Logically-consistent hypothesis testing and the hexagon of oppositions

Autor(es)

Stern, Julio Michael ^[1] ; Izbicki, Rafael ^[2] ; Esteves, Luis Gustavo ^[1] ; Stern, Rafael Bassi ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Fed Sao Carlos, Dept Estat, UFSCar, Rodovia Washington Luis, Km 235, BR-13565905 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: LOGIC JOURNAL OF THE IGPL; v. 25, n. 5, p. 741-757, OCT 2017.
• Citações Web of Science: 1

Resumo

Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for these modalities to be logically consistent. Prisms composed of hexagons of oppositions show how the credal modalities obtained from two agnostic tests vary according to their threshold values. Nested hexagons of oppositions summarize logical relations between the credal modalities in these tests and prove new relations. (AU)

• Processo FAPESP: 14/25302-2 - Uma abordagem flexível para a estimação de uma densidade condicional em problemas com alta dimensionalidade
• Beneficiário: Rafael Izbicki
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 14/50279-4 - Brasil Research Centre for Gas Innovation
• Beneficiário: Julio Romano Meneghini
• Linha de fomento: Auxílio à Pesquisa - Programa Centros de Pesquisa em Engenharia
• Processo FAPESP: 17/03363-8 - Interpretabilidade e eficiência em testes de hipótese
• Beneficiário: Rafael Izbicki
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: José Alberto Cuminato
• Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs