What sort of evidence can confer the strongest support to a hypothesis? A natural answer is that the evidence entails the hypothesis. Roush claims that the likelihood ratio measure of degree of incremental support can deliver this intuitively natural result, and regards it as unifying “[the] account of induction and deduction in the only way that makes sense”. In this paper, we highlight a difficulty in the treatment of this case, and question the great significance that is (...) attached to this measure and its alleged capacity to accommodate the logicality requirement. We contrast the likelihood ratio measure with other measures, and argue that problems still emerge in light of tensions with plausible requirements for confirmation measures more generally. (shrink)

What sort of evidence can confer the strongest support to a hypothesis? A natural answer is that the evidence entails the hypothesis. Roush (Tracking Truth: Knowledge, Evidence, and Science, Clarendon Press, Oxford, 2005) claims that the likelihood ratio measure of degree of incremental support can deliver this intuitively natural result, and regards it as unifying “[the] account of induction and deduction in the only way that makes sense” (p. 163). In this paper, we highlight a difficulty in (...) the treatment of this case, and question the great significance that is attached to this measure and its alleged capacity to accommodate the logicality requirement. We contrast the likelihood ratio measure with other measures (such as the Kemeny–Oppenheim measure and the difference measure), and argue that problems still emerge in light of tensions with plausible requirements for confirmation measures more generally. (shrink)

In the recent literature on confirmation there are two leading approaches to the provision of a probabilistic measure of the degree to which a hypothesis is confirmed by evidence. The first is to construe the degree to which evidence E confirms hypothesis H as a function that is directly proportional to p and inversely proportional to p . I shall refer to this as the probability approach. The second approach construes the notion as a function that is directly proportional (...) to the true-positive rate – the probability of the evidence if the hypothesis is true, p – and inversely proportional to the false-positive rate – the probability of the evidence if the hypothesis is false, p . These reverse conditional probabilities – of the evidence on the truth or falsehood of the hypothesis – are sometimes known as likelihoods. I shall refer to the approach to confirmation that uses them as the likelihood approach.For each of these approaches, there are two obvious options as to how to define the confirmation function. The first is to define it as the difference between the magnitude that is treated as increasing confirmation or p ) and the magnitude that is treated as decreasing confirmation or p ). The second is to define confirmation as the quotient of these two magnitudes.This yields four different measures of confirmation, represented in the following table: Differences RatiosProbabilities PD = p – p1 PR = Graphic2Likelihoods LD = p – p3 LR = Graphic4All these measures agree on whether or not E provides some support for H. Intuitively, we want to say that E provides some support for H just in case learning that E is true would make us assign a higher probability to H, i.e. when p(H …. (shrink)

Probability ratio and likelihood ratio measures of inductive support and related notions have appeared as theoretical tools for probabilistic approaches in the philosophy of science, the psychology of reasoning, and artificial intelligence. In an effort of conceptual clarification, several authors have pursued axiomatic foundations for these two families of measures. Such results have been criticized, however, as relying on unduly demanding or poorly motivated mathematical assumptions. We provide two novel theorems showing that probability ratio and (...) class='Hi'>likelihood ratio measures can be axiomatized in a way that overcomes these difficulties. (shrink)

This paper presents a new argument for the likelihood ratio measure of confirmation by showing that one of the adequacy criteria used in another argument can be replaced by a more plausible and better supported criterion which is a special case of the weak likelihood principle. This new argument is also used to show that the likelihood ratio measure is to be preferred to a measure that has recently received support in the (...) literature. (shrink)

Bayesian confirmation theory is rife with confirmation measures. Zalabardo focuses on the probability difference measure, the probability ratio measure, the likelihood difference measure, and the likelihood ratio measure. He argues that the likelihood ratio measure is adequate, but each of the other three measures is not. He argues for this by setting out three adequacy conditions on confirmation measures and arguing in effect that all of them are met by (...) the likelihood ratio measure but not by any of the other three measures. Glass and McCartney, hereafter “G&M,” accept the conclusion of Zalabardo’s argument along with each of the premises in it. They nonetheless try to improve on Zalabardo’s argument by replacing his third adequacy condition with a weaker condition. They do this because of a worry to the effect that Zalabardo’s third adequacy condition runs counter to the idea behind his first adequacy condition. G&M have in mind confirmation in the sense of increase in probability: the degree to which E confirms H is a matter of the degree to which E increases H’s probability. I call this sense of confirmation “IP.” I set out four ways of precisifying IP. I call them “IP1,” “IP2,” “IP3,” and “IP4.” Each of them is based on the assumption that the degree to which E increases H’s probability is a matter of the distance between p and a certain other probability involving H. I then evaluate G&M’s argument in light of them. (shrink)

