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2018-02-07 The Golem of Prague.Rpres
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The Golem of Prague
========================================================
author: schifferl
date: February 7, 2018
width: 1440
height: 950
McElreath, R. *Statistical Rethinking: A Bayesian Course with Examples in R and
Stan*. (CRC Press/Taylor & Francis Group, 2016).
Clay golems
========================================================
incremental: true
>A golem (goh-lem) is a clay robot known in Jewish folklore, constructed from
dust and fire and water. It is brought to life by inscribing emet, Hebrew for
“truth,” on its brow.
Statistical golems
========================================================
incremental: true
>Scientists also make golems. Our golems rarely have physical form, but they too
are often made of clay, living in silicon as computer code.
Teaching statistics
========================================================
incremental: true
>For some, the toolbox of pre-manufactured golems is all they will ever need.
Innovative research
========================================================
incremental: true
>The classical procedures of introductory statistics tend to be inflexible and
fragile.
<br>
>Instead, what researchers need is some unified theory of golem engineering, a
set of principles for designing, building, and refining special-purpose
statistical procedures.
Statistical rethinking
========================================================
incremental: true
>Instead, we need some statistical epistemology, an appreciation of how
statistical models relate to hypotheses and the natural mechanisms of interest.
Karl Popper
========================================================
incremental: true
Hypotheses are not models
========================================================
incremental: true
>All models are wrong; some models are useful. - _George Box_
<p style="text-align: center;">
<img src="figures/figure_1.2.png">
</p>
Alternative models
========================================================
incremental: true
>If it turns out that all of the process models of interest make very similar
predictions, then you know to search for a different description of the
evidence, a description under which the processes look different.
Measurement matters
========================================================
incremental: true
>First, observations are prone to error, especially at the boundaries of
scientific knowledge. Second, most hypotheses are quantitative, concerning
degrees of existence, rather than discrete, concerning total presence or
absence.
<br>
- Continuous hypotheses also exists
- Falsification is consensual
Three tools for golem engineering
========================================================
incremental: true
<br>
<br>
1. Bayesian data analysis
2. Multilevel models
3. Model comparison using information criteria
Left unsaid
========================================================
incremental: true
<p style="text-align: center;">
<a href="http://www.is-there-a-god.info/blog/clues/two-scientists-probability-and-god/">
<img src="http://www.is-there-a-god.info/blog/wp-content/uploads/2016/02/Bayes_Theorem.jpg">
</a>
</p>
>Bayes Theorem is a formula for calculating a new probability of a hypothesis
being true, after new evidence is considered. It is based on the idea that if a
new piece of evidence is more likely if a hypothesis is true than if it is
false, then it raises the probability that the hypothesis is true.
Thomas Bayes
========================================================
incremental: true
<p style="text-align: center;">
<img src="https://upload.wikimedia.org/wikipedia/commons/d/d4/Thomas_Bayes.gif">
</p>
[An Essay towards solving a Problem in the Doctrine of Chances](http://www.stat.ucla.edu/history/essay.pdf)
Multilevel models / Model comparison using information criteria
========================================================
incremental: true
<br>
- Extensive information in the text
- Multilevel models
- To adjust estimates for repeat sampling
- To adjust estimates for imbalance in sampling
- To study variation
- To avoid averaging
- Information criteria
- Evaluate model accuracy based on information theory