Marginal structural models can be used to estimate the causal effect of a potentially time-varying treatment in the presence of time-dependent confounding via weighted regression. The standard approach of using inverse probability of treatment weighting can be sensitive to model misspecification and lead to high-variance estimates due to extreme weights. Various methods have been proposed to partially address this, including covariate balancing propensity score to mitigate treatment model misspecification, and truncation and stabilized-IPTW to temper (...) extreme weights. In this article, we present kernel optimal weighting, a convex-optimization-based approach that finds weights for fitting the MSMs that flexibly balance time-dependent confounders while simultaneously penalizing extreme weights, directly addressing the above limitations. We further extend KOW to control for informative censoring. We evaluate the performance of KOW in a simulation study, comparing it with IPTW, sIPTW, and CBPS. We demonstrate the use of KOW in studying the effect of treatment initiation on time-to-death among people living with human immunodeficiency virus and the effect of negative advertising on elections in the United States. (shrink)

In causal inference, a variety of causal effect estimands have been studied, including the sample, uncensored, target, conditional, optimal subpopulation, and optimal weighted average treatment effects. Ad hoc methods have been developed for each estimand based on inverse probability weighting and on outcome regression modeling, but these may be sensitive to model misspecification, practical violations of positivity, or both. The contribution of this article is twofold. First, we formulate the generalized average treatment effect to unify these (...) causal estimands as well as their IPW estimates. Second, we develop a method based on Kernel optimal matching to optimally estimate GATE and to find the GATE most easily estimable by KOM, which we term the Kernel optimal weighted average treatment effect. KOM provides uniform control on the conditional mean squared error of a weighted estimator over a class of models while simultaneously controlling for precision. We study its theoretical properties and evaluate its comparative performance in a simulation study. We illustrate the use of KOM for GATE estimation in two case studies: comparing spine surgical interventions and studying the effect of peer support on people living with HIV. (shrink)

In the presence of heterogeneity between the randomized controlled trial (RCT) participants and the target population, evaluating the treatment effect solely based on the RCT often leads to biased quantification of the real-world treatment effect. To address the problem of lack of generalizability for the treatment effect estimated by the RCT sample, we leverage observational studies with large samples that are representative of the target population. This article concerns evaluating treatment effects on survival outcomes for a (...) target population and considers a broad class of estimands that are functionals of treatment-specific survival functions, including differences in survival probability and restricted mean survival times. Motivated by two intuitive but distinct approaches, i.e., imputation based on survival outcome regression and weighting based on inverse probability of sampling, censoring, and treatment assignment, we propose a semiparametric estimator through the guidance of the efficient influence function. The proposed estimator is doubly robust in the sense that it is consistent for the target population estimands if either the survival model or the weighting model is correctly specified and is locally efficient when both are correct. In addition, as an alternative to parametric estimation, we employ the nonparametric method of sieves for flexible and robust estimation of the nuisance functions and show that the resulting estimator retains the root- n n consistency and efficiency, the so-called rate-double robustness. Simulation studies confirm the theoretical properties of the proposed estimator and show that it outperforms competitors. We apply the proposed method to estimate the effect of adjuvant chemotherapy on survival in patients with early-stage resected non-small cell lung cancer. (shrink)

Two-stage voting is prone to majority inversions, a situation in which the outcome of an election is not backed by a majority of popular votes. We study the probability of majority inversion in a model with two candidates, three states and uniformly distributed fractions of supporters for each candidate. The model encompasses equal or distinct population sizes, with equal, population-based or arbitrary voting weights in the second stage. We prove that, when no state can dictate the outcome of (...) the election by commanding a voting weight in excess of one half, the probability of majority inversion increases with the size disparity among the states. (shrink)

Randomized controlled trials sometimes test interventions that aim to improve existing services targeted to a subset of individuals identified after randomization. Accordingly, the treatment could affect the composition of service recipients and the offered services. With such bias, intention-to-treat estimates using data on service recipients and nonrecipients may be difficult to interpret. This article develops causal estimands and inverse probability weighting estimators for complier populations in these settings, using a generalized estimating equation approach that adjusts the standard (...) errors for estimation error in the IPW weights. While our focus is on more general clustered RCTs, the methods also apply to nonclustered RCTs. Simulations show that the estimators achieve nominal confidence interval coverage under the assumed identification conditions. An empirical application demonstrates the methods using data from a large-scale RCT testing the effects of early childhood services on children’s cognitive development scores. An R program for estimation is available for download. (shrink)

Inverse probability weighting (IPW) is a general tool in survey sampling and causal inference, used in both Horvitz–Thompson estimators, which normalize by the sample size, and Hájek/self-normalized estimators, which normalize by the sum of the inverse probability weights. In this work, we study a family of IPW estimators, first proposed by Trotter and Tukey in the context of Monte Carlo problems, that are normalized by an affine combination of the sample size and a sum of (...) inverse weights. We show how selecting an estimator from this family in a data-dependent way to minimize asymptotic variance leads to an iterative procedure that converges to an estimator with connections to regression control methods. We refer to such estimators as adaptively normalized estimators. For mean estimation in survey sampling, the adaptively normalized estimator has asymptotic variance that is never worse than the Horvitz–Thompson and Hájek estimators. Going further, we show that adaptive normalization can be used to propose improvements of the augmented IPW (AIPW) estimator, average treatment effect (ATE) estimators, and policy learning objectives. Appealingly, these proposals preserve both the asymptotic efficiency of AIPW and the regret bounds for policy learning with IPW objectives, and deliver consistent finite sample improvements in simulations for all three of mean estimation, ATE estimation, and policy learning. (shrink)