There are different Bayesian measures to calculate the degree of confirmation of a hypothesis H in respect of a particular piece of evidence E. Zalabardo (Analysis 69:630–635, 2009) is a recent attempt to defend the likelihood-ratio measure (LR) against the probability-ratio measure (PR). The main disagreement between LR and PR concerns their sensitivity to prior probabilities. Zalabardo invokes intuitive plausibility as the appropriate criterion for choosing between them. Furthermore, he claims that it favours the ordering (...) of pairs evidence/hypothesis generated by LR. We will argue, however, that the intuitive non-numerical example provided by Zalabardo does not show that prior probabilities do not affect the degree of confirmation. On account of this, we conclude that there is no compelling reason to endorse LR qua measure of degree of confirmation. On the other side, we should not forget some technicalities which still benefit PR. (shrink)

I shall offer some very plausible assumptions for the measure of confirmation and show that they imply that E confirms H relative to background K to degree f/PK), where f is a strictly increasing function. An additional assumption about how measures of confirmation combine then makes f be proportional to a logarithm.

This article shows that a slight variation of the argument in Milne 1996 yields the log‐likelihood ratio l rather than the log‐ratio measure r as “the one true measure of confirmation. ” *Received December 2006; revised December 2007. †To contact the author, please write to: Formal Epistemology Research Group, Zukunftskolleg and Department of Philosophy, University of Konstanz, P.O. Box X906, 78457 Konstanz, Germany; e‐mail: franz.huber@uni‐konstanz.de.

The old evidence problem affects any probabilistic confirmation measure based on comparing pr(H/E) and pr(H). The article argues for the following points: (1) measures based on likelihood ratios also suffer old evidence difficulties; (2) the less-discussed synchronic old evidence problem is, in an important sense, the most acute; (3) prominent attempts to solve or dissolve the synchronic problem fail; (4) a little-discussed variant of the standard measure avoids the problem, in an appealing way; and (5) this (...) class='Hi'>measure nevertheless reveals a different problem for probabilistic confirmation measures, a problem that is unlikely to lend itself to formal solution. (shrink)

Likelihoodism is the view that the degree of evidential support should be analysed and measured in terms of likelihoods alone. The paper considers and responds to a popular criticism that a likelihoodist framework is too restrictive to guide belief. First, I show that the most detailed and rigorous version of this criticism, as put forward by Gandenberger (2016), is unsuccessful. Second, I provide a positive argument that a broadly likelihoodist framework can accommodate guidance for comparative belief, even when objectively well-grounded (...) prior probabilities are not available. As I show, the shift from non-relational to comparative probabilities opens up a new space for addressing the belief guidance problem for likelihoodism. (shrink)

There are some candidates that have been thought to measure the degree to which evidence incrementally confirms a hypothesis. This paper provides an argument for one candidate—the log-likelihood ratio measure. For this purpose, I will suggest a plausible requirement that I call the Requirement of Collaboration. And then, it will be shown that, of various candidates, only the log-likelihood ratio measure \(l\) satisfies this requirement. Using this result, Jeffrey conditionalization will be reformulated so (...) as to disclose explicitly what determines new credences after experience. (shrink)

Bayesian epistemology suggests various ways of measuring the support that a piece of evidence provides a hypothesis. Such measures are defined in terms of a subjective probability assignment, pr, over propositions entertained by an agent. The most standard measure (where “H” stands for “hypothesis” and “E” stands for “evidence”) is: the difference measure: d(H,E) = pr(H/E) - pr(H).0 This may be called a “positive (probabilistic) relevance measure” of confirmation, since, according to it, a piece of evidence E (...) qualitatively confirms a hypothesis H if and only if pr(H/E) > pr(H), where qualitative disconfirmation is characterized by replacing “>” with “ “ with “=”. Other more or less standard positive relevance measures that have been proposed are: the log-ratio measure: r(H,E) = log[pr(H/E)/pr(H)] and the log-likelihood-ratio measure: l(H,E) = log[pr(E/H)/pr(E/~H)]. (shrink)

