切片采样算法在光释光年龄模型参数估计中的应用

doi:10.18306/dlkxjz.2016.01.009

Abstract

Abstract:

In Optically Stimulated Luminescence (OSL) dating, statistical age models used for equivalent dose (De) determination are probabilistic models constructed according to mathematical statistics. They are applied to distinguish De populations that are sedimentologically different or to determine a De value that represents the burial dose of a sample. Maximum likelihood estimation (MLE) method is routinely used to optimize parameters of an age model. In the present study, we used the Slice sampling algorithm to determine the parameters of age models. Slice sampling is a Markov chain Monte Carlo (MCMC) sampling method, which enables the sampling distributions of parameters to be obtained from the joint likelihood function that is determined by observations and the specified model. This study applied easily implemented and openly accessible numeric routines to performing the algorithm. We used artificial and measured datasets to check the reliability of the estimates. MCMC method is insensitive to the parameters’ initial states, and the standard errors (or confidence intervals) of parameters assessed using this method are more reliable compared to those based on the Fisher information matrix constructed through numerical differentiation. Our results indicate that the Slice sampling method provides an alternative for age model optimization. Slice sampling method generates an informative estimation for the results of MLE method in age model application.

Key words: OSL dating, equivalent dose, statistical age models, parameter optimization, stochastic sampling

Jun PENG, Zhibao DONG, Fengqing HAN. Application of slice sampling method for optimizing OSL age models used for equivalent dose determination[J].PROGRESS IN GEOGRAPHY, 2016, 35(1): 78-88.

Figures/Tables 11

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References 39

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样品名称	实际参数	MCMC算法参数估计	MLE算法参数估计
S₁-MAM₃	p=0.1	p=0.09±0.06 (0.005, 0.22)	p=0.08±0.09 (-0.10, 0.25)
	γ=10	γ=9.92±0.13 (9.64, 10.17)	γ=9.92±0.19 (9.54, 10.29)
	σ=0.25	σ=0.25±0.01 (0.23, 0.28)	σ=0.25±0.01 (0.22, 0.28)
S₂-MAM₃	p=0.3	p=0.20±0.04 (0.12, 0.28)	p=0.20±0.04 (0.12, 0.28)
	γ=10	γ=9.82±0.08 (9.66, 9.98)	γ=9.83±0.08 (9.68, 9.98)
	σ=0.5	σ=0.54±0.03 (0.48, 0.60)	σ=0.54±0.03 (0.48, 0.59)

样品名称	实际参数	MCMC算法参数估计	MLE算法参数估计
S₁-FMM₃	p₁=0.1; μ₁=10	p₁=0.12±0.02 (0.08, 0.17); μ₁=10.06±0.11 (9.85, 10.28)	p₁=0.12±0.02 (0.08, 0.16); μ₁=10.04±0.11 (9.83, 10.26)
	p₂=0.5; μ₂=15	p₂=0.47±0.03 (0.40, 0.53); μ₂=15.08±0.07 (14.94, 15.23)	p₂=0.47±0.03 (0.41, 0.54); μ₂=15.08±0.07 (14.94, 15.22)
	p₃=0.4; μ₃=20	p₃=0.41±0.03 (0.35, 0.47); μ₃=20.10±0.11 (19.89, 20.32)	p₃=0.41±0.03 (0.34, 0.47); μ₃=20.10±0.11 (19.89, 20.32)
S₂-FMM₃	p₁=0.3; μ₁=10	p₁=0.27±0.03 (0.22, 0.33); μ₁=10.07±0.06 (9.97, 10.18)	p₁=0.27±0.03 (0.21, 0.33); μ₁=10.07±0.06 (9.96, 10.18)
	p₂=0.35; μ₂=20	p₂=0.41±0.03 (0.35, 0.47); μ₂=20.12±0.09 (19.94, 20.30)	p₂=0.41±0.03 (0.35, 0.48); μ₂=20.12±0.09 (19.94, 20.30)
	p₃=0.35; μ₃=30	p₃=0.32±0.03 (0.26, 0.38); μ₃=29.95±0.16 (29.64, 30.26)	p₃=0.32±0.03 (0.26, 0.38); μ₃=29.95±0.16 (29.64, 30.26)

样品名称	MCMC算法参数估计	MLE算法参数估计
142/SC08-03	p=0.14±0.07 (0.01, 0.29)	p=0.14±0.08 (-0.02, 0.30)
	γ=1.06±0.05 (0.95, 1.15)	γ=1.07±0.05 (0.97, 1.18)
	σ=1.18±0.12 (0.97, 1.44)	σ=1.15±0.11 (0.92, 1.37)
	L=-59.34	L=-59.26
AL3	p=0.22±0.14 (0.01, 0.51)	p=0.20±0.21 (-0.21, 0.60)
	γ=40.56±1.90 (36.78, 44.10)	γ=40.49±2.58 (35.44, 45.54)
	σ=0.41±0.05 (0.32, 0.52)	σ=0.39±0.05 (0.30, 0.48)
	L=-9.53	L=-9.45

样品名称	MCMC算法参数估计	MLE算法参数估计
142/SC08-03	p₁=0.30±0.05 (0.21, 0.40); μ₁=1.15±0.03 (1.09, 1.21)	p₁=0.30±0.06 (0.19, 0.42) ; μ₁=1.14±0.03 (1.08, 1.20)
	p₂=0.35±0.05 (0.25, 0.45); μ₂=1.94±0.05 (1.86, 2.03)	p₂=0.37±0.06 (0.25, 0.49) ; μ₂=1.94±0.04 (1.85, 2.02)
	p₃=0.22±0.05 (0.13, 0.31); μ₃=4.22±0.14 (3.95, 4.51)	p₃=0.20±0.05 (0.10, 0.30) ; μ₃=4.19±0.14 (3.93, 4.46);
	p₄=0.13±0.04 (0.06, 0.23); μ₄=9.66±0.47 (8.82, 10.65)	p₄=0.12±0.04 (0.04, 0.20); μ₄=9.54±0.42 (8.72, 10.35)
	L=-97.82	L=-97.62
AL3	p₁=0.39±0.11 (0.18, 0.61); μ₁=41.31±1.73 (37.69, 44.55)	p₁=0.39±0.13 (0.14, 0.65); μ₁=41.23±1.77 (37.77, 44.69)
	p₂=0.38±0.10 (0.17, 0.58); μ₂=52.91±3.42 (47.08, 60.79)	p₂=0.40±0.12 (0.15, 0.64); μ₂=53.01±3.08 (46.97, 59.05)
	p₃=0.23±0.06 (0.12, 0.36); μ₃=79.01±4.41 (70.86, 88.12)	p₃=0.21±0.06 (0.10, 0.32); μ₃=79.72±4.14 (71.60, 87.83)
	L=-6.83	L=-6.74

Application of slice sampling method for optimizing OSL age models used for equivalent dose determination

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输入：概率模型,迭代总次数nsim,初始参数状态X₀,模型参数总数N; 输出：随机采样样本及参数估计结果
1. 分配用于随机样本储存的数据矩阵(chain)：chain=matrix(nrow=nsim, ncol=N);
2. 通过如下迭代方式对参数轮流更新： do i=1, nsim do j=1, N 根据切片采样算法以条件概率P(X_j/X₀[-j])生成随机变量X_j X₀[j] = X_j chain[i,j] = X_j end do end do 3. 根据随机样本数据chain 进行参数估计