Conditional independence tests have received special attention lately in machine learning and computational intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of probabilistic graphical models, which includes Bayesian network models, conditional independence tests are especially important for the task of learning the probabilistic graphical model structure from data. In this paper, we propose the full Bayesian significance test for tests of conditional independence for discrete datasets. The full Bayesian (...) significance test is a powerful Bayesian test for precise hypothesis, as an alternative to the frequentist’s significance tests (characterized by the calculation of the p-value). (shrink)

This paper discusses the possibility of an absolute vacuum - a space without any substance. The motivation of this study is the contrast between most philosophers, up to Descartes, who stated that a vacuum was impossible, and the 17th century change of outlook, when the possibility and effective existence of the vacuum was accepted after the experiments of Torricelli and Pascal. This article attempts to show that, contrary to the received opinion, the acceptance of an ether is preferable to the (...) acceptance of a vacuum for several reasons. First: it is impossible to provide an empirical proof of the non-existence of the ether; second, an absolute vacuum is unthinkable; third, the ether concept is useful for the understanding of physical phaenomena; and fourth, the hypothesis of an ether in apparently void spaces is useful for the future development of science. The paper also endeavours to show that no recent advance of science changed those conclusions and that no future development can change them. (shrink)

O desempenho das empresas tem sido estudado sob diferentes perspectivas teóricas, que, em geral a utilizam indicadores econômico-financeiros. Essa abordagem sofre constantes críticas por não contemplar aspectos estratégicos, que podem fornecer informações acerca de vantagem competitiva obtida pela empresa. Fatores macroeconômicos também tendem a impactar de maneira indireta os diferentes setores. Além disso, os setores sofrem esses impactos macroeconômicos conforme o nível de exposição deste às oscilações macroeconômicas. Assim este trabalho buscou analisar como as dimensões de desempenho se relacionam com (...) retorno, para cada setor da bolsa de valores. Para a análise, utilizou-se a modelagem de equações estruturais a partir do software Smart-PLS. Foram utilizados dados do Economática para 82 empresas listadas em 6 setores da B3 no período entre 2011 e 2018. Os resultados indicam que diferentes indicadores compõe os construtos para cada setor analisado, indicando que o retorno tem associações diferentes em cada setor. O construto econômico-financeiro apresenta uma relação positiva na explicação dos retornos para os diferentes setores. Já o construto estratégico relacionou-se positivamente apenas no setor de Materiais Básicos. A dimensão macroeconômica apresentou resultados que evidenciam uma relação negativa com os retornos no período analisado. Assim pode-se apontar que o retorno de cada setor é explicado por diferentes informações, sugerindo que o investidor deve observar critérios específicos de cada setor. Os indicadores macroeconômicos foram similares para os setores analisados, contudo o impacto significativo não pode ser verificado para todos os setores, indicando que existem níveis de exposição diferentes para os setores. Ainda, foram evidenciados tanto efeitos diretos quanto indiretos dos indicadores macroeconômicos sobre o retorno. (shrink)

The diversity in agronomic practices being used by sugarcane producers in Brazil determines differences in economic performance and cost structure. The purpose of this study is to evaluate the cost of six systems of agronomic practices using fixed or variable rates for soil amendment, fertilizer, and defensive applications and assess the profitability of these systems at three scales of sugarcane production. We then describe the data sample related to the 2019–2020 harvest season and collected from fifty-five sugarcane producers in the (...) central-south region of Brazil. Thereafter, using a quantitative approach, a cost analysis was performed, and the cumulative frequency of the net revenue for the three scales of production (small, medium, and large), was calculated using a Monte Carlo simulation. The cost analysis indicated that fertilizer had the highest cost considering the agronomic practices adopted at the three scales of production analyzed. The cumulative frequency analysis results from the Monte Carlo simulation showed the highest net revenue per hectare for medium sugarcane producers. In addition, the presence of economies of scale was not confirmed because the lowest cost was found in small-scale sugarcane producers and the highest net revenue was obtained by medium-scale sugarcane producers. (shrink)

