How Does Uncertainty Influence Potential to Make Decisions when Integrating Complex Datasets?

class: center, middle, inverse, title-slide

.title[
# How Does Uncertainty Influence Potential to Make Decisions when Integrating Complex Datasets?
]
.author[
### Peter Green, Esther Meenken, Delphine Rapp
]
.institute[
### AgResearch
]
.date[
### 2023/11/29
]

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# Introduction

- Data Integration

- Uncertainty

- Modelled and unmodelled

- Sensitivity

- Goal: incorporate sensitivity analysis into case studies

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# Case Study

- "Integrating Data Along the Supply Chain to Determine the Impact of Length of Drought on Food Safety Risks"

- Data from:
    - Processors
    - Weather indices
    
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- About 500 processed animals

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# Case Study - Data

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# Simplified Research Question

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# Carcass Weight

# Carcass Weight

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# Modelling Principles

- Placeholder model

- Simple but not too simple

- Access to internals

- Makes for nice visualisations

- `\(\Rightarrow\)` Gaussian Graphical Model

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# Gaussian Graphical Model

`\(\Sigma = \begin{bmatrix}157.02 & 23.10 & 60.86 & -0.83 & 1.53 \\23.10 & 19.71 & 5.55 & -0.18 & -0.40 \\60.86 & 5.55 & 27.88 & -0.31 & 0.92 \\-0.83 & -0.18 & -0.31 & 0.09 & -0.02 \\1.53 & -0.40 & 0.92 & -0.02 & 0.16\end{bmatrix}\)`

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# Gaussian Graphical Model

`\(\Sigma^{-1} = \begin{bmatrix}0.06 & -0.03 & -0.12 & 0.07 & 0.08 \\-0.03 & 0.08 & 0.04 & 0.08 & 0.27 \\-0.12 & 0.04 & 0.31 & -0.07 & -0.52 \\0.07 & 0.08 & -0.07 & 12.16 & 1.45 \\0.08 & 0.27 & -0.52 & 1.45 & 9.62\end{bmatrix}\)`

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# Gaussian Graphical Model

`\(\hat \Sigma \vphantom{\Sigma}^{-1} = \begin{bmatrix}- & - & -0.12 & - & 0.08 \\- & 0.08 & - & 0.08 & 0.27 \\-0.12 & - & 0.31 & - & -0.52 \\- & 0.08 & - & 12.16 & 1.45 \\0.08 & 0.27 & -0.52 & 1.45 & 9.62\end{bmatrix}\)`

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# Gaussian Graphical Model

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# Modelled Network

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# Modelled Network

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# Modelled Network

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# Kinds of Sensitivity

- input sensitivity: `\(\frac{\partial f}{\partial x}\)`

- parameter sensitivity: `\(\frac{\partial f}{\partial \beta}\)`

- uncertainty sensitivity: `\(\frac{\partial \sigma(f)}{\partial \sigma(x)}\)`

- uncertainty propagation: `\(\frac{\partial \sigma(f)}{\partial \sigma(\beta)}\)`

- data sensitivity: `\(\frac{\partial f}{\partial X_j}\)`

- sensitivity of uncertainty to the data:  `\(\frac{\partial \sigma(f)}{\partial X_j}\)`

- sensitivity to latent variables: `\(\frac{\partial f}{\partial\lambda}\)`

- model sensitivity: `\(\frac{\partial f}{\partial \operatorname{Model}}\)`

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# Sensitivity for Simple Models

- `\(\hat y_i = \hat\beta_0 + \hat\beta_1 x_i\)`
    - `\(\Delta y_i = \hat\beta_1 \Delta x_i\)`

- `\(\log\left(\frac{\hat\pi_i}{1-\hat\pi_i}\right) = \hat\beta_0 + \hat\beta x_i\)`

- `\(\mathbf{y}_i = \operatorname{DNN}(\mathbf{x}_i; \mathbf{w})\)`

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# Sensitivity Visualisation

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# Sensitivity Visualisation

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# Sensitivity Visualisation

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# Sensitivity Visualisation

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# Sensitivity Visualisation

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# Sensitivity Visualisation

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# Sensitivity Visualisation

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# Sensitivity Visualisation

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# Discussion

- Any questions
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 ... or statements?
 
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- Or suggestions