Density Estimation, Stochastic Processes and Prior Information
Density Estimation, Stochastic Processes and Prior Information
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DOI：
10.1111/j.2517-6161.1978.tb01655.x
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发表时间：
1978
期刊：
影响因子：
--
通讯作者：
Tom Leonard
中科院分区：
文献类型：
--
作者：
Tom Leonard
摘要提出了一种基于有限数量的观测和关于密度平滑度的先验信息的概率密度的非参数估计方法。一个逻辑密度变换和再生内积从一阶自回归随机过程被用来表示先验信息，该变换的衍生物是不太可能从根本上改变在小的间隔。密度的后验估计具有连续的二阶导数;它通常满足渐进一致性的频率论性质。一个直接的类比是证明与时间相关的泊松过程的平滑方法，这是类似的精神正常的理论卡尔曼滤波器。直方图中分组观测的程序提供了Boneva，Kendall和Stefanov的histos样条方法的替代方法。五个实际的例子，包括两个调查的正态性，行人到达的分析，在派力肯交叉口和直方图平滑方法的地雷爆炸数据。
SUMMARY A method is proposed for the non-parametric estimation of a probability density, based upon a finite number of observations and prior information about the smoothness of the density. A logistic density transform and a reproducing inner product from the first-order autoregressive stochastic process are employed to represent prior information that the derivative of the transform is unlikely to change radically within small intervals. The posterior estimate of the density possesses a continuous second derivative; it typically satisfies the frequentist property of asymptotic consistency. A direct analogy is demonstrated with a smoothing method for the time-dependent Poisson process; this is similar in spirit to the normal theory Kalman filter. A procedure for grouped observations in a histogram provides an alternative to the histospline method of Boneva, Kendall and Stefanov. Five practical examples are presented, including two investigations of normality, an analysis of pedestrian arrivals at a Pelican crossing and a histogram smoothing method for mine explosions data.