask]
-    x2 = res["x2"][mask]
-    lo = np.minimum(x1, x2)
-    hi = np.maximum(x1, x2)
-    intervals = np.stack([lo, hi], axis=1)
-    return mask, intervals
-
-
-import numpy as np
-import matplotlib.pyplot as plt
-
-
-def plot_intervals_from_res(
-    res, p, *, show_points=False, title=None, include_ties=False, ax=None
-):
-    """Plot horizontal intervals from `res` at heights given by `p`.
-
-    args
-        res (ArrayLike) : Structured array with fields ('distance', 'x1', 'x2').
-
-        p (ArrayLike) : 1D array of same length as `res`, giving y-coordinate (height) of each interval.
-
-        show_points (Boolean): If True, shows markers at interval endpoints.
-
-        title (str): Plot title. Optional
-
-        include_ties (bool): If True, also include intervals where distance == 0 but argmax picked c-b or a-d.
-
-        ax (matplotlib.axes.Axes) :  Axis to plot on. If None, a new figure and axis are created. Optional
-
-    returns
-        ax (matplotlib.axes.Axes): The matplotlib axis used for plotting.
-    """
-    res = np.asarray(res)
-    p = np.asarray(p)
-    if res.shape[0] != p.shape[0]:
-        raise ValueError("p must have the same number of rows as res")
-
-    # Select rows to plot
-    if include_ties:
-        mask = ~((res["x1"] == 0) & (res["x2"] == 0))
-    else:
-        mask = res["distance"] > 0
-
-    if ax is None:
-        fig, ax = plt.subplots()
-
-    if not np.any(mask):
-        ax.set_xlabel("x")
-        ax.set_ylabel("p (height)")
-        if title:
-            ax.set_title(title)
-        return ax
-
-    x1 = res["x1"][mask]
-    x2 = res["x2"][mask]
-    y = p[mask]
-
-    lo = np.minimum(x1, x2)
-    hi = np.maximum(x1, x2)
-
-    # Draw intervals
-    for xi0, xi1, yi in zip(lo, hi, y):
-        ax.plot([xi0, xi1], [yi, yi], color="lavender")  # horizontal segment
-        if show_points:
-            ax.plot([xi0, xi1], [yi, yi], "o", color="C0")
-
-    ax.set_xlabel("x")
-    ax.set_ylabel("p (height)")
-    if title:
-        ax.set_title(title)
-
-    # Set limits dynamically based on data
-    ax.set_xlim(lo.min() - 0.1, hi.max() + 0.1)
-    ax.set_ylim(y.min() - 0.1, y.max() + 0.1)
-
-    return ax
-
-
-import numpy as np
-
-
-def integrate_distance(res, p):
-    """
-    Integrate distance vs p with the trapezoidal rule,
-    matching: np.trapz(y=diff, x=p)
-
-    No masking; uses all rows. Sorts by p to avoid signed/ordering issues.
-    """
-    res = np.asarray(res)
-    p = np.asarray(p)
-    if res.shape[0] != p.shape[0]:
-        raise ValueError("`p` must have the same length as `res`.")
-
-    order = np.argsort(p)
-    y = res["distance"][order].astype(float, copy=False)
-    x = p[order].astype(float, copy=False)
-
-    return np.trapz(y=y, x=x)
-
-
 # def plot_intervals_from_res(res, p, *, show_points=False, title=None, ax=None):
 #     """
 #     For each row where res['distance'] != 0, plot a horizontal segment from
diff --git a/src/pyuncertainnumber/pba/intervals/intervalOperators.py b/src/pyuncertainnumber/pba/intervals/intervalOperators.py
index 8e053c32..185aa6dc 100644
--- a/src/pyuncertainnumber/pba/intervals/intervalOperators.py
+++ b/src/pyuncertainnumber/pba/intervals/intervalOperators.py
@@ -166,7 +166,8 @@ def make_vec_interval(vec):
     """
     from ...characterisation.uncertainNumber import UncertainNumber as UN
 