BackgroundDepression is a serious mental disorder often accompanied by emotional and physiological disorders. Visceral fat index is the current standard method in the evaluation of visceral fat deposition. In this study, we explored the association between VAI and depression in the American population using NHANES data.MethodsA total of 2,577 patients were enrolled for this study. Data were collected through structured questionnaires. Subgroup analysis for the relationship between VAI and depression was evaluated using multivariate regression analysis after adjustment for potential confounding (...) factors.ResultsFor every 1 unit increase in VAI, the clinical depression increased by 14%. High VAI scores increased the highest risk of developing depression. Subgroup analysis demonstrated a strong and stable association between VAI and the development of depression.ConclusionOur study showed that depressive symptoms are associated with a high ratio of visceral adiposity index after controlling confounding factors. (shrink)

The main point of the paper is to show how popular probabilistic measures of incremental confirmation and statistical relevance with qualitatively different features can be embedded smoothly in generalized parametric families. In particular, I will show that the probability difference, log probability ratio, log likelihood ratio, odds difference, so-called improbability difference, and Gaifman’s measures of confirmation can all be subsumed within a convenient biparametric continuum. One intermediate step of this project may have interest on its own, as (...) it provides a unified representation of graded belief of which both probabilities and odds are special cases. (shrink)

Hacking’s Law of Likelihood says—paraphrasing—that data support hypothesis H1 over hypothesis H2 whenever the likelihood ratio for H1 over H2 exceeds 1. But Hacking later noted a seemingly fatal flaw in the LR itself: it cannot be interpreted as the degree of “evidential significance” across applications. I agree with Hacking about the problem, but I do not believe the condition is incurable. I argue here that the LR can be properly calibrated with respect to the underlying evidence, (...) and I sketch the rudiments of a methodology for so doing. (shrink)

Hacking’s Law of Likelihood says – paraphrasing– that data support hypothesis H1 over hypothesis H2 whenever the likelihood ratio for H1 over H2 exceeds 1. But Hacking noted a seemingly fatal flaw in the LR itself: it cannot be interpreted as the degree of “evidential significance” across applications. I agree with Hacking about the problem, but I don’t believe the condition is incurable. I argue here that the LR can be properly calibrated with respect to the underlying (...) evidence, and I sketch the rudiments of a methodology for so doing. (shrink)

Stanley Stevens draws a useful distinction among ordinal scales, interval scales, and ratio scales. Most recent discussions of confirmation measures have proceeded on the ordinal level of analysis. In this article, I give a more quantitative analysis. In particular, I show that the requirement that our desired confirmation measure be at least an interval measure naturally yields necessary conditions that jointly entail the log-likelihood measure. Thus, I conclude that the log-likelihood measure is the (...) only good candidate interval measure. (shrink)

In both theoretical and applied modeling in behavioral sciences, it is common to choose a mathematical specification of functional form and distribution of unobservables on grounds of analytic convenience without support from explicit theoretical postulates. This article discusses the issue of deriving particular qualitative hypotheses about functional form restrictions in structural models from intuitive theoretical axioms. In particular, we focus on a family of postulates known as dimensional invariance. Subsequently, we discuss how specific qualitative postulates can be reformulated so as (...) to allow for conventional statistical hypothesis testing, and we also derive details of a particular likelihood ratio test procedure. An empirical application of the testing procedure is carried out, based on data from a Stated Preference survey. (shrink)

