AM nest sampling algorithm based groundwater model evaluation method
AM nest sampling algorithm based groundwater model evaluation method
 CN 106,650,293 A
 Filed: 01/05/2017
 Published: 05/10/2017
 Est. Priority Date: 01/05/2017
 Status: Active Application
First Claim
1. it is a kind of based on AM nesting sampling algorithm groundwater model evaluation method, it is characterised in that：
 Comprise the following steps：
(1) according to the hydrogeologic condition in research area, the conceptual model M of one group of different structure is set up^{k}(k=1,2 ..., K) carrys out tableShow actual ground water regime；
(2) according to the one group of hydrogeological parameter of selection that studies a question as parameter vector θ and
determine its prior probability distribution p (θ
M^{k})；
(3) from prior distribution p (θ
 M^{k}) in random generation parameter vector θ
set S={ θ
_{1}, θ
_{2}..., θ
_{N}As active set, andCalculate active set in each parameter vector joint likelihood function L (θ
 D, M^{k}),；
(4) determine the iterations R of the main algorithm of nested sampling, parameter worst in active set S is selected in each iterative processVector calculates increment Delta Z of edge likelihood value as sample according to trapezoid formula；
(5) in each iterative process, new parameter is generated from prior distribution p by the local limit sampling based on AM algorithmsVectorial θ
_{new}As candidate samples, to substitute active set in worst sample；
(6) complete after iteration, according to active set S and increment Delta Z of edge likelihood value, calculate the edge likelihood of each conceptual modelValue Z；
(7) according to the edge likelihood value for calculating, each conceptual model is evaluated.
Chinese PRB Reexamination
Abstract
The invention provides an AM nest sampling algorithm based groundwater model evaluation method which includes improving the constrained local sampling algorithm of the nest sampling algorithm into the AM algorithm, taking the marginal likelihood value and posterior probability (weight) of the model as index for evaluating the representation of the groundwater model, and converting the complex and difficulttosolve highdimensional integration marginal likelihood value into onedimensional integration easy to compute according to the Bayesian analysis theory and the nest sampling algorithm. In analysis on cases of computing the groundwater model marginal likelihood values, the AM nest sampling algorithm based groundwater model evaluation method guarantees sampling quality and precision through selfadaptive updating of AM; as compared with the conventional NSEMH algorithm, the AM nest sampling algorithm based groundwater model evaluation method has the advantages that computing efficiency and convergence rate of computing results are improved to some degree, and accuracy and stability of the computing results are also improved.

2 Citations
No References
Thermal conduction model calibrating method based on doubledeck nesting uncertainty propagation  
Patent #
CN 105,183,997 A
Filed 09/14/2015

Current Assignee

Spacecraft transient thermal analysis model inversion correction method  
Patent #
CN 105,930,676 A
Filed 05/09/2016

Current Assignee

6 Claims

1. it is a kind of based on AM nesting sampling algorithm groundwater model evaluation method, it is characterised in that：
 Comprise the following steps：
(1) according to the hydrogeologic condition in research area, the conceptual model M of one group of different structure is set up^{k}(k=1,2 ..., K) carrys out tableShow actual ground water regime； (2) according to the one group of hydrogeological parameter of selection that studies a question as parameter vector θ and
determine its prior probability distribution p (θ
M^{k})；(3) from prior distribution p (θ
 M^{k}) in random generation parameter vector θ
set S={ θ
_{1}, θ
_{2}..., θ
_{N}As active set, andCalculate active set in each parameter vector joint likelihood function L (θ
 D, M^{k}),；(4) determine the iterations R of the main algorithm of nested sampling, parameter worst in active set S is selected in each iterative processVector calculates increment Delta Z of edge likelihood value as sample according to trapezoid formula； (5) in each iterative process, new parameter is generated from prior distribution p by the local limit sampling based on AM algorithmsVectorial θ
_{new}As candidate samples, to substitute active set in worst sample；(6) complete after iteration, according to active set S and increment Delta Z of edge likelihood value, calculate the edge likelihood of each conceptual modelValue Z； (7) according to the edge likelihood value for calculating, each conceptual model is evaluated.
 Comprise the following steps：

2. it is according to claim 1 based on AM nesting sampling algorithm groundwater model evaluation method, it is characterised in that：
 StepSuddenly (3) calculate joint likelihood function L (θ
 D, M^{k})：
 StepSuddenly (3) calculate joint likelihood function L (θ

3. it is according to claim 1 based on AM nesting sampling algorithm groundwater model evaluation method, it is characterised in that：
 StepSuddenly (4) calculate parameter vector θ
minimum in active set S for the secondary iteration of ith (i=1 ..., R)_{worst}And its corresponding likelihood letterNumber L_{worst}, make L_{i}=L_{worst}, calculate prior distribution accumulation X_{i}, edge likelihood value Z each time in iteration_{i}And edge likelihood valueIncrement Delta Z, wherein Z_{0}=0, L_{0}=0：
 StepSuddenly (4) calculate parameter vector θ

4. it is according to claim 3 based on AM nesting sampling algorithm groundwater model evaluation method, it is characterised in that：
 StepSuddenly (5) are sampled by local limit and new parameter vector θ
are generated from parameter prior distribution_{new}If, L (θ
_{new} D, M) ＞
L_{worst}, thenUse θ
_{new}Replace original θ
_{worst}；
Otherwise, continue to generate θ
from local limit sampling algorithm_{new}, until meeting L (θ
_{new} D, M) ＞
L_{worst}Or till reaching the artificially defined frequency in sampling upper limit.
 StepSuddenly (5) are sampled by local limit and new parameter vector θ

5. it is according to claim 4 based on AM nesting sampling algorithm groundwater model evaluation method, it is characterised in that：
 StepSuddenly the local limit sampling of (5) based on AM algorithms is comprised the following steps：
1. a certain parameter vector θ
is randomly choosed from active set S as initial parameter vector2. cycleindex H of AM algorithms is determined, for the secondary circulation of jth (j=1 ..., H), from normal distributionMiddle generationNew samples ξ
, calculates corresponding joint likelihood function value L_{ξ}, wherein C_{j}For covariance matrix；In T_{0}Fixed value C is taken before secondary iteration_{0}, afterwards adaptive updates covariance matrix computing formula is as follows：
 StepSuddenly the local limit sampling of (5) based on AM algorithms is comprised the following steps：

6. it is according to claim 3 based on AM nesting sampling algorithm groundwater model evaluation method, it is characterised in that：
 StepSuddenly (6) calculate respectively the N number of parameter vector θ
in the currently active collection S_{1}, θ
_{2}..., θ
_{N}Corresponding likelihood function L_{1}, L_{2}..., L_{N}, meterCalculation obtains edge likelihood value Z：
 StepSuddenly (6) calculate respectively the N number of parameter vector θ
Specification(s)