The costs of agricultural inputs added to those of labor represent almost a third of the total cost of Brazilian sugarcane production. This study analyzes the behavior of the price per ton of sugarcane in Brazil, relating it to the main production costs of this cultivation. Twelve price indicators from January 2015 to December 2020 were evaluated. First, the data were adjusted to a multiple linear regression model to identify the significant variables on variation in the price per ton of (...) sugarcane. Then, the Monte Carlo simulation was used to measure the level of certainty of occurrence of these variables, and forecasts were obtained from the adjustment of ARIMA models. The results showed the influence of the costs of diesel oil, two agricultural pesticides, and daily laborers on the price of sugarcane, besides an increasing trend of its, providing relevant short-term projections for decision-making about investments in the agribusiness sector. (shrink)

This paper studies Lamarck's scientific method both from the point of view of his methodological discourse and according to his scientific praxis. Lamarck's methodology is compared to Condillac's as well as to that of the idéologues - a group in which Lamarck is usually included. The analysis of this paper shows that Lamarck's methodological discourse is very similar to Condillac's, but his scientific praxis does not follow this view. Instead of following an empiricist approach, Lamarck's work is grounded upon general (...) metaphysical principles concerning nature. Thus, from the ideologues's point of view, Lamarck's work should have been rejected -and that is what really happened - as being a mere metaphysical system grupo no qual se costuma incluir o próprio Lamarck. Mostra-se que o discurso metodológico de Lamarck assemelha-se ao dos ideólogos; no entanto, sua prática científica não se coaduna com esse enfoque. Em vez de seguir uma abordagem empirista, a obra de Lamarck se fundamenta em princípios metafísicos gerais sobre a natureza. Sob o ponto de vista dos ideólogos, seu trabalho deveria ser rejeitado - o que de fato ocorreu - como um mero sistema metafísico - no sentido pejorativo utilizado pelos seguidores de Condillac. No entanto, o presente artigo argumenta que esse é justamente um importante e inovador aspecto da obra de Lamarck, que permitiu a eclosão do evolucionismo moderno. (shrink)

In this article we defend a moral conception of cosmopolitanism and its relevance for moral education. Our moral conception of cosmopolitanism presumes that persons possess an inherent dignity in the Kantian sense and therefore they should be recognised as ends‐in‐themselves. We argue that cosmopolitan ideals can inspire moral educators to awaken and cultivate in their pupils an orientation and inclination to struggle against injustice. Moral cosmopolitanism, in other words, should more explicitly inform the work that moral educators do. Real‐world constraints (...) on moral action and the need to prioritise one’s sometimes conflicting responsibilities will often qualify cosmopolitan justice as supererogatory. This fact does not absolve persons from aspiring to see themselves as having the moral obligation to help others in need, while recognising that their factual obligations are more modest in being bound by what they are actually able to do. (shrink)

In this paper we provide a defence of cosmopolitanism from a liberal perspective, examining its moral underpinnings, including moral obligations predicated on a belief in common humanity and the fundamental dignity of human people, cultural capacities that include an embrace of pluralism and a fallibilist disposition, and pragmatist resolve in finding humanitarian solutions to real problems that people face. We also scrutinise the ideal of cosmopolitanism by considering the ‘deeply religious’ as the sort of people about whom it may be (...) said that irreconcilable tensions exist between certain types of commitment and/or belonging and what the demands of cosmopolitanism involve. (shrink)

Livro-texto de introdução à lógica, com (mais do que) pitadas de filosofia da lógica, produzido como uma versão revista e ampliada do livro Forallx: Calgary. Trata-se da versão de 13 de outubro de 2022. Comentários, críticas, correções e sugestões são muito bem-vindos.

We describe the rationale for an application ontology covering the domain of human body fluids that is designed to facilitate representation, reuse, sharing and integration of diagnostic, physiological, and biochemical data, We briefly review the Blood Ontology (BLO), Saliva Ontology (SALO) and Kidney and Urinary Pathway Ontology (KUPO) initiatives. We discuss the methods employed in each, and address the project of using them as starting point for a unified body fluids ontology resource. We conclude with a description of how the (...) body fluids ontology initiative may provide support to basic and translational science. (shrink)

Neste artigo propomos uma reconceitualização do amor como um modo de engajamento intersubjetivo normativamente guiado pela busca constante do equilíbrio entre a sub- e a sobredeterminação de seu objeto, que se efetiva em relações deconfiança marcadas pelo cuidado com o(a) outro(a). Esta reconceitualização permite que o amor participe da epistemologia como uma virtude intelectual responsabilista, que nos torna membros mais confiáveis de nossas comunidades epistêmicas e nos aproxima de descrições verdadeiras sobre o mundo, ao deixar que diversos pontos de vista (...) sobre esses objetos sejam reconhecidos e valorizados. (shrink)

An intuitive and widely accepted view is that (a) beliefs aim at truth, (b) many citizens have stable and meaningful political beliefs, and (c) citizens choose to support political candidates or parties on the basis of their political beliefs. We argue that all three claims are false. First, we argue that political beliefs often differ from ordinary world-modelling beliefs because they do not aim at truth. Second, we draw on empirical evidence from political science and psychology to argue that most (...) people lack stable and meaningful political beliefs. Third, we claim that the true psychological basis for voting behavior is not an individual’s political beliefs but rather group identity. Along the way, we reflect on what this means for normative democratic theory. (shrink)

According to the simple modal account of essence, an object has a property essentially just in case it has it in every world in which it exists. As many have observed, the simple modal account is implausible for a number of reasons. This has led to various proposals for strengthening the account, for example, by adding a restriction to the intrinsic or sparse properties. I argue, however, that these amendments to the simple modal account themselves fail. Drawing on lessons from (...) these failures, I propose a new version of a modal account, inspired by Ruth Barcan Marcus's defense of the coherence of quantified modal logic, according to which an object has a property essentially just in case (i) it has it in every world in which it exists, (ii) the property is discriminating (or non-trivial), and (iii) the property is qualitative. The resulting account of essence does not face any of the standard objections other accounts face, and I defend it from other potential objections. (shrink)

An intuitive objection to modal realism is that merely possible worlds and their inhabitants seem to be irrelevant to an analysis of modality. Kripke originally phrased the objection in terms of being concerned about one’s modal properties without being concerned about the properties one’s other-worldly counterparts have. The author assesses this objection in a variety of forms, and then provides his own formulation that does not beg the question against the modal realist. Finally, the author considers two potential answers to (...) the objection so understood and concludes that only one of them has a chance of succeeding. (shrink)

In this article we aim to open a new line of debate about religion in public schools by focusing on religious ideals. We begin with an elucidation of the concept ‘religious ideals’ and an explanation of the notion of reasonable pluralism, in order to be able to explore the dangers and positive contributions of religious ideals and their pursuit on a liberal democratic society. We draw our examples of religious ideals from Christianity and Islam, because these religions have most adherents (...) in Western liberal democracies that are the focus of this article. The fifth and most important section ‘‘Reasonable pluralism and the inclusion of religious ideals in public secondary schools’’ provides three arguments for our claim that public schools should include religious ideals, namely that they are important to religious people, that they are conducive for the development of pupils into citizens of a liberal democracy, and that the flourishing of pupils as adults is advanced by encountering religious ideals. We also offer a more practical reason: religious ideals can more easily be included within public education than religious dogmas and rules. (shrink)

In this paper, I argue that Plotinus does not limit the sphere of free human agency simply to intellectual contemplation, but rather extends it all the way to human praxis. Plotinus’s goal in the first six chapters of Ennead 6.8 is, accordingly, to demarcate the space of freedom within human practical actions. He ultimately concludes that our external actions are free whenever they actualize, in unhindered fashion, the moral principles derived from intellectual contemplation. This raises the question of how the (...) freedom of practical actions might relate to the freedom of intellectual contemplation. After considering two previously offered models—a model of double activity, and an Aristotelian model of practical syllogism—I offer a third alternative, namely a model of moral attunement, according to which our rational desires assume a kind of ‘care of the soul’ through active supervision. Practical life is thus imbued with freedom to the extent that the soul supervises its actions to conform to its will and choice of the good. (shrink)

