This article gives a conceptual review of the e-value, ev (H | X)-the epistemic value of hypothes... more This article gives a conceptual review of the e-value, ev (H | X)-the epistemic value of hypothesis H given observations X. This statistical significance measure was developed in order to allow logically coherent and consistent tests of hypotheses, including sharp or precise hypotheses, via the Full Bayesian Significance Test (FBST). Arguments of analysis allow a full characterization of this statistical test by its logical or compositional properties, showing a mutual complementarity between results of mathematical statistics and the logical desiderata lying at the foundations of this theory.
Brazilian Journal of Probability and Statistics, 2016
Our purpose is to recommend a change in the paradigm of testing by generalizing a very natural id... more Our purpose is to recommend a change in the paradigm of testing by generalizing a very natural idea, originated perhaps in Jeffreys [Proceedings of the Cambridge Philosophy Society 31 (1935) 203-222; The Theory of Probability (1961) Oxford Univ. Press] and clearly exposed by DeGroot [Probability and Statistics (1975) Addison-Wesley], with the aim of developing an approach that is attractive to all schools of statistics, resulting in a procedure better suited to the needs of science. The essential idea is to base testing statistical hypotheses on minimizing a weighted sum of type I and type II error probabilities instead of the prevailing paradigm, which is fixing type I error probability and minimizing type II error probability. For simple vs simple hypotheses, the optimal criterion is to reject the null using the likelihood ratio as the evidence (ordering) statistic, with a fixed threshold value instead of a fixed tail probability. By defining expected type I and type II error probabilities, we generalize the weighting approach and find that the optimal region is defined by the evidence ratio, that is, a ratio of averaged likelihoods (with respect to a prior measure) and a fixed threshold. This approach yields an optimal theory in complete generality, which the classical theory of testing does not. This can be seen as a Bayesian/non-Bayesian compromise: using a weighted sum of type I and type II error probabilities is Frequentist, but basing the test criterion on a ratio of marginalized likelihoods is Bayesian. We give arguments to push the theory still further, so that the weighting measures (priors) of the likelihoods do not have to be proper and highly informative, but just "well calibrated." That is, priors that give rise to the same evidence (marginal likelihoods) using minimal (smallest) training samples. The theory that emerges, similar to the theories based on objective Bayesian approaches, is a powerful response to criticisms of the prevailing approach of hypothesis testing. For criticisms see, for example, Ioannidis [PLoS Medicine 2 (2005) e124] and Siegfried [Science News 177 (2010) 26-29], among many others.
This article presents a Bayesian nonparametric approach to the estimation of a system and its com... more This article presents a Bayesian nonparametric approach to the estimation of a system and its components' survival functions arising from observing the failure of a series system or a competing risk model. A Dirichlet multivariate process is used as a prior for the vector of the components' random subsurvival function to derive Bayes estimator of the survival function when the cause of failure belongs to a certain risk subset. This is done as follows. First, Peterson's formula is evaluated using the Bayes estimators of the subsurvival functions corresponding to the risk subset, to obtain a plugged-in nonparametric estimator of the survival function associated with the risk subset. Then, using the product-integration approach, it is proved that this nonparametric estimator is in fact the Bayes estimator of the survival function corresponding to the risk subset under quadratic loss function and the Dirichlet multivariate process. The weak convergence and the strong consistency of the estimator is established. The special case when the system has only two components corresponds to well studied randomly censored model.
principal components. Compared to Mclust (model-based clustering), our method shows more consiste... more principal components. Compared to Mclust (model-based clustering), our method shows more consistent results.
The article presents a Bayesian analysis for the environmental stress screening problem. The deci... more The article presents a Bayesian analysis for the environmental stress screening problem. The decision problem of deriving optimal stress screen durations is solved. Given a screen duration, the optimal stress level can also be determined. Indicators of the quality of a screen of any duration are derived. A statistical model is presented which allows a posterior density for the rate of early failures of the production process to be calculated. This enables the user to update his opinion about the quality of the process.
The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine... more 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 Sufficiency Principle states that it is equal for the Statistician to observe the full data o... more The Sufficiency Principle states that it is equal for the Statistician to observe the full data or a sufficient statistic. Nevertheless, it can only be used as a criterion for the comparison of random functions which are coupled on the same measure space. On the other hand, when analyzing experiments usually only their marginal distributions are given. Thus the Sufficiency Principle alone, in general, is not enough to compare them. In this article we show that Blackwell's Equivalence relation between experiments is equal to the Sufficiency Principle and the Coupling Invariance Principle which are, in some manner, weaker than the Likelihood Principle.
