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weights_of_evidence_calibration [2026/08/10 15:07] hermann |
weights_of_evidence_calibration [2026/08/12 01:22] (current) hermann |
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| Weights of Evidence is a Bayesian method, originally used in geology to map favorability for events such as mineralization, adapted here to relate a land-use transition to a set of predictive spatial variables. | Weights of Evidence is a Bayesian method, originally used in geology to map favorability for events such as mineralization, adapted here to relate a land-use transition to a set of predictive spatial variables. | ||
| - | For a transition from category i to category j, each class of a predictive variable (a category, or a range of a continuous gray-tone variable) is assigned two numbers: a positive weight (W+), reflecting how the transition's likelihood changes for cells that fall inside that class, and a negative weight (W-), reflecting the same for cells that fall outside it. | + | For a transition from category i to category j, each class of a predictive variable (a category, or a range of a continuous gray-tone variable) is assigned two numbers: a positive weight (W<sup>+</sup>), reflecting how the transition's likelihood changes for cells that fall inside that class, and a negative weight (W<sup>-</sup>), reflecting the same for cells that fall outside it. |
| [[calc_w._of_e._probability_map|Calc W. Of E. Probability Map]] combines these weights with a transition's baseline probability to produce a probability for each cell, based on which range or category the cell falls into for each variable. This is why a weight's sign has a consistent meaning: | [[calc_w._of_e._probability_map|Calc W. Of E. Probability Map]] combines these weights with a transition's baseline probability to produce a probability for each cell, based on which range or category the cell falls into for each variable. This is why a weight's sign has a consistent meaning: | ||
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| * **Negative** -- lowers the probability below baseline. Cells in that range are less likely than average to make the transition -- the range repels it. | * **Negative** -- lowers the probability below baseline. Cells in that range are less likely than average to make the transition -- the range repels it. | ||
| - | **Contrast** (C = W+ - W-) measures a range's overall association with the transition: it is what determines whether the range meaningfully favors or repels the transition, or has close to no effect. This is the number the significance test applies to (see [[#determining_coefficients|Determining Coefficients]] below). A range with a Weight_Coefficient near zero and a non-significant Contrast are two ways of saying the same thing: the range isn't doing meaningful explanatory work for the transition. | + | **Contrast** (C = W<sup>+</sup> - W<sup>-</sup>) measures a range's overall association with the transition: it is what determines whether the range meaningfully favors or repels the transition, or has close to no effect. This is the number the significance test applies to (see [[#determining_coefficients|Determining Coefficients]] below). A range with a Weight_Coefficient near zero and a non-significant Contrast are two ways of saying the same thing: the range isn't doing meaningful explanatory work for the transition. |
| Every variable's weights combine together to produce a transition's overall probability at each cell, which is why the method requires its input variables to be spatially independent of one another (see [[#checking_variable_independence|Checking Variable Independence]] below). | Every variable's weights combine together to produce a transition's overall probability at each cell, which is why the method requires its input variables to be spatially independent of one another (see [[#checking_variable_independence|Checking Variable Independence]] below). | ||
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| Determine Weights Of Evidence Ranges finds range boundaries by watching how the transition's weight changes as it sweeps across a continuous variable's values, rather than requiring pre-set cut points. | Determine Weights Of Evidence Ranges finds range boundaries by watching how the transition's weight changes as it sweeps across a continuous variable's values, rather than requiring pre-set cut points. | ||