-    assert len(vec) > 1, "Interval must have more than one element"
+    # TODO: this is bugg. Interval vector has len(x)=1
+    # assert len(vec) > 1, "Interval must have more than one element"
 
     if isinstance(vec, Interval):
         return vec
diff --git a/src/pyuncertainnumber/pba/intervals/number.py b/src/pyuncertainnumber/pba/intervals/number.py
index 11526159..2de32197 100644
--- a/src/pyuncertainnumber/pba/intervals/number.py
+++ b/src/pyuncertainnumber/pba/intervals/number.py
@@ -146,7 +146,7 @@ def __getitem__(self, i: Union[int, slice]):  # make class indexable
     def to_numpy(self) -> np.ndarray:
         """transform interval objects to numpy arrays"""
         if self.scalar:
-            return np.array([self.lo.item(), self.hi.item()])
+            return np.array([self.lo, self.hi])
         else:
             return np.asarray((self.lo, self.hi)).T
 
@@ -222,14 +222,20 @@ def ravel(self):
 
     @property
     def lo(self) -> Union[ndarray, float]:
-        return self._lo
+        if self.scalar:
+            return self._lo.item()
+        else:
+            return self._lo
 
     # if len(self.shape)==0: return self._lo
     # return self._lo # return transpose(transpose(self.__val)[0]) # from shape (3,7,2) to (2,7,3) to (3,7)
 
     @property
     def hi(self) -> Union[ndarray, float]:
-        return self._hi
+        if self.scalar:
+            return self._hi.item()
+        else:
+            return self._hi
 
     @property
     def left(self):
@@ -397,9 +403,7 @@ def __rtruediv__(self, left):
         leftType = left.__class__.__name__
         # lo,hi = numpy.empty(self._lo.shape),numpy.empty(self._hi.shape)
         self_lo, self_hi = self.lo, self.hi
-        self_straddle_zero = numpy.any(
-            (self_lo.flatten() <= 0) & (self_hi.flatten() >= 0)
-        )
+        self_straddle_zero = numpy.any((self_lo <= 0) & (self_hi >= 0))
         if self_straddle_zero:
             raise ZeroDivisionError
         if (leftType == "ndarray") | (leftType in NUMERIC_TYPES):
@@ -467,6 +471,33 @@ def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
         if "out" in kwargs and kwargs["out"] is not None:
             return NotImplemented
 
+        binary = {
+            np.add: ("__add__", "__radd__"),
+            np.subtract: ("__sub__", "__rsub__"),
+            np.multiply: ("__mul__", "__rmul__"),
+            np.true_divide: ("__truediv__", "__rtruediv__"),
+            np.floor_divide: ("__floordiv__", "__rfloordiv__"),
+            np.power: ("__pow__", "__rpow__"),
+            np.maximum: ("__max__", "__rmax__"),
+            np.minimum: ("__min__", "__rmin__"),
+        }
+
+        if ufunc in binary and len(inputs) == 2:
+            left, right = inputs
+            l_name, r_name = binary[ufunc]
+
+            if left is self:
+                # self (op) right
+                return getattr(self, l_name)(right)
+            elif right is self:
+                # left (op) self
+                return getattr(self, r_name)(left)
+            else:
+                return NotImplemented
+
+        if len(inputs) != 1 or inputs[0] is not self:
+            return NotImplemented
+
         if ufunc is np.sin:
             return self.sin()
         if ufunc is np.cos:
diff --git a/src/pyuncertainnumber/pba/pbox_abc.py b/src/pyuncertainnumber/pba/pbox_abc.py
index 18224e96..539bfdb9 100644
--- a/src/pyuncertainnumber/pba/pbox_abc.py
+++ b/src/pyuncertainnumber/pba/pbox_abc.py
@@ -863,7 +863,9 @@ def display(self, *args, **kwargs):
         self.plot(*args, **kwargs)
         plt.show()
 
-    def plot_probability_bound(self, x: float, ax=None, **kwargs):
+    def plot_probability_bound(
+        self, x: float, ax=None, linecolor="r", markercolor="r", **kwargs
+    ):
         """plot the probability bound at a certain quantile x
 
         note:
@@ -880,12 +882,12 @@ def plot_probability_bound(self, x: float, ax=None, **kwargs):
         ax.plot(
             [x, x],
             [p_lo, p_hi],
-            c="r",
+            c=linecolor,
             label="probability bound",
             zorder=50,
         )
-        ax.scatter(x, p_lo, c="r", marker="^", zorder=50)
-        ax.scatter(x, p_hi, c="r", marker="v", zorder=50)
+        ax.scatter(x, p_lo, c=markercolor, marker="^", zorder=50)
+        ax.scatter(x, p_hi, c=markercolor, marker="v", zorder=50)
         return ax
 
