From c04fb0717608ab35fc10e16342436cd2f067585a Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Mon, 5 Jan 2026 21:18:11 +0000 Subject: [PATCH 01/20] added `filter_hdi_bounds` function --- src/pyuncertainnumber/calibration/tmcmc.py | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) diff --git a/src/pyuncertainnumber/calibration/tmcmc.py b/src/pyuncertainnumber/calibration/tmcmc.py index ed0f9ae..afaa0c9 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__low, hdi__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. From 32e8a28e03077ce5157c4c0a11ec990eefb0f27b Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Wed, 7 Jan 2026 11:23:05 +0000 Subject: [PATCH 02/20] postpone the import of jax in specific functions --- .../propagation/taylor_expansion.py | 13 ++++++++----- 1 file changed, 8 insertions(+), 5 deletions(-) diff --git a/src/pyuncertainnumber/propagation/taylor_expansion.py b/src/pyuncertainnumber/propagation/taylor_expansion.py index 5aceb1b..6f420e0 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) From 0670684e982e54dd220a95a60808cbb4a50b583f Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Sat, 10 Jan 2026 16:06:57 +0000 Subject: [PATCH 03/20] mark a bug to be fixed. --- src/pyuncertainnumber/pba/intervals/intervalOperators.py | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/src/pyuncertainnumber/pba/intervals/intervalOperators.py b/src/pyuncertainnumber/pba/intervals/intervalOperators.py index 8e053c3..185aa6d 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 From 6f8a7c1e4d5e27bf16b46a175d53a1c8961c7ab2 Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Tue, 3 Feb 2026 09:42:03 +0000 Subject: [PATCH 04/20] added a TODO in docstring --- src/pyuncertainnumber/pba/aggregation.py | 1 + 1 file changed, 1 insertion(+) diff --git a/src/pyuncertainnumber/pba/aggregation.py b/src/pyuncertainnumber/pba/aggregation.py index 7a49eda..b7c5655 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], *, From 7c7e77d418eece09f881cba3c0a32795c09536f2 Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Tue, 3 Feb 2026 11:18:05 +0000 Subject: [PATCH 05/20] updated the numpy compatbility on binary ops for p-boxes --- src/pyuncertainnumber/pba/pbox_abc.py | 29 ++++++++++++++++++++++-- tests/test_numpy_binary_compatability.py | 0 2 files changed, 27 insertions(+), 2 deletions(-) create mode 100644 tests/test_numpy_binary_compatability.py diff --git a/src/pyuncertainnumber/pba/pbox_abc.py b/src/pyuncertainnumber/pba/pbox_abc.py index 18224e9..2e86d73 100644 --- a/src/pyuncertainnumber/pba/pbox_abc.py +++ b/src/pyuncertainnumber/pba/pbox_abc.py @@ -982,9 +982,34 @@ 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__"), # only if you define these + np.minimum: ("__min__", "__rmin__"), # only if you define these + } + + 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: diff --git a/tests/test_numpy_binary_compatability.py b/tests/test_numpy_binary_compatability.py new file mode 100644 index 0000000..e69de29 From 1fc2f233816c3303f5da82306c298ad4afb7b9e5 Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Tue, 3 Feb 2026 13:16:02 +0000 Subject: [PATCH 06/20] a fix for Numpy compatibility with Interval --- src/pyuncertainnumber/pba/intervals/number.py | 27 +++++++++++++++++++ src/pyuncertainnumber/pba/pbox_abc.py | 4 +-- 2 files changed, 29 insertions(+), 2 deletions(-) diff --git a/src/pyuncertainnumber/pba/intervals/number.py b/src/pyuncertainnumber/pba/intervals/number.py index 1152615..7225920 100644 --- a/src/pyuncertainnumber/pba/intervals/number.py +++ b/src/pyuncertainnumber/pba/intervals/number.py @@ -467,6 +467,33 @@ 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 2e86d73..559d15d 100644 --- a/src/pyuncertainnumber/pba/pbox_abc.py +++ b/src/pyuncertainnumber/pba/pbox_abc.py @@ -992,8 +992,8 @@ def __array_ufunc__(self, ufunc, method, *inputs, **kwargs): np.true_divide: ("__truediv__", "__rtruediv__"), np.floor_divide: ("__floordiv__", "__rfloordiv__"), np.power: ("__pow__", "__rpow__"), - np.maximum: ("__max__", "__rmax__"), # only if you define these - np.minimum: ("__min__", "__rmin__"), # only if you define these + np.maximum: ("__max__", "__rmax__"), + np.minimum: ("__min__", "__rmin__"), } if ufunc in binary and len(inputs) == 2: From f447e4f6bc832607a3e4bc968e3c4d1905869c0b Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Mon, 9 Feb 2026 09:42:10 +0000 Subject: [PATCH 07/20] update the function `plot_probability_bound` with more controls on styles --- src/pyuncertainnumber/pba/pbox_abc.py | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/src/pyuncertainnumber/pba/pbox_abc.py b/src/pyuncertainnumber/pba/pbox_abc.py index 559d15d..da19a7d 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): From 9ae3516fa83d764c54126b7e20b62793fb4c8616 Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Mon, 9 Feb 2026 09:43:32 +0000 Subject: [PATCH 08/20] housekeeping --- src/pyuncertainnumber/pba/core.py | 14 ++------------ 1 file changed, 2 insertions(+), 12 deletions(-) diff --git a/src/pyuncertainnumber/pba/core.py b/src/pyuncertainnumber/pba/core.py index e85c93c..bb83769 100644 --- a/src/pyuncertainnumber/pba/core.py +++ b/src/pyuncertainnumber/pba/core.py @@ -2,12 +2,13 @@ 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 bisect import bisect_left +import numpy as np +import matplotlib.pyplot as plt class Joint(ABC): @@ -226,10 +227,6 @@ def am_diff_register(A, B, debug=False): 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', @@ -246,10 +243,6 @@ def intervals_from_res(res): 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 ): @@ -317,9 +310,6 @@ def plot_intervals_from_res( return ax -import numpy as np - - def integrate_distance(res, p): """ Integrate distance vs p with the trapezoidal rule, From 0bef3d67947a91451754c3651630b61e1ddf100b Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Mon, 9 Feb 2026 10:05:37 +0000 Subject: [PATCH 09/20] left and right of Interval now will return scalars where applicable --- src/pyuncertainnumber/pba/intervals/number.py | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/src/pyuncertainnumber/pba/intervals/number.py b/src/pyuncertainnumber/pba/intervals/number.py index 7225920..b861e08 100644 --- a/src/pyuncertainnumber/pba/intervals/number.py +++ b/src/pyuncertainnumber/pba/intervals/number.py @@ -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): From f8e1d0c3ff788e62fd04783dccdb0c3ba14a36a2 Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Mon, 9 Feb 2026 11:00:11 +0000 Subject: [PATCH 10/20] added "double_metric" and "conformal_double_metric" to the validation module --- src/pyuncertainnumber/pba/core.py | 33 +++++++++++++++++++ src/pyuncertainnumber/pba/intervals/number.py | 2 +- 2 files changed, 34 insertions(+), 1 deletion(-) diff --git a/src/pyuncertainnumber/pba/core.py b/src/pyuncertainnumber/pba/core.py index bb83769..f2505a1 100644 --- a/src/pyuncertainnumber/pba/core.py +++ b/src/pyuncertainnumber/pba/core.py @@ -6,6 +6,7 @@ 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 @@ -120,6 +121,13 @@ 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 @@ -521,3 +529,28 @@ def slide_pbox_towards_scalar(a, b): d2 = proposal_dd return Staircase(a.left - d1, a.right + d2) + + +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)) diff --git a/src/pyuncertainnumber/pba/intervals/number.py b/src/pyuncertainnumber/pba/intervals/number.py index b861e08..1fdcd93 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 From a12d174bca0d7e3e87acfce1de1900511ad1df97 Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Mon, 9 Feb 2026 16:57:54 +0000 Subject: [PATCH 11/20] added test file for double metric --- tests/test_double_metric.py | 38 +++++++++++++++++++++++++++++++++++++ 1 file changed, 38 insertions(+) create mode 100644 tests/test_double_metric.py diff --git a/tests/test_double_metric.py b/tests/test_double_metric.py new file mode 100644 index 0000000..ae4db2e --- /dev/null +++ b/tests/test_double_metric.py @@ -0,0 +1,38 @@ +from pyuncertainnumber import pba +from pyuncertainnumber.pba.core 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 From 8aada6835786ef96a64008b98807f2564bf4362c Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Mon, 2 Mar 2026 15:30:06 +0000 Subject: [PATCH 12/20] fix an issue of Interval div for numpy --- src/pyuncertainnumber/pba/intervals/number.py | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) diff --git a/src/pyuncertainnumber/pba/intervals/number.py b/src/pyuncertainnumber/pba/intervals/number.py index 1fdcd93..2de3219 100644 --- a/src/pyuncertainnumber/pba/intervals/number.py +++ b/src/pyuncertainnumber/pba/intervals/number.py @@ -403,9 +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): From 9800bdc3742f47f7eee463554a86e30dd3c1f106 Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Mon, 2 Mar 2026 15:30:31 +0000 Subject: [PATCH 13/20] Added sampling precise deviates from a p-box --- src/pyuncertainnumber/pba/pbox_abc.py | 20 ++++++++++++++++++++ 1 file changed, 20 insertions(+) diff --git a/src/pyuncertainnumber/pba/pbox_abc.py b/src/pyuncertainnumber/pba/pbox_abc.py index da19a7d..539bfdb 100644 --- a/src/pyuncertainnumber/pba/pbox_abc.py +++ b/src/pyuncertainnumber/pba/pbox_abc.py @@ -1062,6 +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 From a86e0c8495dbf5370a4bb92584bb84291e0c47c6 Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Mon, 9 Mar 2026 12:33:31 +0000 Subject: [PATCH 14/20] Moved area metric related to validation module --- src/pyuncertainnumber/__init__.py | 2 +- src/pyuncertainnumber/pba/__init__.py | 1 - src/pyuncertainnumber/pba/core.py | 282 ----------------- .../validation/area_metric.py | 289 ++++++++++++++++++ tests/test_double_metric.py | 5 +- 5 files changed, 294 insertions(+), 285 deletions(-) create mode 100644 src/pyuncertainnumber/validation/area_metric.py diff --git a/src/pyuncertainnumber/__init__.py b/src/pyuncertainnumber/__init__.py index c3b9405..7df9833 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/pba/__init__.py b/src/pyuncertainnumber/pba/__init__.py index ba3bb43..c075dd4 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/core.py b/src/pyuncertainnumber/pba/core.py index f2505a1..03f6252 100644 --- a/src/pyuncertainnumber/pba/core.py +++ b/src/pyuncertainnumber/pba/core.py @@ -80,263 +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) - - -#! 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.") - - -# * --------------------------- 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) - - # 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 @@ -529,28 +272,3 @@ def slide_pbox_towards_scalar(a, b): d2 = proposal_dd return Staircase(a.left - d1, a.right + d2) - - -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)) diff --git a/src/pyuncertainnumber/validation/area_metric.py b/src/pyuncertainnumber/validation/area_metric.py new file mode 100644 index 0000000..b0001a8 --- /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 index ae4db2e..4fee692 100644 --- a/tests/test_double_metric.py +++ b/tests/test_double_metric.py @@ -1,5 +1,8 @@ from pyuncertainnumber import pba -from pyuncertainnumber.pba.core import double_metric, conformal_double_metric +from pyuncertainnumber.validation.area_metric import ( + double_metric, + conformal_double_metric, +) def test_double_metric(): From f0a77d3a012e2e586b83b2e6c4a80d31f4c3f9af Mon Sep 17 00:00:00 2001 From: leslieDLcy Date: Mon, 9 Mar 2026 13:34:34 +0000 Subject: [PATCH 15/20] update the docs to include guides on VVUQ --- 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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. @@ -35,6 +37,29 @@ Validation is a process of determining the degree to which a (non-deterministic) 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 of VVUQ on aerodynamics diff --git a/docs/source/tutorials/validation_assessment.ipynb b/docs/source/tutorials/validation_assessment.ipynb new file mode 100644 index 0000000..95938a2 --- /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": [ + "