Page 1. 05791 ANÁLISE DOS EFEITOS DO FIPRONIL (INGREDIENTE ATIVO DO FRONTLINE ® ) NAS CÉLULAS DAS... more Page 1. 05791 ANÁLISE DOS EFEITOS DO FIPRONIL (INGREDIENTE ATIVO DO FRONTLINE ® ) NAS CÉLULAS DAS GLÂNDULAS SALIVARES DE FÊMEAS DE Rhipicephalus sanguineus (LATREILLE, 1806) (ACARI: IXODIDAE) ...
This is a review article on statistical identifiability. Besides the definition of the main conce... more This is a review article on statistical identifiability. Besides the definition of the main concepts, we deal with several questions relevant to the statistician: parallelism between parametric identifiability and sample sufficiency; relationship of identifiability with measures of sample information and with the inferential concept of estimability; several strategies of making inferences in unidentifiable models with emphasis on the distinct behaviour of the classical and Bayesian approaches. The concepts, ideas and methods discussed are illustrated with simple examples of statistical models.
Geometric percolation in polydisperse systems of finite-diameter rods: Effects due to particle cl... more Geometric percolation in polydisperse systems of finite-diameter rods: Effects due to particle clustering and interparticle correlations J. Chem. Phys. 137, 134903 (2012) Wigner surmises and the two-dimensional Poisson-Voronoi tessellation J. Math. Phys. 53, 103507 (2012) Bulk universality of general β-ensembles with non-convex potential J. Math. Phys. 53, 095221 Fully synchronous solutions and the synchronization phase transition for the finite-N Kuramoto model Chaos 22, 033133 Additional information on AIP Conf. Proc.
We revisit Birnbaum's results on the Likelihood Principle, reorganizing and making a few formal c... more We revisit Birnbaum's results on the Likelihood Principle, reorganizing and making a few formal changes which address some of the criticisms at the original development. The meaning of the residts for different theories of statistical inference is exemplified, and the role of the Likelihood Principle as means to assess the consistency of those theories is emphasized.
Objective: To determine the influence of diabetes on the use of arterial reconstruction, the rate... more Objective: To determine the influence of diabetes on the use of arterial reconstruction, the rate of amputation and death, and the quality of life of patients with severe limb ischaemia. Design: A prospective study of patients with the first episode of ischaemia. Setting: University tertiary referral centre. Methods: Thirty-seven patients with diabetes and 50 without diabetes, were studied over a 12 month period with complete follow-up. Main outcome measures: The proportion of patients undergoing an arterial reconstruction, amputation rate, death rate, and quality-of-life scores. Results: Patients with diabetes underwent an arterial reconstruction less often than patients without diabetes (7/37 vs. 18/50). The odds of patients with diabetes having a higher incidence of adverse outcome was 1666:1 for minor amputation, 26:1 for major amputation, and 4.7:1 for death. There was a tendency towards a lower quality of life for patients with diabetes at 3 (OR 1.94, p = 0.036), 6 (OR 1.58, p = 0.117), and 12 (OR 1.47, p = 0.185) months. Conclusions: In patients with diabetes, (1) the opportunity of undergoing an arterial reconstruction is lower, (2) morbidity and mortality are higher, and (3) the quality of life tends to be worse.
The goal of this paper is to illustrate how two significance indices-the frequentist p-value and ... more The goal of this paper is to illustrate how two significance indices-the frequentist p-value and Bayesian e-valuehave a straight mathematical relationship. We calculate these indices for standard statistical situations in which sharp null hypotheses are being tested. The p-value considered here is based on the likelihood ratio statistic. The existence of a functional relationship between these indices could surprise readers because they are computed in different spaces: p-values in the sample space and e-values in the parameter space.
The usual finite population model—where information provided by a subset of units is used to redu... more The usual finite population model—where information provided by a subset of units is used to reduce uncertainty about functions of the complete population list of values—is explored from a predictivistic point of view. Under this approach, only operationally meaningful quantities (operational parameters) are considered and therefore no superpopulation parameters are involved. This paper addresses the estimation of both population total
This work presents a method to analyze characteristics of a set of genes that can have an influen... more This work presents a method to analyze characteristics of a set of genes that can have an influence in a certain anomaly, such as a particular type of cancer. A measure is proposed with the objective of diagnosing individuals regarding the anomaly under study and some characteristics of the genes are analyzed. Maximum likelihood equations for general and particular cases are presented.
