{ "cells": [ { "cell_type": "markdown", "id": "5968442e", "metadata": {}, "source": [ "(free_empirical_information)=\n", "# Characterise the uncertainty given what you know" ] }, { "cell_type": "markdown", "id": "ba6670a1", "metadata": {}, "source": [ "It is vital to know what you do not know in terms of trustworthy modelling and predictions, suggesting that all models are wrong but some are useful on the condition of knowing their assumptions and applicability, hence building the credibility of the computational results. It is often a challenge, in modelling complex physical phenomena, to construct mathematical models in a quantitative manner, on one hand, without ignoring significant information and, on the other hand, without introducing unwarranted assumptions. The bottleneck is usually the limited information in terms of both knowledge and experimental data." ] }, { "cell_type": "markdown", "id": "dc01003d", "metadata": {}, "source": [ "
\n", " \n", "
Empirical knowledge serving as constraints in characterising an uncertain number
\n", "
" ] }, { "cell_type": "markdown", "id": "3a07ef32", "metadata": {}, "source": [ "Often there is little empirical information pertaining some parameters of a mathematical model. A faithful characterisation entails that all of the available statistical information should be utilised but without introducing any extra assumptions beyond what are empirically justified.\n", "\n", "The bounding approach presents as a natural reflection of the state of epistemic uncertainty, which tightens the bounds with extra empirical information. \n", "\n", "\n", "Conveniently, pyuncertainnumber provides a bespoke constructor to facilitate the faithful characterisation of uncertain quantities based on known information, which includes limits on quantiles, information about summary statistics such as mean, mode or variance, and qualitative information about distribution shape, such as whether it is symmetric or unimodal." ] }, { "cell_type": "code", "execution_count": 1, "id": "d87eb224", "metadata": {}, "outputs": [], "source": [ "import pyuncertainnumber as pun" ] }, { "cell_type": "markdown", "id": "f45dd671", "metadata": {}, "source": [ "For example, the level of information specifies constraints to accordingly construct the uncertain number, which may start as little as a coarse estimated range" ] }, { "cell_type": "code", "execution_count": 2, "id": "3c7fafb5-2a58-4b0e-91ec-b4d1171fddf2", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# specify available empirical information as constraints\n", "pun.known_properties(minimum=-1, maximum=4).display()" ] }, { "cell_type": "markdown", "id": "081a4a1a", "metadata": {}, "source": [ "further one may have statistical moment information, for example the mean value from domain experts" ] }, { "cell_type": "code", "execution_count": 3, "id": "94e4a5ee", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pun.known_properties(minimum=-1, maximum=4., mean=1).display()" ] }, { "cell_type": "markdown", "id": "39114a35", "metadata": {}, "source": [ "beyond the central tendency(i.e. mean), one may also have the variability information" ] }, { "cell_type": "code", "execution_count": 4, "id": "17c027cb", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pun.known_properties(minimum=-1, maximum=4., mean=1, var=0.25).display()" ] }, { "cell_type": "markdown", "id": "d982769c", "metadata": {}, "source": [ "Further, expert eclicitation may have strong beliefs as to the knowledge of shape such that uncertainties can be pinched to a precise distribution." ] }, { "cell_type": "markdown", "id": "c8a9bcfd", "metadata": {}, "source": [ "```{tip}\n", "The empirical knowledge naturally serves as constraints to contract the bounds associated with an uncertain number. However, it should be noted that in some cases constraints may not converge, which suggests that the applied knoweledge may contradict with each other. For example, if an expert claims the distribution shape to be lognormal, this shape may not be consistent with the other information.\n", "```" ] }, { "cell_type": "code", "execution_count": 7, "id": "1e31bf49", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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