Uncertainty operators

`sensitivity.analyze`#

The indices of a global sensitivity analysis from its runs and their outputs (SALib's analyses, the same numbers): Morris's μ, μ* (the mean absolute elementary effect: the importance) and σ (the interactions and non-linearity) with μ*'s bootstrap interval; or Sobol's first order (S1: the share of the output's variance due to the factor alone), total (ST: with its interactions) and second order (S2: of pairs) indices with their bootstrap intervals.

Input	Type	What it is
`design`required	table	the runs (sensitivity.design's table)
`results`required	table	the outputs of the runs, a row each in the same order

Output	Type	What it is
`indices`	table	a row per factor (in the design's order): factor (1..), then mu, mu_star, sigma, mu_star_conf (morris) or s1, s1_conf, st, st_conf (sobol)
`s2`	table	sobol: the second order indices, a row and a column per factor
`s2_conf`	table	sobol: their intervals

Setting	Type	What it is
`method`required	text	morris or sobol
`column`	text	the results' column (default its last)
`levels`	integer	morris: the grid's levels, as the design's (default 4)
`second_order`	bool	sobol: as the design (default true)
`resamples`	integer	the bootstraps of the intervals (default 100)
`confidence`	number	the level of the intervals (default 0.95)
`seed`	integer	the seed of the bootstraps (default 1)

`sensitivity.design`#

The runs of a global sensitivity analysis (SALib's samplers, the same values): Morris's trajectories (a factor changed at a time on a grid of levels; n trajectories of factors + 1 runs) or Saltelli's runs of Sobol's method (a scrambled Sobol' sequence; n base points, a power of 2, of 2 × factors + 2 runs, or factors + 2 without the second order). Run the model at every row (terraflux sensitivity, or a loop) and give the outputs to sensitivity.analyze.

Output	Type	What it is
`table`	table	a row per run: run, then a column per factor

Setting	Type	What it is
`method`required	text	morris or sobol
`factors`required	any	the factors and their ranges: [[name, low, high], ...] (or {name: [low, high]}); a model's input ($name) or setting (node.setting) for terraflux sensitivity
`n`	integer	trajectories (morris) or base points (sobol; default 10 / 64)
`levels`	integer	morris: the grid's levels (default 4)
`second_order`	bool	sobol: the pairs' indices too (default true)
`seed`	integer	the seed of numpy's default_rng (default 1)

`uncertainty.delta`#

The uncertainty of an expression of the node's maps and numbers (raster.calc's) from the uncertainty of its parameters, by the delta method (landschaft's delta_method, the GUM's first order): the derivatives by finite differences (central, or forward as Strassburg et al. 2020), the standard deviation sqrt(sum (df/dp sigma)^2) (quadratic) or sum |df/dp sigma| (linear).

Output	Type	What it is
`value`	any	the expression at the parameters (a map or a number)
`sd`	any	its standard deviation

Setting	Type	What it is
`expression`required	text	e.g. carbon * factor + base
`parameters`required	any	[["factor", 0.47, 0.02], ...]: name, value, sd
`method`	text	quadratic (default) or linear
`scheme`	text	central (default) or forward
`step`	any	the finite-difference step (one, or one per parameter)

Takes any other inputs by name (any).

`uncertainty.interval`#

The normal confidence interval of a value: value -/+ z sd, z the normal quantile of the level (landschaft's interval; scipy's norm.ppf, cephes' ndtri; Strassburg et al. 2020 fix z at 1.96).

Input	Type	What it is
`value`required	any	a map or a number
`sd`required	any	its standard deviation

Output	Type	What it is
`low`	any	the lower bound
`high`	any	the upper bound

Setting	Type	What it is
`level`	number	the confidence level, 0 to 1 (0.95)

`uncertainty.monte_carlo`#

The uncertainty of an expression of the node's maps and numbers by drawing its parameters (landschaft's monte_carlo): n draws from normal distributions with numpy's generator and seed, the expression computed for each, their mean, standard deviation and quantiles (numpy's).

Output	Type	What it is
`mean`	any	the mean over the draws (a map or a number)
`sd`	any	the standard deviation over the draws
`quantiles`	any	a layer (or a row) per quantile

Setting	Type	What it is
`expression`required	text	e.g. carbon * factor + base
`parameters`required	any	[["factor", 0.47, 0.02], ...]: name, mean, sd
`n`	integer	the draws (1000)
`seed`	integer	of numpy's generator (0)
`quantiles`	any	[0.025, 0.975] (default)

Takes any other inputs by name (any).

`uncertainty.product_sd`#

The standard deviation of the product of two independent uncertain values x v (landschaft's product_sd): Goodman's exact variance x^2 sigma_v^2 + v^2 sigma_x^2 + sigma_x^2 sigma_v^2, cell by cell, or of the sum of the products (total: quadratic or linear).

Input	Type	What it is
`x`required	any	a map or a number
`sd_x`required	any	its standard deviation
`v`required	any	a map or a number
`sd_v`required	any	its standard deviation

Output	Type	What it is
`sd`	any	a map (or a number) of standard deviations, or the total's

Setting	Type	What it is
`total`	bool	the standard deviation of the sum of the products
`method`	text	of the total: quadratic (default) or linear

`uncertainty.sum_sd`#

The standard deviation of a total of uncertain values, the sum of w v (landschaft's sum_sd): independent errors sqrt(sum (sigma w)^2), errors adding up sum |sigma w|, or with a correlation rho of every pair sqrt((1 - rho) sum s^2 + rho (sum s)^2). Missing cells left out.

Input	Type	What it is
`sd`required	map	the values' standard deviations
`weights`	any	a map or a number (default 1)

Output	Type	What it is
`sd`	number	the total's standard deviation

Setting	Type	What it is
`method`	text	quadratic (default) or linear
`correlation`	number	of every pair of errors, -1 to 1

sensitivity.analyze#

sensitivity.design#

uncertainty.delta#

uncertainty.interval#

uncertainty.monte_carlo#

uncertainty.product_sd#

uncertainty.sum_sd#