Logically-consistent hypothesis testing and the hexagon of oppositions
Full text
| |
| Author(s): |
Stern, Julio Michael
[1]
;
Izbicki, Rafael
[2]
;
Esteves, Luis Gustavo
[1]
;
Stern, Rafael Bassi
[2]
Total Authors: 4
|
| Affiliation: | [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
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | LOGIC JOURNAL OF THE IGPL; v. 25, n. 5, p. 741-757, OCT 2017. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 14/50279-4 - Brasil Research Centre for Gas Innovation |
| Grantee: | Julio Romano Meneghini |
| Support type: | Research Grants - Research Centers in Engineering Program |
| FAPESP's process: | 14/25302-2 - A flexible approach to high-dimensional conditional density estimation |
| Grantee: | Rafael Izbicki |
| Support type: | Regular Research Grants |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | José Alberto Cuminato |
| Support type: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 17/03363-8 - Interpretability and efficiency in hypothesis tests |
| Grantee: | Rafael Izbicki |
| Support type: | Regular Research Grants |