Proposal of an epistemological model for teaching Bayesian inference

Paredes-Cancino, Cristian G.; Montiel-Espinosa, Gisela

doi:10.1590/1980-4415v39a230278

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ARTICLE • Bolema 39 • 2025 • https://doi.org/10.1590/1980-4415v39a2302781 linkcopy

Proposal of an epistemological model for teaching Bayesian inference

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

The teaching of Bayesian statistics at school is characterized by promoting the meaning of subjective probability as a calculation algorithm. Regarding the limited development of meanings at school, the history of mathematics is a source of data that provides epistemic elements that configure new meanings about mathematical notions. Therefore, to characterize the stochastic activity that underlies Bayesian problems and the context associated with their genesis, a documentary study is proposed through qualitative content analysis from the socio-epistemological perspective. The results show an organization of stochastic practices directed by estimating the ‘true value’ of the unknown parameter, from which an epistemological reference model is built as a proposal to reorient the didactic intervention of Bayesian inference.

Historical Genesis; Inference; Stochastic practices; Bayes Theorem; Socioepistemology

Contextual analysis	Text analysis
The external critical history of knowledge through the characterization of the context of meaning	The internal critical history of knowledge through the pragmatic reconstruction of mathematical activity
Cultural context:	Socially Shared Practice:
Social characteristics of cultural groups that reflect ideological, political, and economic needs that shape a worldview and influence the rationality of the subject.	The organization of actions and activities carried out by the subject in an iterative and deliberate manner, related to the treatment of specific situations that characterize a mathematical task.
Situational context:	Activity:
Spatiotemporal factors or circumstances that affect the subject regarding mathematical knowledge.	Coordination of intentional actions of the subject directed toward a purpose to address a specific situation within the framework of a mathematical task.
Context of the specific situation:	Action:
Mathematical and situational elements that determine problems within which mathematical knowledge emerges.	The doing and/or saying of the subject before the object (what a mathematical task demands).

Source Type	Source
Primary	■ Bayes, T. (1763). An Essay Towards Solving a Problem in The Doctrine of Chances
Secondary	■ Bellhouse, D. R. (2004). The Reverend Thomas Bayes, FRS: A Biography to Celebrate the Tercentenary of His Birth
	■ Dale, A. (1999). A history of inverse probability from Thomas Bayes to Karl Pearson
	■ Hald, A. (1990). A history of probability and statistics and their applications before 1750
	■ Hald, A. (2007). A history of parametric statistical inference from Bernoulli to Fisher, 1713–1935
	■ Todhunter, I. (1865). A history of the mathematical theory of probability from the time of Pascal to that of Laplace
Tertiary	■ Daston, L. (1988). Classical Probability in the Enlightenment
	■ Gorroochurn, P. (2012). Classic Problems of Probability
	■ Hacking, I. (2006). The emergence of probability: A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference

Action	Activity	Socially shared practice:
1. Establish a probability distribution a priori about the unknown parameter 𝜃	Measure the uncertainty about the unknown parameter and interpret that measurement	Estimate the “true value” of the unknown parameter 𝜃
2. Build a binomial statistical model that fits the sampling data
3. Generate the probability distribution model a posteriori
4. Determine the area under the model curve a posteriori in a specific interval (α < θ < b)
1. Collect different data samples	Update the measure of uncertainty about the parameter and interpret that measure.
2. Measure the probability P(α < θ < b\| p,q) for a specific interval in different samples
1. Compare two probability measures P(α < θ < b\| p,q)	Identify a pattern or trend in the behavior of conditional probability measures
2. Analyze the series of probability measures P(α < θ < b\| p,q)

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UNESP - Universidade Estadual Paulista, Pró-Reitoria de Pesquisa, Programa de Pós-Graduação em Educação Matemática Avenida 24-A, 1515, Caixa Postal 178, 13506-900 - Rio Claro - SP - Brazil
E-mail: bolema.contato@gmail.com

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