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avalanche_protection_in_davos_switzerland [2019/05/16 15:27] – [2. Quantifying the network (CPTs)] stritihaavalanche_protection_in_davos_switzerland [2023/04/21 15:30] (current) – external edit 127.0.0.1
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   p(Crown_cover_Lidar | Crown_cover) = NormalDist(Crown_cover_Lidar, Crown_cover, 0.12*Crown_cover)   p(Crown_cover_Lidar | Crown_cover) = NormalDist(Crown_cover_Lidar, Crown_cover, 0.12*Crown_cover)
      
-{{:measurement_cpt_distribution.png?200 |}}+{{:measurement_cpt_distribution.png?180 |}}
 // Distribution of actual crown cover, given a measurement of crown cover. The CPT of Crown cover (Lidar) is defined as a normal distribution around the actual crown cover.// // Distribution of actual crown cover, given a measurement of crown cover. The CPT of Crown cover (Lidar) is defined as a normal distribution around the actual crown cover.//
  
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 However, this procedure results in a very large CPT for the node (a line for each combination of parameters and predictor variables). Since the parameter nodes will not be modified with evidence, we can reduce the CPT by using the function “Absorb nodes”, which removes the nodes from the network, but retains the associated information in the reduced CPT.  However, this procedure results in a very large CPT for the node (a line for each combination of parameters and predictor variables). Since the parameter nodes will not be modified with evidence, we can reduce the CPT by using the function “Absorb nodes”, which removes the nodes from the network, but retains the associated information in the reduced CPT. 
  
-{{:empirical_cpt.png?800|}}+{{:empirical_cpt.png?700|}}
  
 //The parameters of an empirical model can be included explicitly as nodes in the network, to account for model uncertainty when calculating the CPT. Then, these nodes can be "absorbed" to reduce the size of the CPT.// //The parameters of an empirical model can be included explicitly as nodes in the network, to account for model uncertainty when calculating the CPT. Then, these nodes can be "absorbed" to reduce the size of the CPT.//
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 For nodes where no data was available (e.g. “Potential detrainment”), we used expert knowledge to quantify the CPT.  To avoid overconfidence, we used the “four-point estimation method” ([[https://doi.org/10.1111/j.1539-6924.2009.01337.x|Speirs-Bridge et al. 2010]]), where we asked the expert to estimate the lowest and highest value they would expect, the most likely value, and their confidence that the true value is within this range ([[https://doi.org/10.1016/j.biocon.2013.03.005|Metcalf and Wallace 2013]]). For example, for a dense evergreen forest on rough terrain, the expert estimated the lowest possible detrainment factor to be 24 Pa, the highest 96 Pa, and the best estimate at 48 Pa, with a confidence of 80%. This gives us the quantiles and mode of the distribution, to which we fitted a simple asymmetric triangular distribution (see figure below).  For nodes where no data was available (e.g. “Potential detrainment”), we used expert knowledge to quantify the CPT.  To avoid overconfidence, we used the “four-point estimation method” ([[https://doi.org/10.1111/j.1539-6924.2009.01337.x|Speirs-Bridge et al. 2010]]), where we asked the expert to estimate the lowest and highest value they would expect, the most likely value, and their confidence that the true value is within this range ([[https://doi.org/10.1016/j.biocon.2013.03.005|Metcalf and Wallace 2013]]). For example, for a dense evergreen forest on rough terrain, the expert estimated the lowest possible detrainment factor to be 24 Pa, the highest 96 Pa, and the best estimate at 48 Pa, with a confidence of 80%. This gives us the quantiles and mode of the distribution, to which we fitted a simple asymmetric triangular distribution (see figure below). 
  
-{{:expert_cpt.png?600|}}+{{:expert_cpt.png?500|}}
  
 //Expert-based distribution of potential detrainment for a dense evergreen forest on rough terrain.// //Expert-based distribution of potential detrainment for a dense evergreen forest on rough terrain.//
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 The model and the resulting maps of avalanche protection provision and demand, as well as the underlying ecosystem functions, were presented and discussed with local experts. In addition, we performed a sensitivity analysis of the model, using the Netica function “Sensitivity to findings” to calculate the reduction of entropy (uncertainty) on the target nodes in response to findings on other nodes in the network. The entropy reduction (also called mutual information) gives us an indication of which variables in the system have the highest influence on the ecosystem service.  The model and the resulting maps of avalanche protection provision and demand, as well as the underlying ecosystem functions, were presented and discussed with local experts. In addition, we performed a sensitivity analysis of the model, using the Netica function “Sensitivity to findings” to calculate the reduction of entropy (uncertainty) on the target nodes in response to findings on other nodes in the network. The entropy reduction (also called mutual information) gives us an indication of which variables in the system have the highest influence on the ecosystem service. 
  
-We also performed a stepwise sensitivity analysis to visualize the flow of information in the network. For each node X, we calculated the proportion of its entropy that can be reduced by a finding on each of its parents. These relative mutual information values were used as weights for links between nodes in a Sankey diagram of the network (Figure 6.1-8)  For each node, the thickness of incoming (from the left) links show how much the entropy on the node can be reduced by findings on preceding nodes. Mutual information is not additive, i.e. if both parent nodes can reduce the entropy of a child by 50%, this does not mean that findings on both parents will result in complete certainty on the child node. Nonetheless, plotting the MI gives an indication of the main sources of uncertainty in the model. When the value of MI for all the parents of a node is rather low, this means that the node will have a wide probability distribution even when the states of its parents are known, implying high uncertainty in the corresponding links. If such a node has a large influence on the outcome of the network, this indicates a knowledge gap. +We also performed a stepwise sensitivity analysis to visualize the flow of information in the network. For each node X, we calculated the proportion of its entropy that can be reduced by a finding on each of its parents. These relative mutual information values were used as weights for links between nodes in a Sankey diagram of the network (see figure below). For each node, the thickness of incoming (from the left) links show how much the entropy on the node can be reduced by findings on preceding nodes. Mutual information is not additive, i.e. if both parent nodes can reduce the entropy of a child by 50%, this does not mean that findings on both parents will result in complete certainty on the child node. Nonetheless, plotting the MI gives an indication of the main sources of uncertainty in the model. When the value of MI for all the parents of a node is rather low, this means that the node will have a wide probability distribution even when the states of its parents are known, implying high uncertainty in the corresponding links. If such a node has a large influence on the outcome of the network, this indicates a knowledge gap. 
  
 {{:avalanche_sensitivity.png?800|}}  {{:avalanche_sensitivity.png?800|}} 
avalanche_protection_in_davos_switzerland.1558013243.txt.gz · Last modified: 2023/04/21 15:30 (external edit)