     def plot_quantile_bound(self, p: float, ax=None, **kwargs):
@@ -982,9 +984,34 @@ def __rpow__(self, other: Number):
     def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
         if method != "__call__":
             return NotImplemented
-        if len(inputs) != 1 or inputs[0] is not self:
+        if kwargs.get("out", None) is not None:
             return NotImplemented
-        if "out" in kwargs and kwargs["out"] is not None:
+
+        binary = {
+            np.add: ("__add__", "__radd__"),
+            np.subtract: ("__sub__", "__rsub__"),
+            np.multiply: ("__mul__", "__rmul__"),
+            np.true_divide: ("__truediv__", "__rtruediv__"),
+            np.floor_divide: ("__floordiv__", "__rfloordiv__"),
+            np.power: ("__pow__", "__rpow__"),
+            np.maximum: ("__max__", "__rmax__"),
+            np.minimum: ("__min__", "__rmin__"),
+        }
+
+        if ufunc in binary and len(inputs) == 2:
+            left, right = inputs
+            l_name, r_name = binary[ufunc]
+
+            if left is self:
+                # self (op) right
+                return getattr(self, l_name)(right)
+            elif right is self:
+                # left (op) self
+                return getattr(self, r_name)(left)
+            else:
+                return NotImplemented
+
+        if len(inputs) != 1 or inputs[0] is not self:
             return NotImplemented
 
         if ufunc is np.sin:
@@ -1035,6 +1062,26 @@ def sample(self, n_sam):
         alpha = np.squeeze(qmc.LatinHypercube(d=1).random(n=n_sam))
         return self.alpha_cut(alpha)
 
+    def precise_sample(
+        self,
+        n_a: int,
+        theta: float = None,
+        n_e: int = None,
+    ):
+        """Generate precise samples from a p-box"""
+        if (theta is None) and (n_e is None):
+            raise ValueError("Either theta or n_e must be provided.")
+        if theta is not None and n_e is None:
+            assert 0 <= theta <= 1, "Theta must be in the range [0, 1]."
+            focal_elements = self.sample(n_a)
+            return (focal_elements.hi - focal_elements.lo) * theta + focal_elements.lo
+        if n_e is not None and theta is None:
+            theta = np.random.uniform(0, 1, size=n_e)
+            focal_elements = self.sample(n_a)
+            return (focal_elements.hi - focal_elements.lo)[None, :] * theta[
+                :, None
+            ] + focal_elements.lo[None, :]
+
     def discretise(self, n=None) -> Interval:
         """alpha-cut discretisation of the p-box without outward rounding
 
diff --git a/src/pyuncertainnumber/propagation/taylor_expansion.py b/src/pyuncertainnumber/propagation/taylor_expansion.py
index 5aceb1bb..6f420e0a 100644
--- a/src/pyuncertainnumber/propagation/taylor_expansion.py
+++ b/src/pyuncertainnumber/propagation/taylor_expansion.py
@@ -1,10 +1,5 @@
 import os
 
-os.environ["JAX_PLATFORMS"] = "cpu"
-import jax
-import jax.numpy as jnp
-
-
 """ Taylor expansions for the moments of functions of random variables """
 
 
@@ -36,6 +31,8 @@ def taylor_expansion_method(func, mean, *, var=None, cov=None) -> tuple:
         >>> mu_, var_ = taylor_expansion_method(func=bar, mean=MEAN, cov=COV)
 
     """
+    os.environ["JAX_PLATFORMS"] = "cpu"
+
     if mean.ndim == 1:  # random vector
         return taylor_expansion_method_vector(func, mean, cov)
     elif mean.ndim == 0:  # scalar random variable
@@ -45,6 +42,9 @@ def taylor_expansion_method(func, mean, *, var=None, cov=None) -> tuple:
 def taylor_expansion_method_scalar(func, mean, var) -> tuple:
     """For scalar random variable only"""
 
+    import jax
+    import jax.numpy as jnp
+
     # gradient
     d1f = jax.grad(func)(mean)
 
@@ -61,6 +61,9 @@ def taylor_expansion_method_scalar(func, mean, var) -> tuple:
 def taylor_expansion_method_vector(func, mean, cov) -> tuple:
     """For random vector only"""
 
