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Mutual influence between different views of probability and statistical inference

    1. [1] University of Klagenfurt

      University of Klagenfurt

      Klagenfurt, Austria

  • Localización: Paradigma, ISSN 1011-2251, Nº. Extra 1, 2021, págs. 221-256
  • Idioma: inglés
  • DOI: 10.37618/paradigma.1011-2251.2021.p221-256.id1024
  • Títulos paralelos:
    • Influência mútua entre diferentes visões de probabilidade e inferência estatística
    • Influencia mutua entre diferentes puntos de vista de la probabilidad y la inferencia estadística
  • Enlaces
  • Resumen
    • español

      En este trabajo, analizamos los diversos significados de la probabilidad y sus diferentes aplicaciones, y nos centramos especialmente en la visión clásica, la frecuentista y la subjetivista. Describimos los diferentes problemas de cómo se puede medir la probabilidad en cada uno de los enfoques, y cómo cada uno de ellos puede ser bien justificado por una teoría matemática. Analizamos los fundamentos de la probabilidad, donde el análisis científico del enfoque que permite una interpretación frecuentista conduce a problemas insolubles. La teoría axiomática de Kolmogorov no basta para establecer una inferencia estadística sin más definiciones y principios. Por último, mostramos cómo la inferencia estadística determina esencialmente el significado de la probabilidad y se produce un desplazamiento de las posiciones puramente objetivistas a una concepción complementaria de la probabilidad con componentes frecuentistas y subjetivistas. Con fines didácticos, el resultado de los presentes análisis explica los problemas básicos de la enseñanza, originados por un enfoque sesgado de los aspectos frecuentistas de la probabilidad. También indica una alta prioridad para el diseño de vías de aprendizaje adecuadas a una concepción complementaria de la probabilidad. En las aplicaciones, los modelizadores utilizan la información de manera pragmática procesando esta información, independientemente de su connotación, en modelos matemáticos formales, que siempre se consideran esencialmente erróneos pero útiles.

    • português

      Neste artigo, analisamos os vários significados de probabilidade e suas diferentes aplicações, e focamos especialmente na visão clássica, frequentista e subjetivista. Descrevemos os diferentes problemas de como a probabilidade pode ser medida em cada uma das abordagens, e como cada uma delas pode ser bem justificada por uma teoria matemática. Analisamos os fundamentos da probabilidade, onde a análise científica da teoria que permite uma interpretação frequentista leva a problemas insolúveis. A teoria axiomática de Kolmogorov não é suficiente para estabelecer inferência estatística sem mais definições e princípios. Finalmente, mostramos como a inferência estatística essencialmente determina o significado da probabilidade e uma mudança emerge de visões puramente objetivistas para uma concepção complementar da probabilidade com constituintes frequentistas e subjetivistas. Para fins didáticos, o resultado das presentes análises explica problemas básicos do ensino, decorrentes de um enfoque tendencioso em aspectos frequentistas da probabilidade. Também indica uma alta prioridade para a concepção de caminhos de aprendizagem adequados para uma concepção complementar de probabilidade. Nas aplicações, os modeladores usam informações de uma forma pragmática processando essas informações independentemente de sua conotação em modelos matemáticos formais, que são sempre considerados como essencialmente errados, mas úteis.

    • English

      In this paper, we analyse the various meanings of probability and its different applications, and we focus especially on the classical, the frequentist, and the subjectivist view. We describe the different problems of how probability can be measured in each of the approaches, and how each of them can be well justified by a mathematical theory. We analyse the foundations of probability, where the scientific analysis of the theory that allows for a frequentist interpretation leads to unsolvable problems. Kolmogorov’s axiomatic theory does not suffice to establish statistical inference without further definitions and principles. Finally, we show how statistical inference essentially determines the meaning of probability and a shift emerges from purely objectivist views to a complementary conception of probability with frequentist and subjectivist constituents. For didactical purpose, the result of the present analyses explains basic problems of teaching, originating from a biased focus on frequentist aspects of probability. It also indicates a high priority for the design of suitable learning paths to a complementary conception of probability. In the applications, modellers use information in a pragmatic way processing this information regardless of its connotation into formal mathematical models, which are always thought as essentially wrong but useful.

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