An interesting question is whether deflationism about truth (and falsity) extends to related properties and relations on truthbearers. Lionel Shapiro (2011) answers affirmatively by arguing that a certain deflationism about truth is as plausible as an analogous version of deflationism about logical consequence. I argue that the argument fails on two counts. First, it trivializes to any relation between truthbearers, including substantive ones; in other words, his argument can be used to establish that deflationism about truth is as plausible as (...) deflationism about an arbitrary sentential relation. Second, the alleged analogy between the arguments for deflationism about truth and deflationism about consequence fails. Along the way I consider what implications the failure of the equiplausibility thesis has for deflationism about falsity. (shrink)

The discipline of knowledge translation (KT) emerged as a way of systematically understanding and addressing the challenges of applying health and medical research in practice. In light of ongoing and emerging critique of KT from the medical humanities and social sciences disciplines, KT researchers have become increasingly aware of the complexity of the translational process, particularly the significance of culture, tradition and values in how scientific evidence is understood and received, and thus increasingly receptive to pluralistic notions of knowledge. Hence, (...) there is now an emerging view of KT as a highly complex, dynamic, and integrated sociological phenomenon, which neither assumes nor creates knowledge hierarchies and neither prescribes nor privileges scientific evidence. Such a view, however, does not guarantee that scientific evidence will be applied in practice and thus poses a significant dilemma for KT regarding its status as a scientific and practice-oriented discipline, particularly within the current sociopolitical climate. Therefore, in response to the ongoing and emerging critique of KT, we argue that KT must provide scope for relevant scientific evidence to occupy an appropriate position of epistemic primacy in public discourse. Such a view is not intended to uphold the privileged status of science nor affirm the “scientific logos” per se. It is proffered as a counterbalance to powerful social, cultural, political and market forces that are able to challenge scientific evidence and promote disinformation to the detriment of democratic outcomes and the public good. (shrink)

In Posterior Analytics II 16-17, Aristotle seems to claim that there cannot be more than one explanans of the same scientific explanandum. However, this seems to be true only for “primary-universal” demonstrations, in which the major term belongs to the minor “in itself” and the middle term is coextensive with the extremes. If so, several explananda we would like to admit as truly scientific would be out of the scope of an Aristotelian science. The secondary literature has identified a second (...) problem in II 16-17: the middle term of a demonstration is sometimes taken as the definition of the minor term (the subject), other times as the definition (or the causal part of the definition) of the major (the demonstrable attribute). I shall argue that Aristotle’s solution to the first problem involves showing that certain problematic attributes, which appear to admit more than one explanation, actually fall into the privileged scenario of primary-universal demonstrations. In addition, his solution suggests a conciliatory way-out to our second problem (or so I shall argue): the existence of an attribute as a definable unity depends on its subject having the essence it has, which suggests that both the essence of subjects and the essence of demonstrable attributes can play explanatory roles in demonstrations. (shrink)

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on (...) the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes. (shrink)

The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine Bayesian measure of evidence, is discussed in detail. Its behavior in some problems of statistical inference like testing for independence in contingency tables is discussed.

The Generalized Poisson Distribution (GPD) adds an extra parameter to the usual Poisson distribution. This parameter induces a loss of homogeneity in the stochastic processes modeled by the distribution. Thus, the generalized distribution becomes an useful model for counting processes where the occurrence of events is not homogeneous. This model creates the need for an inferential procedure, to test for the value of this extra parameter. The FBST (Full Bayesian Significance Test) is a Bayesian hypotheses test procedure, capable of providing (...) an evidence measure on sharp hypotheses (where the dimension of the parametric space under the null hypotheses is smaller than that of the full parametric space). The goal of this work is study the empirical properties of the FBST for testing the nullity of extra parameter of the generalized Poisson distribution. Numerical experiments show a better performance of FBST with respect to the classical likelihood ratio test, and suggest that FBST is an efficient and robust tool for this application. (shrink)

t Intentional sampling methods are non-randomized procedures that select a group of individuals for a sample with the purpose of meeting specific prescribed criteria. In this paper we extend previous works related to intentional sampling, and address the problem of sequential allocation for clinical trials with few patients. Roughly speaking, patients are enrolled sequentially, according to the order in which they start the treatment at the clinic or hospital. The allocation problem consists in assigning each new patient to one, and (...) only one, of the alternative treatment arms. The main requisite is that the profiles in the alternative arms remain similar with respect to some relevant patients’ attributes (age, gender, disease, symptom severity and others). We perform numerical experiments based on a real case study and discuss how to conveniently set up perturbation parameters, in order to yield a suitable balance between optimality – the similarity among the relative frequencies of patients in the several categories for both arms, and decoupling – the absence of a tendency to allocate each pair of patients consistently to the same arm. (shrink)