+    import jax
+    import jax.numpy as jnp
+
     # gradient
     d1f = jax.grad(func)(mean)
 
diff --git a/src/pyuncertainnumber/validation/area_metric.py b/src/pyuncertainnumber/validation/area_metric.py
new file mode 100644
index 00000000..b0001a87
--- /dev/null
+++ b/src/pyuncertainnumber/validation/area_metric.py
@@ -0,0 +1,289 @@
+import numpy as np
+from numpy.typing import ArrayLike
+from numbers import Number
+from pyuncertainnumber import Pbox, Interval
+from pyuncertainnumber.pba.core import area_metric_ecdf
+import scipy.stats as sps
+import matplotlib.pyplot as plt
+
+
+def am_distance_counter(A, B):
+    """Compute the distance between two sets of intervals as used in the area metric.
+
+    notes:
+        It is essentially doing:
+
+        def f(a, b, c, d):
+            return np.maximum.reduce([c - b, a - d, 0])
+
+    """
+    a, b = A[:, 0], A[:, 1]
+    c, d = B[:, 0], B[:, 1]
+    return np.maximum.reduce([c - b, a - d, np.zeros_like(a)])
+
+
+def function_succeeds(f, *args, **kwargs):
+    try:
+        f(*args, **kwargs)
+        return True
+    except Exception:
+        return False
+
+
+def area_metric_pbox(a: Pbox, b: Pbox):
+    """when a and b are both Pboxes"""
+    # diff = endpoint_distance(a.to_numpy(), b.to_numpy())  # old version busted by Scott
+    diff = am_distance_counter(a.to_numpy(), b.to_numpy())
+    return np.trapz(y=diff, x=a.p_values)
+
+
+def area_metric_pbox_diff(a: Pbox, b: Pbox):
+    """when a and b are both Pboxes"""
+    # diff = endpoint_distance(a.to_numpy(), b.to_numpy())  # old version busted by Scott
+    diff = am_distance_counter(a.to_numpy(), b.to_numpy())
+    return diff
+
+
+def area_metric_sample(a: ArrayLike, b: ArrayLike):
+    return sps.wasserstein_distance(a, b)
+
+
+#! not in use.
+def area_metric_np_numbers(a, b):
+    """when a and b are both numpy arrays of scalar numbers, compute the area metric accordingly"""
+    assert np.isscalar(a) and np.isscalar(b), "Both a and b must be scalar numbers."
+    return abs(a - b)
+
+
+def area_metric_number(a: Pbox | Number, b: Pbox | Number) -> float:
+    """if any of a or b is a number, compute area metric accordingly"""
+    from pyuncertainnumber import pba
+
+    if isinstance(a, Number) and isinstance(b, Number):
+        return abs(a - b)
+    if isinstance(a, Number):
+        a, b = b, a  # swap so b is the number
+    if isinstance(a, Pbox) and a.degenerate:
+        return area_metric_ecdf(a.left, b, a.p_values)
+    if isinstance(a, Pbox) and (not a.degenerate):
+        # make b a Pbox
+        b = pba.I(b).to_pbox()
+        return area_metric_pbox(a, b)
+
+
+def area_metric(a: Number | Pbox | ArrayLike, b: Number | Pbox | ArrayLike) -> float:
+    """Compute the area metric between two objects.
+
+    note:
+        top-level function to compute area metric between any two objects
+    """
+    if isinstance(a, Number) or isinstance(b, Number):
+        return area_metric_number(a, b)
+    if isinstance(a, Pbox) and isinstance(b, Pbox):
+        if a.degenerate and b.degenerate:
+            return area_metric_ecdf(a.left, b.left, a.p_values)
+        elif function_succeeds(a.imp, b):
+            return 0.0
+        else:
+            return area_metric_pbox(a, b)
+    if isinstance(a, (np.ndarray, list)) and isinstance(b, (np.ndarray, list)):
+        return area_metric_sample(a, b)
+    elif (isinstance(a, Pbox) and isinstance(b, np.ndarray)) or (
+        isinstance(a, np.ndarray) and isinstance(b, Pbox)
+    ):
+        # make a a Pbox and b a sample anyway
+        if not isinstance(a, Pbox):
+            a, b = b, a
+
