Classroom interaction

The objective world and mental models

Huaping Hu

[email protected]

Northwest A&F University

2026-10-14

Aims

This is a classroom activity that compares the objective world with mental models, and shows stages of cognitive evolution from an econometrics point of view.

Flow: first complete a single-choice item in the smart classroom, then match the five school labels, and finally enter the counts into the chart.

Quiz

When you face something uncertain (school, going abroad, a business), which approach is closest to yours? (single choice)

A

I watch what is happening and revise my story about the rules behind it—tracking and updating both at once.

B

I already have the rules in mind; what is happening in front of me does not need looking at, and it will not change my view.

C

Never mind the rules behind it; whichever method works today, right in front of me, is the one I use.

D

I first accept a set of rules, then check how often the things in front of me would occur under those rules—whether they repeat.

E

I start with a view, then use newly seen events to revise how sure I am.

Option-to-stage map (do not project school names on this slide, so students answer by behavior, not by identity):

• B → Prior \(P(\Theta)\): trust existing rules, ignore data
• C → Pragmatic \(P(X)\): grab the facts/tools that work today
• D → Frequentist \(P(X\mid\Theta)\): fix a rule, ask how common the data are
• A → Modern \(P(X,\Theta)\): model facts and rules together, test, iterate
• E → Bayesian \(P(\Theta\mid X)\): start with a belief, let evidence rewrite it

Cognitive stages

1 Prior
1 HOMO APRIORIUS

2 Pragmatic
2 HOMO PRAGMATICUS

3 Frequentist
3 HOMO FREQUENTISTUS

4 Modern
4 HOMO SAPIENS

5 Bayesian
5 HOMO BAYESIANIS

[Notation]: \(\Theta\): parameter (rule, regularity)        \(X\): sample (observation)

Pronunciation:

• Homo apriorius (ah-pri-oh-re-us)
• Homo pragmaticus (pra-gma-tic-us)
• Homo frequentistus (fre-kwen-tis-tus)
• Homo sapiens (sa-pi-ens)
• Homo bayesianis (bay-see-an)

Poll

Enter the counts from the smart-classroom poll. Bars follow the order of the five cognitive stages.

B · Prior Θ C · Prac. X D · Freq. X|Θ A · Modern X,Θ E · Bayes Θ|X

Cognitive-model feedback · Total 62

Reality check

• 1 Prior (illiterate villager): Gut and lore—no data needed.
• 2 Pragmatic (wage earner): Grab the tool that works today.
• 3 Frequentist (white-collar): Truth is what repeats forever.
• 4 Modern (Musk): Build a working model, design tests, then keep repairing, iterating, growing.
• 5 Bayesian (Einstein): Theory first—then let evidence rewrite belief.

• Homo apriorius (illiterate villager): Gut and lore—no data needed.
• Homo pragmaticus (wage earner): Grab the tool that works today.
• Homo frequentist (white-collar): Truth is what repeats forever.
• Homo sapiens (Elon Musk): Model the lever, test the design, scale the fix.
• Homo bayesian (Einstein): Theory first—then let evidence rewrite belief.

Background

The five “humans” in the cartoon correspond to five probability objects: \(\Theta\) is the rule/parameter, \(X\) is the observation/data.^{1 2}

• 1 Prior \(P(\Theta)\): Talk only about the rule; even when data arrive, do not change your mind.
• 2 Pragmatic \(P(X)\): Care only about the facts in front of you, and whether they work today.
• 3 Frequentist \(P(X\mid\Theta)\): Assume a rule, then ask how common the data would be under it.³
• 4 Modern \(P(X,\Theta)\): Put facts and rules on the same map; model, check, and revise together.
• 5 Bayesian \(P(\Theta\mid X)\): Start with a belief about the rule, then rewrite it with data; that is \(P(\Theta\mid X)\propto P(X\mid\Theta)\,P(\Theta)\).⁴

Frequentist probability asks how often the same procedure would be right under repetition; Bayesian probability asks how sure I now am about an unknown rule.⁵ In practice people rarely stick to one mode: maximizing a likelihood, checking the model, and updating beliefs are often mixed together.⁶

Reference

1. Back Morrison, D. A. (2014, August 25). The evolution of statistical phylogenetics. The Genealogical World of Phylogenetic Networks. https://phylonetworks.blogspot.com/2014/08/the-evolution-of-statistical.html
2. Back Cross Validated. (2011, October 22). What are the modeling approaches in this cartoon? https://stats.stackexchange.com/q/17417. Image attributed to Michael West, Duke University.
3. Back Neyman, J. (1937). Outline of a theory of statistical estimation based on the classical theory of probability. Philosophical Transactions of the Royal Society of London. Series A, 236(767), 333–380. https://doi.org/10.1098/rsta.1937.0005
4. Back Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370–418. https://doi.org/10.1098/rstl.1763.0053
5. Back Efron, B. (2013). A 250-year argument: Belief, behavior, and the bootstrap. Bulletin of the American Mathematical Society, 50(1), 129–146. https://doi.org/10.1090/S0273-0979-2012-01374-5
6. Back Gelman, A., & Shalizi, C. R. (2013). Philosophy and the practice of Bayesian statistics. British Journal of Mathematical and Statistical Psychology, 66(1), 8–38. https://doi.org/10.1111/j.2044-8317.2011.02037.x

That’s all