arXiv subjects

Luis G. Esteves

Publications and source records attributed to Luis G. Esteves.

4 recordsLinked to original sources

arXiv2022

Logical coherence in Bayesian simultaneous three-way hypothesis tests

This paper studies whether Bayesian simultaneous three-way hypothesis tests can be logically coherent. Two types of results are obtained. First, under the standard error-wise constant loss, only for a limited set of models can a Bayes simultaneous test be logically coherent. Second, if more general loss functions are used, then it is possible to obtain Bayes simultaneous tests that are always logically coherent. An explicit example of such a loss function is provided.

math.ST↗

arXiv2019

Teaching decision theory proof strategies using a crowdsourcing problem

Teaching how to derive minimax decision rules can be challenging because of the lack of examples that are simple enough to be used in the classroom. Motivated by this challenge, we provide a new example that illustrates the use of standard techniques in the derivation of optimal decision rules under the Bayes and minimax approaches. We discuss how to predict the value of an unknown quantity, $θ\! \in \! \{0,1\}$, given the opinions of $n$ experts. An important example of such crowdsourcing problem occurs in modern cosmology, where $θ$ indicates whether a given galaxy is merging or not, and $Y_1, \ldots, Y_n$ are the opinions from $n$ astronomers regarding $θ$. We use the obtained prediction rules to discuss advantages and disadvantages of the Bayes and minimax approaches to decision theory. The material presented here is intended to be taught to first-year graduate students.

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arXiv2019

Logically-consistent hypothesis testing in the hexagon of oppositions

Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. In order to address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This paper 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.

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arXiv2018

Pragmatic hypotheses in the evolution of science

This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise hypotheses. These pragmatic versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais.

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