+        # b has to be a scalar sample
+        b = np.squeeze(b).item()
+        return area_metric_number(a, b)
+    else:
+        raise NotImplementedError("Area metric not implemented for these types.")
+
+
+def double_metric(p: Number | Pbox | Interval, o: Number | Pbox | Interval):
+    """Double metric for two uncertain numbers.
+
+    args:
+        p: a prediction uncertain number (Pbox)
+        o: an observation uncertain number (Pbox or scalar)
+
+    note:
+        Typical case is for validation between prediction and observation where both are uncertain numbers.
+
+    """
+    if isinstance(p, Number):
+        p = Interval(p)
+
+    if isinstance(o, Number):
+        o = Interval(o)
+
+    return area_metric(p.left, o.left), area_metric(p.right, o.right)
+
+
+def conformal_double_metric(p: Number | Pbox | Interval, o: Number | Pbox | Interval):
+    """Propsed conformal version of the double metric, which takes the maximum of the two area metrics."""
+    return max(double_metric(p, o))
+
+
+# * --------------------------- area metric hints plot
+
+
+def am_diff_register(A, B, debug=False):
+    """Register the distance and return a structured array with fields:
+
+    returns:
+        In each tuple of the output array:
+        - distance: float (max of c-b, a-d, 0)
+        - x1: first endpoint (c or a, or 0 if 0 wins)
+        - x2: second endpoint (b or d, or 0 if 0 wins)
+    """
+    A = np.asarray(A)
+    B = np.asarray(B)
+
+    # Expect shape (N, 2): [:,0]=start=a/c, [:,1]=end=b/d
+    a, b = A[:, 0], A[:, 1]
+    c, d = B[:, 0], B[:, 1]
+
+    c_minus_b = c - b
+    a_minus_d = a - d
+    zeros = np.zeros_like(a, dtype=np.result_type(a, b, c, d, float))
+
+    # Stack and argmax exactly mirrors "max(c-b, a-d, 0)" with deterministic tie-breaking.
+    stacked = np.stack([c_minus_b, a_minus_d, zeros], axis=1)
+    max_indices = np.argmax(stacked, axis=1)
+    distances = stacked[np.arange(len(a)), max_indices]
+
+    # Structured result
+    result = np.zeros(len(a), dtype=[("distance", "f8"), ("x1", "f8"), ("x2", "f8")])
+    result["distance"] = distances
+
+    mask_cb = max_indices == 0
+    mask_ad = max_indices == 1
+    mask_0 = max_indices == 2
+
+    result["x1"][mask_cb] = c[mask_cb]
+    result["x2"][mask_cb] = b[mask_cb]
+
+    result["x1"][mask_ad] = a[mask_ad]
+    result["x2"][mask_ad] = d[mask_ad]
+
+    result["x1"][mask_0] = 0.0
+    result["x2"][mask_0] = 0.0
+
+    if debug:
+        print("a:", a)
+        print("b:", b)
+        print("c:", c)
+        print("d:", d)
+        print("c-b:", c_minus_b)
+        print("a-d:", a_minus_d)
+        print("stacked:\n", stacked)
+        print("argmax:", max_indices)
+        print("distances:", distances)
+        print("result:", result)
+
+    return result
+
+
+def intervals_from_res(res):
+    """
+    From a structured array `res` with fields: 'distance', 'x1', 'x2',
+    return:
+      - mask: boolean mask where distance != 0
+      - intervals: (N, 2) array of sorted [lo, hi] endpoints for rows where mask is True
+    """
+    mask = res["distance"] != 0
+    x1 = res["x1"][mask]
+    x2 = res["x2"][mask]
+    lo = np.minimum(x1, x2)
+    hi = np.maximum(x1, x2)
+    intervals = np.stack([lo, hi], axis=1)
+    return mask, intervals
+
+
+def plot_intervals_from_res(
+    res, p, *, show_points=False, title=None, include_ties=False, ax=None
+):
+    """Plot horizontal intervals from `res` at heights given by `p`.
+
+    args
+        res (ArrayLike) : Structured array with fields ('distance', 'x1', 'x2').
+
+        p (ArrayLike) : 1D array of same length as `res`, giving y-coordinate (height) of each interval.