Abstract: The Pull Bayesian Significance Test (FBST) for precise hy- potheses is applied to a Multivariate Normal Structure (MNS) model. In the FBST we compute the evidence against the precise hypothesis. This evi- dence is the probability of the Highest Relative Surprise Set (HRSS) tangent to the sub-manifold (of the parameter space) that defines the null hypothesis. The MNS model we present appears when testing equivalence conditions for genetic expression measurements, using micro-array technology.

Intentional sampling methods are non-probabilistic procedures that select a group of individuals for a sample with the purpose of meeting specific prescribed criteria. Intentional sampling methods are intended for exploratory research or pilot studies where tight budget constraints preclude the use of traditional randomized representative sampling. The possibility of subsequently generalize statistically from such deterministic samples to the general population has been the issue of long standing arguments and debates. Nevertheless, the intentional sampling techniques developed in this paper explore pragmatic (...) strategies for overcoming some of the real or perceived shortcomings and limitations of intentional sampling in practical applications. (shrink)

A Bayesian measure of evidence for precise hypotheses is presented. The intention is to give a Bayesian alternative to significance tests or, equivalently, to p-values. In fact, a set is defined in the parameter space and the posterior probability, its credibility, is evaluated. This set is the “Highest Posterior Density Region” that is “tangent” to the set that defines the null hypothesis. Our measure of evidence is the complement of the credibility of the “tangent” region.

The Full Bayesian Significance Test (FBST) for precise hypotheses is presented, with some applications relevant to reliability theory. The FBST is an alternative to significance tests or, equivalently, to p-ualue.s. In the FBST we compute the evidence of the precise hypothesis. This evidence is the probability of the complement of a credible set "tangent" to the sub-manifold (of the para,rreter space) that defines the null hypothesis. We use the FBST in an application requiring a quality control of used components, based (...) on remaining life statistics. (shrink)

Clearing algorithms are at the core of modern payment systems, facilitating the settling of multilateral credit messages with (near) minimum transfers of currency. Traditional clearing procedures use batch processing based on MILP - mixed-integer linear programming algorithms. The MILP approach demands intensive computational resources; moreover, it is also vulnerable to operational risks generated by possible defaults during the inter-batch period. This paper presents TORC3 - the Token-Ring Clearing Algorithm for Currency Circulation. In contrast to the MILP approach, TORC3 is a (...) real time heuristic procedure, demanding modest computational resources, and able to completely shield the clearing operation against the participating agents’ risk of default. (shrink)

in Oct-14-1998 ordinance INDESP-IO4 established the federal software certification and verification requirements for gaming machines in Brazil. The authors present the rationale behind these criteria, whose basic principles can find applications in several other software authentication applications.

The unit root problem plays a central role in empirical applications in the time series econometric literature. However, significance tests developed under the frequentist tradition present various conceptual problems that jeopardize the power of these tests, especially for small samples. Bayesian alternatives, although having interesting interpretations and being precisely defined, experience problems due to the fact that that the hypothesis of interest in this case is sharp or precise. The Bayesian significance test used in this article, for the unit root (...) hypothesis, is based solely on the posterior density function, without the need of imposing positive probabilities to sets of zero Lebesgue measure. Furthermore, it is conducted under strict observance of the likelihood principle. It was designed mainly for testing sharp null hypotheses and it is called FBST for Full Bayesian Significance Test. (shrink)

This article presents a two level hierarchical forecasting model developed in a consulting project for a Brazilian magazine publishing company. The first level uses a VARMA model and considers econometric variables. The second level takes into account qualitative aspects of each publication issue, and is based on polynomial networks generated by Genetic Programming (GP).

