DataIntervals: Robust Interval Estimation Engine (Machine Gnostics)¶

The DataIntervals class provides robust, adaptive, and diagnostic interval estimation for Gnostic Distribution Function (GDF) classes such as ELDF, EGDF, QLDF, and QGDF. It estimates meaningful data intervals (tolerance, typical intervals) based on the behavior of the GDF's central parameter (Z0) as the data is extended, enforcing ordering constraints and providing detailed diagnostics.

Overview¶

DataIntervals is designed for advanced interval analysis in scientific, engineering, and reliability applications. It adaptively scans the data domain, recomputes the GDF as needed, and extracts intervals that reflect the true structure of the data. The class enforces natural ordering constraints and provides comprehensive diagnostics and visualization.

Adaptive Search: Dense scanning near Z0, sparse near boundaries for efficiency and accuracy.
Robustness: Optional GDF recomputation and gnostic filtering for outlier resistance.
Diagnostics: Tracks warnings, errors, and parameter settings.
Ordering Constraint: Ensures intervals satisfy ZL < Z0L < Z0 < Z0U < ZU.
Visualization: Plots Z0 variation, intervals, and data coverage.

Key Features¶

Adaptive interval scanning and estimation
Robust to outliers and noise
Supports ELDF, EGDF, QLDF, QGDF
Ordering constraint enforcement
Detailed diagnostics and error tracking
Visualization of Z0 variation and intervals
Memory-efficient with optional flushing

Parameters¶

Parameter	Type	Default	Description
`gdf`	ELDF/EGDF/QLDF/QGDF	required	Fitted GDF object to analyze
`n_points`	int	100	Number of search points for interval estimation
`dense_zone_fraction`	float	0.4	Fraction of domain near Z0 for dense search
`dense_points_fraction`	float	0.7	Fraction of points in dense zone
`convergence_window`	int	15	Window size for convergence detection
`convergence_threshold`	float	1e-6	Threshold for Z0 convergence
`min_search_points`	int	30	Minimum search points before checking convergence
`boundary_margin_factor`	float	0.001	Margin to avoid searching at boundaries
`extrema_search_tolerance`	float	1e-6	Tolerance for detecting extrema in Z0 variation
`gdf_recompute`	bool	False	Recompute GDF for each candidate datum
`gnostic_filter`	bool	False	Apply gnostic clustering to filter outlier Z0 values
`catch`	bool	True	Store warnings/errors internally
`verbose`	bool	False	Print detailed progress and diagnostics
`flush`	bool	False	Flush memory after fitting to save resources

Attributes¶

ZL: floatLower bound of the typical data interval
Z0L: floatLower bound of the tolerance interval (Z0-based)
Z0: floatCentral value (Z0) of the original GDF
Z0U: floatUpper bound of the tolerance interval (Z0-based)
ZU: floatUpper bound of the typical data interval
tolerance_interval: floatWidth of the tolerance interval (Z0U - Z0L)
typical_data_interval: floatWidth of the typical data interval (ZU - ZL)
ordering_valid: boolWhether the ordering constraint (ZL < Z0L < Z0 < Z0U < ZU) is satisfied
params: dictDictionary of parameters, warnings, errors, and results
search_results: dict Raw search results for datum values and corresponding Z0s

Methods¶

`fit(plot=False)`¶

Runs the interval estimation process. Optionally plots results.

plot: bool (optional) If True, automatically plot the interval analysis results after fitting.

Returns: None (results stored in attributes and params)

`results()`¶

Returns a dictionary of estimated interval results and bounds.

Returns: dict — Contains keys such as 'LB', 'LSB', 'DLB', 'LCB', 'LSD', 'ZL', 'Z0L', 'Z0', 'Z0U', 'ZU', 'USD', 'UCB', 'DUB', 'USB', 'UB'

-**LB**: Lower Bound
The practical lower limit for the interval (may be set by user or inferred).

-**LSB**: Lower Sample (Membership) Bound
The lowest value for which data is homogeneous.

-**DLB**: Data Lower Bound
The absolute minimum value present in the data.

-**LCB**: Lower Cluster Bound
The lower edge of the main data cluster.

-**LSD**: Lower Standard Deviation Bound
The lowest value as per gnostic standard deviation.

-**ZL**: Z0 Lower Interval
The lower bound of the typical interval.

-**Z0L**: Z0 Lower Bound
The lower bound of the tolerance interval.

-**Z0**: Central Value (Gnostic Mean)
The central parameter of the distribution (gnostic mean).

-**Z0U**: Z0 Upper Bound
The upper bound of the tolerance interval.

-**ZU**: Z0 Upper Interval
The upper bound of the typical interval.

-**USD**: Upper Support/Domain Bound
The highest value in the support or domain of the fitted distribution.

-**UCB**: Upper Cluster Bound
The upper edge of the main data cluster.

-**DUB**: Data Upper Bound
The absolute maximum value present in the data.

-**USB**: Upper Sample (Membership) Bound
The highest value for which data is homogeneous (membership analysis).

-**UB**: Upper Bound
The practical upper limit for the interval (may be set by user or inferred).

`plot_intervals(figsize=(12, 8))`¶

Plots the Z0 variation and estimated intervals.

figsize: tuple (default: (12, 8)) Size of the matplotlib figure

Returns: None (displays plot)

`plot(figsize=(12, 8))`¶

Plots the GDF, PDF, and intervals on the data domain.

figsize: tuple (default: (12, 8)) Size of the matplotlib figure

Returns: None (displays plot)

Example Usage¶

import numpy as np
from machinegnostics.magcal import ELDF, DataIntervals

data = np.array([ -13.5, 0, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10.])

# ELDF
eld = ELDF()
eld.fit(data)

di = DataIntervals(eld, n_points=200, gdf_recompute=True, gnostic_filter=True, verbose=True)
di.fit()

print(di.results())
di.plot_intervals()
di.plot()

Notes¶

For best results, use with ELDF or QLDF and set 'wedf=False' in the GDF.
Increasing 'n_points' improves accuracy but increases computation time.
Enable 'gdf_recompute' and 'gnostic_filter' for maximum robustness, especially with noisy data.
The class is designed for research and diagnostic use; adjust parameters for your data and application.
Ordering constraint is enforced for interval validity; warnings are issued if violated.
All warnings and errors are stored in the params attribute for later inspection.

Author: Nirmal Parmar
Date: 2025-09-24