2022
DOI: 10.21203/rs.3.rs-1348136/v1
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A note on averaging prediction accuracy, Green’s functions and other kernels

Abstract: We present the mathematical context of the predictive accuracy index and then introduce the definition of integral average transform. We establish the relation of our definition with two variables kernels K ( y , x ). As an example of an application we show that integrating against the fundamental solution of the Laplace operator, that is, solving the Poisson equation, can be re-interpreted as an integral of averages of the forcing term over balls. As a result, we obtained a novel integral representation… Show more

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Cited by 2 publications
(2 citation statements)
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“…Relevant statistical metrics are summarized in White and Hunt (2022). Crime analysts should avoid solely using PAI, as it is not a reliable metric (Joshi et al 2021;Galvis, Hernández-Romero, and Gómez 2022). Instead, we suggest analysts use PEI and/or PEI* as outlined here and look for better metrics as they are developed.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…Relevant statistical metrics are summarized in White and Hunt (2022). Crime analysts should avoid solely using PAI, as it is not a reliable metric (Joshi et al 2021;Galvis, Hernández-Romero, and Gómez 2022). Instead, we suggest analysts use PEI and/or PEI* as outlined here and look for better metrics as they are developed.…”
Section: Discussionmentioning
confidence: 99%
“…To address various study areas, one study developed the penalized predictive accuracy index (PPAI), where the area ratio is penalized (Joshi et al 2021). However, mathematicians have shown that PAI and its adaptions are still susceptible to artificial manipulation since PAI increases as subspace size (e.g., grid cell height, street length) decreases (Galvis, Hernández-Romero, and Gómez 2022). Hunt 2016 demonstrates this fact by explicitly showing that from a meso-to macro-place perspective, PAI is sensitive to grid cell size.…”
Section: 𝑛′mentioning
confidence: 99%