a b/experiments/sims/README.md
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# Define a structural causal model
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The structural causal model used in the publication is printed below.
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The setup is easy:
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1. Define the background noise variables (i.e. variables not caused by any other variable)
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   * **variable** is the internal name
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   * **label** is a longer name; when these corerspond to *measurements* of the images (like here size and variance), they will be used to sample images
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   * **type** noise vs dependent
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   * **distribution** where to draw the variable from; for the dependent variables, this is the *conditional* distribution
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   * **param_1** and **param_2** are the canonical parameters for the distribution (e.g. location and scale for Normal)
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2. Define the relationships between the noise variables and the dependent variables, using b_... columns to define coefficients from the noise variable to ... in a linear model.
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| variable | label     | type      | distribution | variable_model | param_1 | param_2 | b_x | b_t   | b_y |
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|----------|-----------|-----------|--------------|----------------|---------|---------|-----|-------|-----|
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| u1       | u1        | noise     | Normal       |                | 0       | 0.7071  | 1   | 0     | -2  |
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| u2       | u2        | noise     | Normal       |                | 0       | 0.7071  | -1  | 1.828 | 0   |
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| z        | variance  | noise     | Normal       |                | 0       | 1       | 0   | 0     | -1  |
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| n_x      | noise_x   | noise     | Normal       |                | 0       | 0.05    | 1   | 0     | 0   |
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| n_t      | noise_t   | noise     | Normal       |                | 0       | 0.05    | 0   | 1     | 0   |
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| n_y      | noise_y   | noise     | Normal       |                | 0       | 0.05    | 0   | 0     | 1   |
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| x        | size      | dependent | Normal       | Linear         | 0       |         | 0   | 0     | 0   |
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| t        | treatment | dependent | Bernoulli    | Logistic       | -0.5    |         | 0   | 0     | 1   |
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| y        | survival  | dependent | Normal       | Linear         | -0.5    |         | 0   | 0     | 0   |