The aim of this study is to develop a valid and reliable measurement tool for determining students' spiritual health and life orientation. For this purpose, the Spiritual Health and Life-Orientation Measure (SHALOM) inventory developed by Fisher (2010) is adapted to Turkish. The adaptation study was carried out on 1591 high school students in three study groups studying in Ankara and Muş. The original English measure consisting of four dimensions and twenty items was translated into Turkish, factor analysis, validity (...) and reliability tests were conducted on the sampling data. As a result of the study, the Turkish-adapted inventory consists of four dimensions (personal, social, environmental and transcendental) which resemble the original inventory. In addition, internal consistency coefficients of the inventory dimensions were in perfect harmony with the original inventory and served the purpose of the scale. In Conclusion The Turkish adaptation of the SHALOM Inventory can be used in different disciplines of psychology, educational sciences, and social sciences. Summary: The concept of religion, which is an important dynamic and carrier of the social field, has gone into a double distinction since the second half of the 18th century; the concept of spirituality has begun to be refined from the concept of religion. The concepts of religion and spirituality are very difficult to define; While the concept of religion focuses ideology and rules of belief, spirituality centers on individual experiences and interrelationships that extend religion. For this reason, different spirituality and religion definitions are made from different perspectives and different spirituality scales were developed within this framework. However, the results of these studies differ significantly from each other; this means that spirituality was defined and conceptualized based on the scale that was used. Early period studies on spirituality mostly focus on religion, health, psychology and work life. In these studies, after defining the concept of spirituality; the relationship between the concept and health, religion, psychology and business life or necessity for human life is discussed. In the West, until the 1950s, the concepts of religion and spirituality were used interrelated. However, today these two concepts are almost completely separated from each other.Literature consists of numerous inventory development studies to measure spirituality. The fact that the inventory works based on different conceptual foundations makes it difficult to draw a general, meaningful and consistent conclusion about spiritual health and life orientation. Furthermore, spirituality measurements reflecting the religion and values ​​of a particular culture cannot be comprehensive or universal. At this point, Fisher criticizes the measurement tools developed for the purpose of measuring spirituality: in terms of "mixing religion and spirituality", "relying on the world of values", "not taking into account cultural differences", "and questioning only the mystical/spiritual experience". As a result, it can be said that no measurement developed in the conceptual structure of the West does not take into account the cultural flexibility and accept its spiritual values as universal or prevalent.The SHALOM inventory developed by Fisher, which adapted to the Turkish culture in present study, is based on four basic (individual, social, environmental and transcendent) areas that constitute the world of interpersonal relationship. In this study, spirituality, as in Fisher's work, emphasizes the interaction with certain concepts of different intensities that are considered as independent from religion and above religions. In this context, the concept of spirituality communicates with one's personal space, social position, nature, and transcendental power. This adaptation study will provide useful information and comments on the students' spiritual health levels. This is the most important motive behind the idea of adapting the SHALOM inventory developed by Fisher to the Turkish culture. In addition, by adapting the SHALOM inventory, which is emphasized to have cultural flexibility and adapted to different languages, a new and different measurement tool will be available to understand the nature of the concept of spirituality.This research was carried out to adapt the inventory of Spiritual Health and Life Orientation scale developed for students to Turkish culture. This inventory adaptation study was performed with the data collected from three working groups in Ankara and Muş provinces and 1591 high school students. The first study group was carried out with 414, the second study group with 788, and the third group with 389 high school students. While the data collected from 414 students were used for Exploratory Factor Analysis (AFA) analysis, data collected from 788 students were used for Confirmatory Factor Analysis (CFA). In addition, 389 students were used to determine the criterion validity of the inventory. The original language of the SHALOM inventory, which is intended to be adapted into Turkish, is English, and translation studies are conducted separately by three linguistic experts who know the grammar and semantic characteristics of both languages. After the translation studies, the scale was applied to the sampling group and AFA was performed on the sample data. The AFA results showed that a factor roof resembling the original inventory was formed. Determining factors are given appropriate names (personal, enviromental, social and transcendental) by taking into consideration the theoretical names and the dimension names in the original form of the SHALOM. The structure was confirmed by DFA, and as a result of the DFA, X2/sd (1.72) ratio and IFI (0.96) fit indicator was found to be the appropiate fit for the model tested. As a result, it is understood that the Spiritual Health and Life Orientation Inventory consists of four dimensions as in the original inventory, the internal consistency coefficients of the inventory dimensions are in harmony with the original inventory and serve the purpose of the scale. In conclusion the Turkish adaptation of the SHALOM Inventory can be used in different disciplines of psychology, educational sciences, and social sciences. Spirituality should not only be defined within the framework of Western theories, but the nature and likelihood of the spirituality predicted by Islam should be discussed. Moreover, the types and dimensions of Islamic spirituality should be determined by taking into account the cultural subjectivity of an Islamic character. In the study of spirituality, the human model which modernity presents universally should not be accepted as the only truth. It should be tried to develop human models that come from Islamic culture and history and which are specific to us and define us. This should be taken into account not only in mental health / religious studies, but also in psychology of religion in general. In addition, culture-specificity should be given importance, and the experience gained from the cultural accumulation developed by the Turkish civilization with the Islamic doctrine should lead to the studies of spirituality. In this respect, this study aims to adapt the value and spiritual orientation of a different culture to Turkish culture, but it is problematic to construct the concept with Western values. Although Western values are similar to Islamic values and principles, it is envisaged that it may be difficult to measure the concept of spirituality in practice. (shrink)

