Spatio-temporal model based on Markov random fields and its application to forest ecology

用马尔可夫随机场模型对巴拿马巴罗科罗拉多群岛新热带森林12年来的冠层高度资料进行了拟合。树冠高度是二值化的，20米以下和20米以上。从考虑树木相邻格局到势函数的各种实验证明，马尔可夫随机场模型可以较好地同时使用1-Bocly、2-Body和4-Body模式模拟二元冠层格局。模型参数首先用最大伪似然法估计，然后用MQMC牛顿-拉夫森精化线索对Huang和Ogata进行精化。在12年的数据中，8个数据显示较好的配件，2年的数据显示良好的配件。两年的数据不能显示良好的拟合度，可能是由于森林系统的时间急剧变化。但可以看出，时间上的不稳定性恢复得很快，显示了森林的生态稳定。结果表明，马尔可夫随机场模型能够很好地描述这类森林系统。分析43正在提交给一份适当的期刊。2001年，首席调查员还出版了包括马尔可夫随机场在内的第一本关于空间统计的日本书籍。

Markov random field models are fitted to 12 years data of canopy heights of neo-tropical forests of Barro Corollado islands, Panama. Canopy heights are binarized, under and over 20m. From various experiments taking account of neighbouring patterns of trees to potential functions, it is verified that Markov random field model can model binary canopy patterns fairly well using 1-bocly, 2-body and 4-body patterns simultaneously. Model parameters are first estimated by the maximum pseudo-likelihood method and they are refined by a MQMC Newton-Raphson refinement clue to Huang and Ogata. Among 12 years data, 8 data shows fairly good fittings and 2 years good fittings. 2 years data cannot show good fittings, probably due to temporal drastic changes of forest systems. But it is seen that temporal unstableness recovers quickly, showing the ecological stableness of the forest. As a result, it is verified that Markov random field model can represent such forest, system. The analysis 43 under the process of submitting to an appropriate journal. Also the head investigator published a first Japanese book on spatial statistics including Markov random field in 2001.