| - | Starting at the variable's minimum value, it grows a sequence of nested buffers outward in steps equal to the Increment: the first buffer covers up to one Increment past the minimum, the second covers up to two Increments past it, and so on, each one containing everything the previous one did plus a bit more. For each buffer, it counts how many cells fall inside it and how many of those cells actually made the transition, and from that pair derives the weight (W+) that buffer's edge would produce if used as a single cutoff. Sweeping through the whole sequence of buffers produces a curve: weight as a function of how far the buffer has grown. | + | Starting at the variable's minimum value, it grows a sequence of nested buffers outward in steps equal to the Increment: the first buffer covers up to one Increment past the minimum, the second covers up to two Increments past it, and so on, each one containing everything the previous one did plus a bit more. For each buffer, it counts how many cells fall inside it and how many of those cells actually made the transition, and from that pair derives the weight (W<sup>+</sup>) that buffer's edge would produce if used as a single cutoff. Sweeping through the whole sequence of buffers produces a curve: weight as a function of how far the buffer has grown. |
| Where this curve stays flat, the variable isn't discriminating anything at that point -- going a bit further out doesn't change the odds. Where the curve bends, that's where crossing that value of the variable starts to matter. So the range boundaries are wherever the curve changes direction, which is a shape-finding problem, not something that can be set analytically in advance. | Where this curve stays flat, the variable isn't discriminating anything at that point -- going a bit further out doesn't change the odds. Where the curve bends, that's where crossing that value of the variable starts to matter. So the range boundaries are wherever the curve changes direction, which is a shape-finding problem, not something that can be set analytically in advance. | ||
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| * **Possible_Transitions** -- the number of cells that could have made this transition, given they started in the "from" category and fell inside this variable's range. What counts as "possible" is controlled by ''potentialTransitionCriteria'' (see below). | * **Possible_Transitions** -- the number of cells that could have made this transition, given they started in the "from" category and fell inside this variable's range. What counts as "possible" is controlled by ''potentialTransitionCriteria'' (see below). | ||
| * **Executed_Transitions** -- of those possible cells, how many actually made the transition during the observed period. | * **Executed_Transitions** -- of those possible cells, how many actually made the transition during the observed period. | ||
| - | * **Weight_Coefficient** -- the resulting weight (W+) for that range or category: its contribution to the transition's probability wherever it applies. | + | * **Weight_Coefficient** -- the resulting weight (W<sup>+</sup>) for that range or category: its contribution to the transition's probability wherever it applies. |
| - | * **Contrast** -- W+ minus W- for that range or category. Positive values favor the transition, negative values repel it, and values near zero mean the range has little effect. See [[#what_is_weights_of_evidence|What Is Weights of Evidence]] above for how this is derived. | + | * **Contrast** -- W<sup>+</sup> minus W<sup>-</sup> for that range or category. Positive values favor the transition, negative values repel it, and values near zero mean the range has little effect. See [[#what_is_weights_of_evidence|What Is Weights of Evidence]] above for how this is derived. |
| * **Significant** -- whether the Contrast passes the 95% confidence threshold (|C| > 1.96 S(C)). Rows marked "No" are exactly the ones the range-tuning loop above targets when adjusting the minimum delta. | * **Significant** -- whether the Contrast passes the 95% confidence threshold (|C| > 1.96 S(C)). Rows marked "No" are exactly the ones the range-tuning loop above targets when adjusting the minimum delta. | ||
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| * The [[name_map|Name Map]] aliases used inside [[determine_weights_of_evidence_ranges|Determine Weights Of Evidence Ranges]] and [[determine_weights_of_evidence_coefficients|Determine Weights Of Evidence Coefficients]] must match exactly between the two containers -- this is how each container knows which named map corresponds to which variable in the Skeleton. | * The [[name_map|Name Map]] aliases used inside [[determine_weights_of_evidence_ranges|Determine Weights Of Evidence Ranges]] and [[determine_weights_of_evidence_coefficients|Determine Weights Of Evidence Coefficients]] must match exactly between the two containers -- this is how each container knows which named map corresponds to which variable in the Skeleton. | ||
| * To inspect or chart a report outside the message log, connect its ''report'' output to [[save_table|Save Table]] and export to CSV. | * To inspect or chart a report outside the message log, connect its ''report'' output to [[save_table|Save Table]] and export to CSV. | ||
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