We propose a new hybrid data mining method for predicting protein-protein interactions combining Likelihood-Ratio with rule induction algorithms. In essence, the new method consists of using a rule induction algorithm to discover rules representing partitions of the data, and then the discovered rules are interpreted as “bins” which are used to compute likelihood ratios. This new method is applied to the prediction of protein-protein interactions in the Saccharomyces Cerevisiae genome, using predictive genomic features in an integrated scheme. (...) The results show that the new hybrid method outperforms a pure likelihood ratio based approach. (shrink)

There is a plethora of confirmation measures in the literature. Zalabardo considers four such measures: PD, PR, LD, and LR. He argues for LR and against each of PD, PR, and LD. First, he argues that PR is the better of the two probability measures. Next, he argues that LR is the better of the two likelihood measures. Finally, he argues that LR is superior to PR. I set aside LD and focus on the trio of PD, PR, and (...) LR. The question I address is whether Zalabardo succeeds in showing that LR is superior to each of PD and PR. I argue that the answer is negative. I also argue, though, that measures such as PD and PR, on one hand, and measures such as LR, on the other hand, are naturally understood as explications of distinct senses of confirmation. (shrink)

According to Bayesian confirmation theory, evidence E (incrementally) confirms (or supports) a hypothesis H (roughly) just in case E and H are positively probabilistically correlated (under an appropriate probability function Pr). There are many logically equivalent ways of saying that E and H are correlated under Pr. Surprisingly, this leads to a plethora of non-equivalent quantitative measures of the degree to which E confirms H (under Pr). In fact, many non-equivalent Bayesian measures of the degree to which E confirms (or (...) supports) H have been proposed and defended in the literature on inductive logic. I provide a thorough historical survey of the various proposals, and a detailed discussion of the philosophical ramifications of the differences between them. I argue that the set of candidate measures can be narrowed drastically by just a few intuitive and simple desiderata. In the end, I provide some novel and compelling reasons to think that the correct measure of degree of evidential support (within a Bayesian framework) is the (log) likelihood ratio. The central analyses of this research have had some useful and interesting byproducts, including: (i ) a new Bayesian account of (confirmationally) independent evidence, which has applications to several important problems in con- firmation theory, including the problem of the (confirmational) value of evidential diversity, and (ii ) novel resolutions of several problems in Bayesian confirmation theory, motivated by the use of the (log) likelihood ratio measure, including a reply to the Popper-Miller critique of probabilistic induction, and a new analysis and resolution of the problem of irrelevant conjunction (a.k.a., the tacking problem). (shrink)

Reasons transmit. If one has a reason to attain an end, then one has a reason to effect means for that end: reasons are transmitted from end to means. I argue that the likelihood ratio (LR) is a compelling measure of reason transmission from ends to means. The LR measure is superior to other measures, can be used to construct a condition specifying precisely when reasons transmit, and satisfies intuitions regarding end-means reason transmission in a broad (...) array of cases. (shrink)