This article gives a conceptual review of the e-value, ev (H | X)-the epistemic value of hypothes... more This article gives a conceptual review of the e-value, ev (H | X)-the epistemic value of hypothesis H given observations X. This statistical significance measure was developed in order to allow logically coherent and consistent tests of hypotheses, including sharp or precise hypotheses, via the Full Bayesian Significance Test (FBST). Arguments of analysis allow a full characterization of this statistical test by its logical or compositional properties, showing a mutual complementarity between results of mathematical statistics and the logical desiderata lying at the foundations of this theory.
Brazilian Journal of Probability and Statistics, 2016
Our purpose is to recommend a change in the paradigm of testing by generalizing a very natural id... more Our purpose is to recommend a change in the paradigm of testing by generalizing a very natural idea, originated perhaps in Jeffreys [Proceedings of the Cambridge Philosophy Society 31 (1935) 203-222; The Theory of Probability (1961) Oxford Univ. Press] and clearly exposed by DeGroot [Probability and Statistics (1975) Addison-Wesley], with the aim of developing an approach that is attractive to all schools of statistics, resulting in a procedure better suited to the needs of science. The essential idea is to base testing statistical hypotheses on minimizing a weighted sum of type I and type II error probabilities instead of the prevailing paradigm, which is fixing type I error probability and minimizing type II error probability. For simple vs simple hypotheses, the optimal criterion is to reject the null using the likelihood ratio as the evidence (ordering) statistic, with a fixed threshold value instead of a fixed tail probability. By defining expected type I and type II error probabilities, we generalize the weighting approach and find that the optimal region is defined by the evidence ratio, that is, a ratio of averaged likelihoods (with respect to a prior measure) and a fixed threshold. This approach yields an optimal theory in complete generality, which the classical theory of testing does not. This can be seen as a Bayesian/non-Bayesian compromise: using a weighted sum of type I and type II error probabilities is Frequentist, but basing the test criterion on a ratio of marginalized likelihoods is Bayesian. We give arguments to push the theory still further, so that the weighting measures (priors) of the likelihoods do not have to be proper and highly informative, but just "well calibrated." That is, priors that give rise to the same evidence (marginal likelihoods) using minimal (smallest) training samples. The theory that emerges, similar to the theories based on objective Bayesian approaches, is a powerful response to criticisms of the prevailing approach of hypothesis testing. For criticisms see, for example, Ioannidis [PLoS Medicine 2 (2005) e124] and Siegfried [Science News 177 (2010) 26-29], among many others.
This article presents a Bayesian nonparametric approach to the estimation of a system and its com... more This article presents a Bayesian nonparametric approach to the estimation of a system and its components' survival functions arising from observing the failure of a series system or a competing risk model. A Dirichlet multivariate process is used as a prior for the vector of the components' random subsurvival function to derive Bayes estimator of the survival function when the cause of failure belongs to a certain risk subset. This is done as follows. First, Peterson's formula is evaluated using the Bayes estimators of the subsurvival functions corresponding to the risk subset, to obtain a plugged-in nonparametric estimator of the survival function associated with the risk subset. Then, using the product-integration approach, it is proved that this nonparametric estimator is in fact the Bayes estimator of the survival function corresponding to the risk subset under quadratic loss function and the Dirichlet multivariate process. The weak convergence and the strong consistency of the estimator is established. The special case when the system has only two components corresponds to well studied randomly censored model.
principal components. Compared to Mclust (model-based clustering), our method shows more consiste... more principal components. Compared to Mclust (model-based clustering), our method shows more consistent results.
The article presents a Bayesian analysis for the environmental stress screening problem. The deci... more The article presents a Bayesian analysis for the environmental stress screening problem. The decision problem of deriving optimal stress screen durations is solved. Given a screen duration, the optimal stress level can also be determined. Indicators of the quality of a screen of any duration are derived. A statistical model is presented which allows a posterior density for the rate of early failures of the production process to be calculated. This enables the user to update his opinion about the quality of the process.
The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine... more 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 Sufficiency Principle states that it is equal for the Statistician to observe the full data o... more The Sufficiency Principle states that it is equal for the Statistician to observe the full data or a sufficient statistic. Nevertheless, it can only be used as a criterion for the comparison of random functions which are coupled on the same measure space. On the other hand, when analyzing experiments usually only their marginal distributions are given. Thus the Sufficiency Principle alone, in general, is not enough to compare them. In this article we show that Blackwell's Equivalence relation between experiments is equal to the Sufficiency Principle and the Coupling Invariance Principle which are, in some manner, weaker than the Likelihood Principle.
