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Add chp2 part 2
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FabsOliveira committed Jun 3, 2024
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40 changes: 1 addition & 39 deletions course/content/chapter_2/1-scenario_trees.md
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Expand Up @@ -69,42 +69,4 @@ In practical settings, we often can rely on pre-existent models of the stochasti

Often, the process of generating scenarios involves a combination of the above. In particular, provided that enough data is available, it is often common that one would define some parametric (e.g., statistical machine learning) model from which observations, or samples, are then generated.

Clearly, this involves considerable care regarding modelling premises, statistical analyses, and experiment design. Questions such as which model better represent the stochastic phenomena, how to sample scenarios and many scenarios are necessary are only some of the questions that must be answered *before* we even obtain a stochastic programming model.

## Quality measures for scenario trees

One crucial aspect related to stochastic programming is that scenario generation plays a significant part of the modelling process. This is a point that is often overlooked in the literature on stochastic programming applications, which has nonnegligible consequences to the quality of the model obtained.

Figure {ref}`SP_flowchart` illustrates how should think about the process of developing stochastic programming models. That diagram highlights the central role that scenario generation has in the process.

(SP_flowchart)=
```{mermaid}
:align: center
:caption: A flowchart representing the modelling process using stochastic programming
%%{ init: { 'flowchart': { 'curve': 'stepAfter' } } }%%
flowchart TB
id1[Decision process]
id2[Stochastic process]
id3[Scenario tree]
id4[Stochastic programming model]
id1 --> id3
id2 --> id3
id3 --> id4
classDef default fill:white, stroke:black, stroke-width:2px;
````
As such, one common saying related to stochastic programming model is "garbage in equals garbage out". This refers to the fact that, having a sophisticated stochastic programming model, perhaps including many of the features we will discuss in the next chapters, is not enough for one to have a reliable model for analyses. One must, just as carefully, consider whether the quality of the uncertainty representation, as they majorly influence the quality of the solutions obtained.
### Measuring error and stability of scenario trees
There are two measures that one must consider when generating scenario trees:
1. Error: scenario trees naturally encode an inherent amount of error, as they are *approximations* of the a stochastic process. On the other hand,
2. Stability
Clearly, this involves considerable care regarding modelling premises, statistical analyses, and experiment design. Questions such as which model better represent the stochastic phenomena, how to sample scenarios and many scenarios are necessary are only some of the questions that must be answered *before* we even obtain a stochastic programming model.
37 changes: 37 additions & 0 deletions course/content/chapter_2/2-quality_measures.md
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# Quality measures for scenario trees

One crucial aspect related to stochastic programming is that scenario generation plays a significant part of the modelling process. This is a point that is often overlooked in the literature on stochastic programming applications, which has nonnegligible consequences to the quality of the model obtained.

Figure {ref}`SP_flowchart` illustrates how should think about the process of developing stochastic programming models. That diagram highlights the central role that scenario generation has in the process.

(SP_flowchart)=
```{mermaid}
:align: center
:caption: A flowchart representing the modelling process using stochastic programming
%%{ init: { 'flowchart': { 'curve': 'stepAfter' } } }%%
flowchart TB
id1[Decision process]
id2[Stochastic process]
id3[Scenario tree]
id4[Stochastic programming model]
id1 --> id3
id2 --> id3
id3 --> id4
classDef default fill:white, stroke:black, stroke-width:2px;
````
As such, one common saying related to stochastic programming model is "garbage in equals garbage out". This refers to the fact that, having a sophisticated stochastic programming model, perhaps including many of the features we will discuss in the next chapters, is not enough for one to have a reliable model for analyses. One must, just as carefully, consider whether the quality of the uncertainty representation, as they majorly influence the quality of the solutions obtained.
## Error and stability of scenario trees
There are two measures that one must consider when generating scenario trees:
1. Error: scenario trees naturally encode an inherent amount of error, as they are *approximations* of the a stochastic process. On the other hand,
2. Stability

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