It is widely believed that one should not become more confident that all swans are white and all lions are brave simply by observing white swans. Irrelevant conjunction or “tacking” of a theory onto another is often thought problematic for Bayesianism, especially given the ratio measure of confirmation considered here. It is recalled that the irrelevant conjunct is not confirmed at all. Using the ratio measure, the irrelevant conjunction is confirmed to the same degree as the (...) relevant conjunct, which, it is argued, is ideal: the irrelevant conjunct is irrelevant. Because the past’s really having been as it now appears to have been is an irrelevant conjunct, present evidence confirms theories about past events only insofar as irrelevant conjunctions are confirmed. Hence the ideal of not confirming irrelevant conjunctions would imply that historical claims are not confirmed. Confirmation measures partially realizing that ideal make the confirmation of historical claims by present evidence depend strongly on the (presumably subjective) degree of belief in the irrelevant conjunct. The unusually good behavior of the ratio measure has a bearing on the problem of measure sensitivity. For non-statistical hypotheses, Bayes’ theorem yields a fractional linear transformation in the prior probability, not a linear rescaling, so even the ratio measure arguably does not aptly measure confirmation in such cases. (shrink)

When the likelihood ratio approach is employed for evidential reasoning in law, it is often necessary to employ subjective probabilities, which are probabilities derived from the opinions and judgement of a human. At least three concerns arise from the use of subjective probabilities in legal applications. Firstly, human beliefs concerning probabilities can be vague, ambiguous and inaccurate. Secondly, the impact of this vagueness, ambiguity and inaccuracy on the outcome of a probabilistic analysis is not necessarily fully understood. Thirdly, (...) the provenance of subjective probabilities and the associated potential sources of vagueness, ambiguity and inaccuracy tend to be poorly understood, making it difficult for the outcome of probabilistic reasoning to be explained and validated, which is crucial in legal applications. The former two concerns have been addressed by a wide body of research in AI. The latter, however, has received little attention. This paper presents a novel approach to employ argumentation to reason about probability distributions in probabilistic models. It introduces a range of argumentation schemes and corresponding sets of critical questions for the construction and validation of argument models that define sets of probability distributions. By means of an extended example, the paper demonstrates how the approach, argumentation schemes and critical questions can be employed for the development of models and their validation in legal applications of the likelihood ratio approach to evidential reasoning. (shrink)

Think of confirmation in the context of the Ravens Paradox this way. The likelihood ratio measure of incremental confirmation gives us, for an observed Black Raven and for an observed non-Black non-Raven, respectively, the following “full” likelihood ratios.

Extensive measurement theory is developed in terms of theratio of two elements of an arbitrary (not necessarily Archimedean) extensive structure; thisextensive ratio space is a special case of a more general structure called aratio space. Ratio spaces possess a natural family of numerical scales (r-scales) which are definable in non-representational terms; ther-scales for an extensive ratio space thus constitute a family of numerical scales (extensive r-scales) for extensive structures which are defined in a non-representational manner. This is (...) interpreted as involving arelational theory of quantity which contrasts in certain respects with thequalitative theory of quantity implicit in standard representational extensive measurement theory. The representational properties of extensiver-scales are investigated, and found to coincide withweak extensive measurement in the sense of Holman. This provides support for the thesis (developed in a separate paper) that weak extensive measurement is a more natural model of actual physical extensive scales than is the standard model using strong extensive measurement. Finally, the present apparatus is applied to slightly simplify the existing necessary and sufficient conditions for strong extensive measurement. (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 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)

In the debate about the legal value of naked statistical evidence, Di Bello argues that (1) the likelihood ratio of such evidence is unknown, (2) the decision-theoretic considerations indicate that a conviction based on such evidence is unacceptable when expected utility maximization is combined with fairness constraints, and (3) the risk of mistaken conviction based on such evidence cannot be evaluated and is potentially too high. We argue that Di Bello’s argument for (1) works in a rather narrow (...) context, and that (1) is not exactly in line with the way expert witnesses are required to formulate their opinions. Consequently, Di Bello’s argument for (2), which assumes (1), does not apply uniformly to all convictions based on naked evidence. Moreover, if Di Bello’s analysis is correct, it applies also to eyewitness testimony, given empirical results about its quality, and so the distinctions drawn by DiBello cut across the distinction between naked statistical evidence and other types of evidence. Finally, if we weaken the rather strong requirement of precise measurability of the risk of mistaken conviction, to the availability of reasonable but imprecise and fallible estimates, many field and empirical studies show that often the risk of mistaken conviction based on naked statistical evidence can be estimated to a similar extent as the risk of mistaken conviction based on any other sort of evidence. (shrink)