Page 1. 05791 ANÁLISE DOS EFEITOS DO FIPRONIL (INGREDIENTE ATIVO DO FRONTLINE ® ) NAS CÉLULAS DAS... more Page 1. 05791 ANÁLISE DOS EFEITOS DO FIPRONIL (INGREDIENTE ATIVO DO FRONTLINE ® ) NAS CÉLULAS DAS GLÂNDULAS SALIVARES DE FÊMEAS DE Rhipicephalus sanguineus (LATREILLE, 1806) (ACARI: IXODIDAE) ...
This is a review article on statistical identifiability. Besides the definition of the main conce... more This is a review article on statistical identifiability. Besides the definition of the main concepts, we deal with several questions relevant to the statistician: parallelism between parametric identifiability and sample sufficiency; relationship of identifiability with measures of sample information and with the inferential concept of estimability; several strategies of making inferences in unidentifiable models with emphasis on the distinct behaviour of the classical and Bayesian approaches. The concepts, ideas and methods discussed are illustrated with simple examples of statistical models.
Geometric percolation in polydisperse systems of finite-diameter rods: Effects due to particle cl... more Geometric percolation in polydisperse systems of finite-diameter rods: Effects due to particle clustering and interparticle correlations J. Chem. Phys. 137, 134903 (2012) Wigner surmises and the two-dimensional Poisson-Voronoi tessellation J. Math. Phys. 53, 103507 (2012) Bulk universality of general β-ensembles with non-convex potential J. Math. Phys. 53, 095221 Fully synchronous solutions and the synchronization phase transition for the finite-N Kuramoto model Chaos 22, 033133 Additional information on AIP Conf. Proc.
We revisit Birnbaum's results on the Likelihood Principle, reorganizing and making a few formal c... more We revisit Birnbaum's results on the Likelihood Principle, reorganizing and making a few formal changes which address some of the criticisms at the original development. The meaning of the residts for different theories of statistical inference is exemplified, and the role of the Likelihood Principle as means to assess the consistency of those theories is emphasized.
Objective: To determine the influence of diabetes on the use of arterial reconstruction, the rate... more Objective: To determine the influence of diabetes on the use of arterial reconstruction, the rate of amputation and death, and the quality of life of patients with severe limb ischaemia. Design: A prospective study of patients with the first episode of ischaemia. Setting: University tertiary referral centre. Methods: Thirty-seven patients with diabetes and 50 without diabetes, were studied over a 12 month period with complete follow-up. Main outcome measures: The proportion of patients undergoing an arterial reconstruction, amputation rate, death rate, and quality-of-life scores. Results: Patients with diabetes underwent an arterial reconstruction less often than patients without diabetes (7/37 vs. 18/50). The odds of patients with diabetes having a higher incidence of adverse outcome was 1666:1 for minor amputation, 26:1 for major amputation, and 4.7:1 for death. There was a tendency towards a lower quality of life for patients with diabetes at 3 (OR 1.94, p = 0.036), 6 (OR 1.58, p = 0.117), and 12 (OR 1.47, p = 0.185) months. Conclusions: In patients with diabetes, (1) the opportunity of undergoing an arterial reconstruction is lower, (2) morbidity and mortality are higher, and (3) the quality of life tends to be worse.
The goal of this paper is to illustrate how two significance indices-the frequentist p-value and ... more The goal of this paper is to illustrate how two significance indices-the frequentist p-value and Bayesian e-valuehave a straight mathematical relationship. We calculate these indices for standard statistical situations in which sharp null hypotheses are being tested. The p-value considered here is based on the likelihood ratio statistic. The existence of a functional relationship between these indices could surprise readers because they are computed in different spaces: p-values in the sample space and e-values in the parameter space.
The usual finite population model—where information provided by a subset of units is used to redu... more The usual finite population model—where information provided by a subset of units is used to reduce uncertainty about functions of the complete population list of values—is explored from a predictivistic point of view. Under this approach, only operationally meaningful quantities (operational parameters) are considered and therefore no superpopulation parameters are involved. This paper addresses the estimation of both population total
This work presents a method to analyze characteristics of a set of genes that can have an influen... more This work presents a method to analyze characteristics of a set of genes that can have an influence in a certain anomaly, such as a particular type of cancer. A measure is proposed with the objective of diagnosing individuals regarding the anomaly under study and some characteristics of the genes are analyzed. Maximum likelihood equations for general and particular cases are presented.
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