Interpretable Transformed ANOVA Approximation on the Example of the Prevention of Forest Fires

Potts, Daniel; Schmischke, Michael

doi:10.3389/fams.2022.795250

Cited by 6 publications

(4 citation statements)

References 23 publications

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“…For the examples of the Chebyshev density, which is a special case of our examples, [20, Section 10.3], [13] propose the Chebyshev polynomials η k pyq " cospk arccospyqq as basis in L 2 pr´1, 1s d , ̺q where the inner function coincides with our transformation. The case that the samples are normally distributed was considered in [30]. This approach coincides with our transformation.…”

Section: Related Work and Other Approachesmentioning

confidence: 99%

Variable Transformations in combination with Wavelets and ANOVA for high-dimensional approximation

Lippert¹,

Potts²

2022

Preprint

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We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet basis on the torus. With a variable transformation we are able to transform the approximation rates and fast algorithms from the torus to other domains. We perform and analyze scattered-data approximation for smooth but arbitrary density functions by using a least squares method. The corresponding system matrix is sparse due to the compact support of the wavelets, which leads to a significant acceleration of the matrix vector multiplication. For non-periodic functions we propose a new extension method. A proper choice of the extension parameter together with the piece-wise polynomial Chui-Wang wavelets extends the functions appropriately. In every case we are able to bound the approximation error with high probability. Additionally, if the function has low effective dimension (i.e. only interactions of few variables), we qualitatively determine the variable interactions and omit ANOVA terms with low variance in a second step in order to decrease the approximation error. This allows us to suggest an adapted model for the approximation. Numerical results show the efficiency of the proposed method.

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Section: Related Work and Other Approachesmentioning

confidence: 99%

Variable Transformations in combination with Wavelets and ANOVA for high-dimensional approximation

Lippert¹,

Potts²

2022

Preprint

Self Cite

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“…2 There are some variations of this analysis, and they depend mainly on whether the measurements are repeated or not (independent measures ANOVA and repeated measures ANOVA), and on the number of independent variables that are considered in the study design (one-way ANOVA, two-way ANOVA, etc.). 4 This paper deals in a practical way with a problem to be solved by means of the statistical technique of one-way analysis of variance for independent samples using the Jamovi statistical package. 5…”

Section: Introductionmentioning

confidence: 99%

Step-by-step one-way ANOVA analysis with the Jamovi program

Milanes-Baños

2024

Mex J Med Res

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ANOVA is the acronym for Analysis of Variance, which stands for Analysis of Variance, and is used to establish statistically significant differences between the means of two groups. Currently there are several programs that synthesize this work allowing us to analyse statistical data in a simpler way. In this manuscript we will address a one-way or one-factor analysis of variance, which means that we must have an explanatory variable, also known as an independent variable, which must have two or more categories, we must also have a dependent or response variable of the type quantitatively discrete, in a fictitious case we will observe with this method how the independent variables shifted to the dependent variable, using the JAMOVI program, which is a free and easy-to-install advanced calculation program that allows the creation of complex statistical calculations efficiently. for manipulation, filtering, selection and combination of data.

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“…Deep forest re prevention is crucial in forestry work ("Forest Fire Prevention Tips, https://portal.ct.gov/DEEP/Forestry/Forest-Fire/Forest-Fire-Prevention-Tips," ; Potts et al, 2022;Toledo-Castro et al, 2022). The theoretical research on forest re ecology is signi cant for forest protection.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Simulations of the fallen leaves in the Sino-Russian border

Zhou,

Liu,

Zhang

et al. 2023

Preprint

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Herein, we conducted a comparative analysis of the experimental data of falling leaf distance obtained in Chunhua Town, located at the border between China and Russia, Hunchun, and established falling leaf models under different conditions using the numerical simulation method. The Monte Carlo statistical method was used to calculate the falling leaf distance, after which the experimental data and the numerical simulation results were compared between different types of leaves, tree heights, and wind speeds. We introduced the main factors affecting the falling distance of leaves and calculated the average variance to reflect the convergence of the experimental measurement results and numerical simulation results. By estimating the falling distance of leaves, we provided effective theoretical support for preventing deep forest fires.

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Interpretable Transformed ANOVA Approximation on the Example of the Prevention of Forest Fires

Cited by 6 publications

References 23 publications

Variable Transformations in combination with Wavelets and ANOVA for high-dimensional approximation

Variable Transformations in combination with Wavelets and ANOVA for high-dimensional approximation

Step-by-step one-way ANOVA analysis with the Jamovi program

Monte Carlo Simulations of the fallen leaves in the Sino-Russian border

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