In the homogeneous case of one-dimensional objects, we show that any relation that is positive and homothetic can be represented by a ratio-scale and a unique and constant biasing factor. This factor may favor or disfavor the preference for an object over another. In the first case, preferences are complete but not transitive and an object may be preferred even when its value is lower. In the second case, preferences are asymmetric and transitive but not negatively transitive and it (...) may not be sufficient for an object to have a greater value to be preferred. In this manner, the biasing factor reflects the extent to which preferences may depart from a maximization process. (shrink)

Tsui and Weymark (Economic Theory, 1997) have shown that the only continuous social welfare orderings on the whole Euclidean space which satisfy the weak Pareto principle and are invariant to individual-specific similarity transformations of utilities are strongly dictatorial. Their proof relies on functional equation arguments which are quite complex. This note provides a simpler proof of their theorem.

Ordinary measurement using a standard scale, such as a ruler or a standard set of weights, has two fundamental properties. First, the results are approximate, for example, within 0.1 g. Second, the resulting indistinguishability is transitive, rather than nontransitive, as in the standard psychological comparative judgments without a scale. Qualitative axioms are given for structures having the two properties mentioned. A representation theorem is then proved in terms of upper and lower measures.

Sharpe’s ratio is the most widely used index for establishing an order of priority for the portfolios to which the investor has access, and the purpose of this investigation is to verify that Sharpe’s ratio allows decisions to be made in investment portfolios considering different financial market conditions. The research is carried out by autoregressive model of the financial series of returns using Sharpe’s ratio for evaluations looking over the priority of financial assets which the investor can (...) access while observing the effects that can cause autocorrelated series in evaluation measures for financial assets. The results presented in this study confirm the hypothesis proposed in which Sharpe’s ratio allows decisions to be made in the selection of investment portfolios under normal conditions thanks to the definition of a robustness function, whose empirical estimation shows an average 73% explanation of the variance in the degradation of the Spearman coefficient for each of the performance measures; however, given the presence of autocorrelation in the financial series of returns, this similarity is broken. (shrink)

Dr Edwards' stimulating and provocative book advances the thesis that the appropriate axiomatic basis for inductive inference is not that of probability, with its addition axiom, but rather likelihood - the concept introduced by Fisher as a measure of relative support amongst different hypotheses. Starting from the simplest considerations and assuming no more than a modest acquaintance with probability theory, the author sets out to reconstruct nothing less than a consistent theory of statistical inference in science.

This paper introduces the likelihood method for decision under uncertainty. The method allows the quantitative determination of subjective beliefs or decision weights without invoking additional separability conditions, and generalizes the Savage–de Finetti betting method. It is applied to a number of popular models for decision under uncertainty. In each case, preference foundations result from the requirement that no inconsistencies are to be revealed by the version of the likelihood method appropriate for the model considered. A unified treatment of (...) subjective decision weights results for most of the decision models popular today. Savage’s derivation of subjective expected utility can now be generalized and simplified. In addition to the intuitive and empirical contributions of the likelihood method, we provide a number of technical contributions: We generalize Savage’s nonatomiticy condition (“P6”) and his assumption of (sigma) algebras of events, while fully maintaining his flexibility regarding the outcome set. Derivations of Choquet expected utility and probabilistic sophistication are generalized and simplified similarly. The likelihood method also reveals a common intuition underlying many other conditions for uncertainty, such as definitions of ambiguity aversion and pessimism. (shrink)

The likelihood principle of Bayesian statistics implies that information about the stopping rule used to collect evidence does not enter into the statistical analysis. This consequence confers an apparent advantage on Bayesian statistics over frequentist statistics. In the present paper, I argue that information about the stopping rule is nevertheless of value for an assessment of the reliability of the experiment, which is a pre-experimental measure of how well a contemplated procedure is expected to discriminate between hypotheses. I (...) show that, when reliability assessments enter into inquiries, some stopping rules prescribing optional stopping are unacceptable to both Bayesians and frequentists. (shrink)