Gene clustering is a useful exploratory technique to group together genes with similar expression levels under distinct cell cycle phases or distinct conditions. It helps the biologist to identify potentially meaningful relationships between genes. In this study, we propose a clustering method based on multivariate normal mixture models, where the number of clusters is predicted via sequential hypothesis tests: at each step, the method considers a mixture model of m components (m = 2 in the first step) and tests if (...) in fact it should be m - 1. If the hypothesis is rejected, m is increased and a new test is carried out. The method continues (increasing m) until the hypothesis is accepted. The theoretical core of the method is the full Bayesian significance test, an intuitive Bayesian approach, which needs no model complexity penalization nor positive probabilities for sharp hypotheses. Numerical experiments were based on a cDNA microarray dataset consisting of expression levels of 205 genes belonging to four functional categories, for 10 distinct strains of Saccharomyces cerevisiae. To analyze the method’s sensitivity to data dimension, we performed principal components analysis on the original dataset and predicted the number of classes using 2 to 10 principal components. Compared to Mclust (model-based clustering), our method shows more consistent results. (shrink)

The data analyzed in this paper are part of the results described in Bueno et al. (2000). Three cytogenetics endpoints were analyzed in three populations of a species of wild rodent – Akodon montensis – living in an industrial, an agricultural, and a preservation area at the Itajaí Valley, State of Santa Catarina, Brazil. The polychromatic/normochromatic ratio, the mitotic index, and the frequency of micronucleated polychromatic erythrocites were used in an attempt to establish a genotoxic profile of each area. It (...) was assumed that the three populations were in the same conditions with respect to the influence of confounding factors such as animal age, health, nutrition status, presence of pathogens, and intra- and inter-populational genetic variability. Therefore, any differences found in the endpoints analyzed could be attributed to the external agents present in each area. The statistical models used in this paper are mixtures of negative-binomials and Poisson variables. The Poisson variables are used as approximations of binomials for rare events. The mixing distributions are beta densities. The statistical analyzes are under the bayesian perspective, as opposed to the frequentist ones often considered in the literature, as for instance in Bueno et al. (2000). (shrink)

To estimate causal relationships, time series econometricians must be aware of spurious correlation, a problem first mentioned by Yule (1926). To deal with this problem, one can work either with differenced series or multivariate models: VAR (VEC or VECM) models. These models usually include at least one cointegration relation. Although the Bayesian literature on VAR/VEC is quite advanced, Bauwens et al. (1999) highlighted that “the topic of selecting the cointegrating rank has not yet given very useful and convincing results”. The (...) present article applies the Full Bayesian Significance Test (FBST), especially designed to deal with sharp hypotheses, to cointegration rank selection tests in VECM time series models. It shows the FBST implementation using both simulated and available (in the literature) data sets. As illustration, standard non informative priors are used. (shrink)

We present a module based criterion, i.e. a sufficient condition based on the absolute value of the matrix coefficients, for the convergence of Gauss–Seidel method (GSM) for a square system of linear algebraic equations, the Generalized Line Criterion (GLC). We prove GLC to be the “most general” module based criterion and derive, as GLC corollaries, some previously know and also some new criteria for GSM convergence. Although far more general than the previously known results, the proof of GLC is simpler. (...) The results used here are related to recent research in stability of dynamical systems and control of manufacturing systems. (shrink)

The Fully Bayesian Significance Test (FBST) is a coherent Bayesian significance test for sharp hypotheses. This paper proposes the FBST as a model selection tool for general mixture models, and compares its performance with Mclust, a model-based clustering software. The FBST robust performance strongly encourages further developments and investigations.

The Gompertz distribution is commonly used in biology for modeling fatigue and mortality. This paper studies a class of models proposed by Adham and Walker, featuring a Gompertz type distribution where the dependence structure is modeled by a lognormal distribution, and develops a new multivariate formulation that facilitates several numerical and computational aspects. This paper also implements the FBST, the Full Bayesian Significance Test for pertinent sharp (precise) hypotheses on the lognormal covariance structure. The FBST’s e-value, ev(H), gives the epistemic (...) value of hypothesis, H, or the value of evidence in the observed in support of H. (shrink)