Statistical population modelling for census support

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# Statistical population modelling for census support
## Quiz 1
### Edith Darin

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# Quiz

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# Bayesian concepts

![](pic/mcq_tuto1_bayes_diagram.png)
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# Bayesian concepts

$$ \text{posterior} \quad = \quad \frac{\text{prior } \cdot \text{ likelihood}}{\text{normalizing constant}} \; $$
--
<br>
.center[![](mcq_tuto1_bayes.jpg)]

.footnote[https://twitter.com/andrewheiss/status/1441857561297260548/photo/1
https://www.tjmahr.com/bayes-theorem-in-three-panels/]
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# Bayesian concepts

.center2[Priors represent the contextual knowledge around a phenomenon (eg, from past experience)
1. TRUE
2. FALSE]
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# Bayesian concepts

.center2[Priors are derived from the data
1. TRUE
2. FALSE]

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# Bayesian concepts

.center2[*The **Bechdel test** measures the representation of women in film. It is based on three criteria
and films either pass the test or fail. *

Let π, a random value between 0 and 1, 
denote the unknown proportion of movies that pass the Bechdel test. ]

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# Bayesian concepts

.center2[Three friends – the **feminist**, the **clueless**, and the **optimist** – have some prior ideas about π.

<br>

![](pic/mcq_tuto1_Bechdelprior.PNG)]

.footnote[https://www.bayesrulesbook.com/chapter-4.html#fig:ch4-bechdel-priors]

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.pull-left[
#### Distribution 1
![](pic/mcq_tuto1_normal.png)
#### Distribution 2
![](pic/mcq_tuto1_poisson.png)]
.pull-right[
#### Distribution 3
![](pic/mcq_tuto1_lognormal.png)]

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# Bayesian estimation

.center2[What does the parameter `warmup` control in stan?
1. the number of iterations
2. the length of the chain
3. the number of iterations post-tuning
4. the length of the chain pre-tuning]

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# Bayesian estimation

.pull-left[
<img src="pic/mcq_tuto1_traceplot.PNG" alt="drawing" width="300"/>]

.pull-right[
This is a **traceplot**.

*NB: we can see that the model run for 750 iterations.*

Can we consider that the model converged?
1. Yes
2. No
]

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# Writing Stan model

```stan
// Stan code
data {
}
parameters {

}
model {
}
```
<br>
.center[
If I want to **modify priors**, which block shall I modify?

1.data block <br/>
2.parameter block <br/>
3.model block
]

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# Model evaluation

*Let's consider a population model with full convergence of the estimates.*

*We evaluate it by comparing the predicted population counts versus 
the observed population counts*

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# Model evaluation

*Let's consider a population model with full convergence of the estimates.*

*We evaluate it by comparing the predicted population counts versus 
the observed population counts and we obtain the following goodness-of-fit metrics*

<br>

![](pic/mcq_tuto1_goodness.PNG)

<br>
.center[
Can we be confident about the model results? <br/>
1.Yes <br/>
2.No
]