Theoretically, people’s justification of a sentencing decision involves a hybrid structure comprising retribution, incapacitation, general deterrence, and rehabilitation. In this study, a new ratio-type measure was developed to assess this structure and was tested to detect changes in the weighting of justification according to the content emphasized in a particular crime. Two child neglect scenarios were presented to participants, where they read either a severe-damage scenario or a moderate-damage scenario. Participants then indicated the proportion of importance they placed (...) on each justification in determining the defendant’s punishment, with an overall proportion of 100%, along with responding to the sentence on an 11-point scale. This study involved a two-factor analysis of variance for justification ratios, a t-test for the sentence, and a multiple regression analysis with three demographic variables, the four justifications as independent variables, and the sentence as the dependent variable. The ratio of retribution to rehabilitation was reversed depending on the scenario: in the severe-damage scenario, retribution was weighted highest at 27.0% and rehabilitation was weighted at only 19.0%. By contrast, in the moderate-damage scenario, rehabilitation had the highest weighting of about 26.2%, while retribution was weighted at 21.5%. The sentence was more severe in the severe-damage scenario. Multiple regression analysis suggested that in the severe-damage scenario, most participants failed to deviate from choosing retribution by default and decided on heavier sentences, while some who considered rehabilitation and incapacitation opted for lighter sentences. The present measure succeeded in detecting changes in the weighting of justification, which can be difficult to detect with common Likert Scales. In addition, it was found that not only retribution but utilitarian justification was considered in the sentencing decisions of serious cases. (shrink)

The measurement of sensory intensity has had a long history, attracting the attention of investigators from many disciplines including physiology, psychology, physics, mathematics, philosophy, and even chemistry. While there has been a continuing doubt by some that sensation has the properties necessary for measurement, experiments designed to obtain estimates of sensory intensity have found that a general rule applies: Equal stimulus ratios produce equal sensory ratios. Theories concerning the basis for this simple psychophysical rule are discussed, with emphasis given to (...) the physical correlate theory, which considers judgments of subjective magnitudes to be based upon estimates of physical dimensions that vary regularly with changes in degree of stimulation. For the most thoroughly investigated sensory scales, brightness and loudness, the physical correlate is considered to be distance. Our “tacit knowledge” of the sensory effects of changing distance plays an essential role in matching motor activities to environmental conditions and in ensuring accurate perceptual evaluations through brightness and loudness constancies. In psychophysical experiments, subjects apparently use this same tacit knowledge when required to estimate relative subjective magnitudes. The evidence related to the physical correlate theory is summarized, and it is concluded that, while under appropriate conditions we demonstrate considerable skill in evaluating environmental relationships, we are quite unable to estimate the neurophysiological nature or quantity of sensory response. A psychophysics devoted to studying conditions required for accuracy and conditions producing errors in the perception of environmental relationships would seem to be more valuable than one devoted to subjective magnitudes. (shrink)

An adequate account of laws should satisfy at least five desiderata: it should provide a unified account of laws and chances, it should yield plausible relations between laws and chances, it should vindicate numerical chance assignments, it should accommodate dynamical and non-dynamical chances, and it should accommodate a plausible range of nomic possibilities. No extant account of laws satisfies these desiderata. This paper presents a non-Humean account of laws, the Nomic Likelihood Account, that does.

Measurement is any process by which a value is assigned to the level or state of some quality of an object of study. This value is given numerical form, and measurement therefore involves the expression of information in quantities rather than by verbal statement. It provides a powerful means of reducing qualitative data to more condensed form for summarization, manipulation and analysis. The classical distinctions made by S S S Stevens between nominal, ordinal, interval and ratio measurement are a (...) common starting point for discussion of social science measurement and the use of statistical techniques. This article considers the applicability of this model to research in the social sciences, particularly sociology and political science. Differences between classical measurement theory and practice in the social sciences are discussed. Problems in social science conceptualization, operationalization and measurement are examined, and a number of issues raised. Three cases are given particular attention, the Social Indicators movement, the variable of social class, and measures of race and ethnicity. The article concludes that the 'ineluctable fuzziness' of many social science concepts is inescapable, and that social measurement remains a difficult and challenging issue. (shrink)