+
+        show_points (Boolean): If True, shows markers at interval endpoints.
+
+        title (str): Plot title. Optional
+
+        include_ties (bool): If True, also include intervals where distance == 0 but argmax picked c-b or a-d.
+
+        ax (matplotlib.axes.Axes) :  Axis to plot on. If None, a new figure and axis are created. Optional
+
+    returns
+        ax (matplotlib.axes.Axes): The matplotlib axis used for plotting.
+    """
+    res = np.asarray(res)
+    p = np.asarray(p)
+    if res.shape[0] != p.shape[0]:
+        raise ValueError("p must have the same number of rows as res")
+
+    # Select rows to plot
+    if include_ties:
+        mask = ~((res["x1"] == 0) & (res["x2"] == 0))
+    else:
+        mask = res["distance"] > 0
+
+    if ax is None:
+        fig, ax = plt.subplots()
+
+    if not np.any(mask):
+        ax.set_xlabel("x")
+        ax.set_ylabel("p (height)")
+        if title:
+            ax.set_title(title)
+        return ax
+
+    x1 = res["x1"][mask]
+    x2 = res["x2"][mask]
+    y = p[mask]
+
+    lo = np.minimum(x1, x2)
+    hi = np.maximum(x1, x2)
+
+    # Draw intervals
+    for xi0, xi1, yi in zip(lo, hi, y):
+        ax.plot([xi0, xi1], [yi, yi], color="lavender")  # horizontal segment
+        if show_points:
+            ax.plot([xi0, xi1], [yi, yi], "o", color="C0")
+
+    ax.set_xlabel("x")
+    ax.set_ylabel("p (height)")
+    if title:
+        ax.set_title(title)
+
+    # Set limits dynamically based on data
+    ax.set_xlim(lo.min() - 0.1, hi.max() + 0.1)
+    ax.set_ylim(y.min() - 0.1, y.max() + 0.1)
+
+    return ax
+
+
+def integrate_distance(res, p):
+    """
+    Integrate distance vs p with the trapezoidal rule,
+    matching: np.trapz(y=diff, x=p)
+
+    No masking; uses all rows. Sorts by p to avoid signed/ordering issues.
+    """
+    res = np.asarray(res)
+    p = np.asarray(p)
+    if res.shape[0] != p.shape[0]:
+        raise ValueError("`p` must have the same length as `res`.")
+
+    order = np.argsort(p)
+    y = res["distance"][order].astype(float, copy=False)
+    x = p[order].astype(float, copy=False)
+
+    return np.trapz(y=y, x=x)
diff --git a/tests/test_double_metric.py b/tests/test_double_metric.py
new file mode 100644
index 00000000..4fee6927
--- /dev/null
+++ b/tests/test_double_metric.py
@@ -0,0 +1,41 @@
+from pyuncertainnumber import pba
+from pyuncertainnumber.validation.area_metric import (
+    double_metric,
+    conformal_double_metric,
+)
+
+
+def test_double_metric():
+    x_left = 7
+    y_left = pba.I(14, 19)
+
+    x_middle = pba.I(4, 9)
+    y_middle = pba.I(13, 18)
+
+    x_right = pba.I(3, 11)
+    y_right = pba.I(8, 17)
+
+    for a, b in [(x_left, y_left), (x_middle, y_middle), (x_right, y_right)]:
+        print(double_metric(a, b))
+
+    assert double_metric(x_left, y_left) == (7, 12)
+    assert double_metric(x_middle, y_middle) == (9, 9)
+    assert double_metric(x_right, y_right) == (5, 6)
+
+
+def test_conformal_double_metric():
+    x_left = 7
+    y_left = pba.I(14, 19)
+
+    x_middle = pba.I(4, 9)
+    y_middle = pba.I(13, 18)
+
+    x_right = pba.I(3, 11)
+    y_right = pba.I(8, 17)
+
+    for a, b in [(x_left, y_left), (x_middle, y_middle), (x_right, y_right)]:
+        print("conformal version", conformal_double_metric(a, b))
+
+    assert conformal_double_metric(x_left, y_left) == 12
+    assert conformal_double_metric(x_middle, y_middle) == 9
+    assert conformal_double_metric(x_right, y_right) == 6
diff --git a/tests/test_numpy_binary_compatability.py b/tests/test_numpy_binary_compatability.py
new file mode 100644
index 00000000..e69de29b