Bayesian modeling and decision theory for non-homogeneous Poisson point processes

Chen, Jiaxun; Micheas, Athanasios C.; Holan, Scott H.

doi:10.1016/j.spasta.2020.100412

Cited by 5 publications

(5 citation statements)

References 24 publications

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“…This paper takes 10 data on China's domestic heat consumption from 2011 to 2020 as the research object [22], and establishes the traditional GM(1,1) model, NGM(1,1, k , c ) model [12], GM(1,1, k , 2 k ) model [13], IANGM(1,1, k ) model [21] and the new model of IANGM(1,1, k , 2 k ). The simulation results of the five models from 2011 to 2019 and the prediction results in 2020 are listed in Table 2.…”

Section: Data Analysis Of China's Domestic Heat Consumption From 2011...mentioning

confidence: 99%

“…Due to the existence of different characteristics of data in real life, most of the models constructed by such methods cannot achieve better modeling results. Therefore, scholars have studied the optimization methods of the model from different angles and integrated the research methods: First, the improvement of the model, such as optimizing the grey derivative [9,10], the grey action [11][12][13], etc; the second is the improvement of the sequence generation method, such as reverse accumulation [14][15][16][17][18][19]and one-time accumulation [20,21]. These new optimization methods have achieved certain practical application results and further broadened the application scope of the grey model.…”

Section: Introductionmentioning

confidence: 99%

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A New Grey Prediction IANGM (1,1, k, k²) Model

Dong

2024

JAMC

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In this paper, a new grey prediction IANGM (1,1, k , 2 k ) model with quadratic time-varying function is constructed, which is suitable for approximate homogeneous exponential type, approximate non-homogeneous exponential type, exponential linear combination type, and exponential parabolic combination type characteristic sequence. The undetermined coefficient method is used to determine the shadow equation matching the model, and the time response formula of the IANGM (1,1, k , 2 k ) model is derived based on the constant variation method. Through numerical simulation and double modeling analysis of China's domestic heat consumption and soft soil foundation settlement data from 2011 to 2020, the results show that the IANGM (1,1, k , 2 k ) model has higher simulation and prediction accuracy.

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Section: Data Analysis Of China's Domestic Heat Consumption From 2011...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Grey Prediction IANGM (1,1, k, k²) Model

Dong

2024

JAMC

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“…We should draw a sharp distinction line between the method we use and such popular approach as a Poisson point process ( Chen, Micheas & Holan, 2020 ; Eckardt, González & Mateu, 2021 ; Ghazal & Aly, 2004 ; Komori et al, 2020 ; Marmarelis & Berger, 2005 ): we employ not a single Poisson point process, but rather a set of all possible Poisson point processes, squeezed into a single discrete model.…”

Section: Literature Reviewmentioning

confidence: 99%

Generalized relational tensors for chaotic time series

Gromov

Beschastnov

Tomashchuk

2023

PeerJ Computer Science

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The article deals with a generalized relational tensor, a novel discrete structure to store information about a time series, and algorithms (1) to fill the structure, (2) to generate a time series from the structure, and (3) to predict a time series. The algorithms combine the concept of generalized z-vectors with ant colony optimization techniques. To estimate the quality of the storing/re-generating procedure, a difference between the characteristics of the initial and regenerated time series is used. For chaotic time series, a difference between characteristics of the initial time series (the largest Lyapunov exponent, the auto-correlation function) and those of the time series re-generated from a structure is used to assess the effectiveness of the algorithms in question. The approach has shown fairly good results for periodic and benchmark chaotic time series and satisfactory results for real-world chaotic data.

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“…Bayesian theory is regarded as the core theory of artificial intelligence in algorithms [19][20]. As a method that can calculate the target probability by prior knowledge and conditional probability, Bayesian theory has outstanding contributions in various fields, such as medical detection, grammar error correction, and so on.…”

Section: Application Of Gaussian Processmentioning

confidence: 99%

A theoretical and practical study on the components of intelligent physical education courses in colleges and universities based on Bayesian non-parametric model

Wei

2023

Applied Mathematics and Nonlinear Sciences

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This paper performs feature extraction based on the Bayesian nonparametric model for smart sports courses to analyze the Gaussian process principle for composing random variables. The probability distribution of the parameters is estimated based on the known data set, given the input data vector to decompose the likelihood function. To calculate the posterior probabilities of the parameters, the kernel function features are analyzed to give the expressions of eigenvalues and eigenvectors, and data normalization is performed. According to the results, the experimental group had higher sports test scores than the control group, and the third test score of high-speed running reached 9 points. Therefore, colleges and universities should focus on cultivating students' innovative thinking abilities and helping them master sports knowledge and skills to achieve their educational goals.

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Bayesian modeling and decision theory for non-homogeneous Poisson point processes

Cited by 5 publications

References 24 publications

A New Grey Prediction IANGM (1,1, k, k²) Model

A New Grey Prediction IANGM (1,1, k, k²) Model

Generalized relational tensors for chaotic time series

A theoretical and practical study on the components of intelligent physical education courses in colleges and universities based on Bayesian non-parametric model

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Bayesian modeling and decision theory for non-homogeneous Poisson point processes

Cited by 5 publications

References 24 publications

A New Grey Prediction IANGM (1,1, k, k2) Model

A New Grey Prediction IANGM (1,1, k, k2) Model

Generalized relational tensors for chaotic time series

A theoretical and practical study on the components of intelligent physical education courses in colleges and universities based on Bayesian non-parametric model

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A New Grey Prediction IANGM (1,1, k, k²) Model

A New Grey Prediction IANGM (1,1, k, k²) Model