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# Probability of Deriving a Yearly Transition Probability Matrix for Land-Use Dynamics

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 Title: Probability of Deriving a Yearly Transition Probability Matrix for Land-Use Dynamics Authors: Hasegawa, Shigeaki F. Browse this author Takada, Takenori Browse this author Keywords: land-use dynamics transition probability matrix yearly transition power root of matrix Issue Date: Nov-2019 Publisher: MDPI Journal Title: Sustainability Volume: 11 Issue: 22 Start Page: 6355 Publisher DOI: 10.3390/su11226355 Abstract: Takada's group developed a method for estimating the yearly transition matrix by calculating the mth power roots of a transition matrix with an interval of m years. However, the probability of obtaining a yearly transition matrix with real and positive elements is unknown. In this study, empirical verification based on transition matrices from previous land-use studies and Monte-Carlo simulations were conducted to estimate the probability of obtaining an appropriate yearly transition probability matrix. In 62 transition probability matrices of previous land-use studies, 54 (87%) could provide a positive or small-negative solution. For randomly generated matrices with differing sizes or power roots, the probability of obtaining a positive or small-negative solution is low. However, the probability is relatively large for matrices with large diagonal elements, exceeding 90% in most cases. These results indicate that Takada et al.'s method is a powerful tool for analyzing land-use dynamics. Rights: http://creativecommons.org/licenses/BY/4.0/ Type: article URI: http://hdl.handle.net/2115/76859 Appears in Collections: 低温科学研究所 (Institute of Low Temperature Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 長谷川 成明