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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": [
+       "
\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": [
+       "
\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": [
+       "
\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": [
+       "
\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
+}

From 225911997908de98d08080dcfee84d1d17d5541d Mon Sep 17 00:00:00 2001
From: leslieDLcy 
Date: Mon, 9 Mar 2026 16:41:22 +0000
Subject: [PATCH 17/20] update the doc

---
 docs/source/guides/vvuq.md     | 4 ++--
 docs/source/tutorials/index.md | 9 +++++++++
 2 files changed, 11 insertions(+), 2 deletions(-)

diff --git a/docs/source/guides/vvuq.md b/docs/source/guides/vvuq.md
index 58fb2d6..61f3376 100644
--- a/docs/source/guides/vvuq.md
+++ b/docs/source/guides/vvuq.md
@@ -61,14 +61,14 @@ Predictive capability
 
 
 
-## An open challenge of VVUQ on aerodynamics
+## 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: 400px
+:width: 600px
 :align: center
 
 Problem statement of the AIAA Second Uncertainty Quantification Challenge Problem for Aerodynamics
diff --git a/docs/source/tutorials/index.md b/docs/source/tutorials/index.md
index 7afd81b..e5b7de4 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.
+:::
+
 ::::

From 4f9d0d88a96f64a594f7fcfea2eb4fe907cb5ee2 Mon Sep 17 00:00:00 2001
From: leslieDLcy 
Date: Mon, 9 Mar 2026 17:11:31 +0000
Subject: [PATCH 18/20] fixes typos

---
 docs/source/tutorials/uncertainty_propagation.ipynb | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/docs/source/tutorials/uncertainty_propagation.ipynb b/docs/source/tutorials/uncertainty_propagation.ipynb
index f0ee416..8b3b21b 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"
    ]
   },
   {

From 14afdaaefb68bae86f1f8cf8f816ac81a45ee226 Mon Sep 17 00:00:00 2001
From: leslieDLcy 
Date: Mon, 9 Mar 2026 17:11:57 +0000
Subject: [PATCH 19/20] new version 0.0.15

---
 pyproject.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pyproject.toml b/pyproject.toml
index c3deee3..884925e 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 = "0.1.5"
 
 [project.optional-dependencies]
 test = [

From 2061c317178655ae6bf7e896ce70f483297f91f3 Mon Sep 17 00:00:00 2001
From: leslieDLcy 
Date: Mon, 9 Mar 2026 17:15:21 +0000
Subject: [PATCH 20/20] correct typo V0.0.15

---
 pyproject.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pyproject.toml b/pyproject.toml
index 884925e..1929302 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -38,7 +38,7 @@ maintainers = [
 name = "pyuncertainnumber"
 readme = "README.md"
 requires-python = ">= 3.11"
-version = "0.1.5"
+version = "0.1.15"
 
 [project.optional-dependencies]
 test = [