Doubly robust (DR) estimators are an important class of statistics derived from a theory of semiparametric efficiency. They have become a popular tool in causal inference, including applications to dynamic treatment regimes. The doubly robust estimators for the mean response to a dynamic treatment regime may be conceived through the augmented inverse probability weighted (AIPW) estimating function, defined as the sum of the inverse probability weighted (IPW) estimating function and an augmentation term. The IPW (...) estimating function of the causal estimand via marginal structural model is defined as the complete-case score function for those subjects whose treatment sequence is consistent with the dynamic regime in question divided by the probability of observing the treatment sequence given the subject's treatment and covariate histories. The augmentation term is derived by projecting the IPW estimating function onto the nuisance tangent space and has mean-zero under the truth. The IPW estimator of the causal estimand is consistent if (i) the treatment assignment mechanism is correctly modeled and the AIPW estimator is consistent if either (i) is true or (ii) nested functions of intermediate and final outcomes are correctly modeled.Hence, the AIPW estimator is doubly robust and, moreover, the AIPW is semiparametric efficient if both (i) and (ii) are true simultaneously. Unfortunately, DR estimators can be inferior when either (i) or (ii) is true and the other false. In this case, the misspecified parts of the model can have a detrimental effect on the variance of the DR estimator. We propose an improved DR estimator of causal estimand in dynamic treatment regimes through a technique originally developed by [4] which aims to mitigate the ill-effects of model misspecification through a constrained optimization.In addition to solving a doubly robust system of equations, the improved DR estimator simultaneously minimizes the asymptotic variance of the estimator under a correctly specified treatment assignment mechanism but misspecification of intermediate and final outcome models. We illustrate the desirable operating characteristics of the estimator through Monte Carlo studies and apply the methods to data from a randomized study of integrilin therapy for patients undergoing coronary stent implantation. The methods proposed here are new and may be used to further improve personalized medicine, in general. (shrink)

Numerous studies have convincingly shown that prospect theory can better describe risky choice behavior than the classical expected utility model because it makes the plausible assumption that risk aversion is driven not only by the degree of sensitivity toward outcomes, but also by the degree of sensitivity toward probabilities. This article presents the results of an experiment aimed at testing whether agents become more sensitive toward probabilities over time when they repeatedly face similar decisions, receive feedback on the consequences of (...) their decisions, and are given ample incentives to reflect on their decisions, as predicted by Plott’s Discovered Preference Hypothesis (DPH). The results of a laboratory experiment with N = 62 participants support this hypothesis. The elicited subjective probability weighting function converges significantly toward linearity when respondents are asked to make repeated choices and are given direct feedback after each choice. Such convergence to linearity is absent in an experimental treatment where respondents are asked to make repeated choices but do not experience the resolution of risk directly after each choice, as predicted by the DPH. (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities (...) are not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

Numerous studies have convincingly shown that prospect theory can better describe risky choice behavior than the classical expected utility model because it makes the plausible assumption that risk aversion is driven not only by the degree of sensitivity toward outcomes, but also by the degree of sensitivity toward probabilities. This article presents the results of an experiment aimed at testing whether agents become more sensitive toward probabilities over time when they repeatedly face similar decisions, receive feedback on the consequences of (...) their decisions, and are given ample incentives to reflect on their decisions, as predicted by Plott’s Discovered Preference Hypothesis (DPH). The results of a laboratory experiment with N = 62 participants support this hypothesis. The elicited subjective probability weighting function converges significantly toward linearity when respondents are asked to make repeated choices and are given direct feedback after each choice. Such convergence to linearity is absent in an experimental treatment where respondents are asked to make repeated choices but do not experience the resolution of risk directly after each choice, as predicted by the DPH. (shrink)

We propose a discrete time branching process to model the appearance of drug resistance under treatment. Under our assumptions at every discrete time a pathogen may die with probability 1−p or divide in two with probability p. Each newborn pathogen is drug resistant with probability μ. We start with N drug sensitive pathogens and with no drug resistant pathogens. We declare the treatment successful if all pathogens are eradicated before drug resistance appears. The model predicts (...) that success is possible only if p<1/2. Even in this case the probability of success decreases exponentially with the parameter m=μN. In particular, even with a very potent drug (i.e. p very small) drug resistance is likely if m is large. (shrink)

This article presents the results of an experiment that completely measures the utility function and probability weighting function for different positive and negative monetary outcomes, using a representative sample of N = 1,935 from the general public. The results confirm earlier findings in the lab, suggesting that utility is less pronounced than what is found in classical measurements where expected utility is assumed. Utility for losses is found to be convex, consistent with diminishing sensitivity, and the obtained loss-aversion coefficient (...) of 1.6 is moderate but in agreement with contemporary evidence. The estimated probability weighting functions have an inverse-S shape and they imply pessimism in both domains. These results show that probability weighting is also an important phenomenon in the general population. Women and lower educated individuals are found to be more risk averse, in agreement with common findings. In contrast to previous studies that ascribed gender differences in risk attitudes solely to differences in the degree utility curvature, however, our results show that this finding is primarily driven by loss aversion and, for women, also by a more pessimistic psychological response toward the probability of obtaining the best possible outcome. (shrink)

This article presents the results of an experiment that completely measures the utility function and probability weighting function for different positive and negative monetary outcomes, using a representative sample of N = 1,935 from the general public. The results confirm earlier findings in the lab, suggesting that utility is less pronounced than what is found in classical measurements where expected utility is assumed. Utility for losses is found to be convex, consistent with diminishing sensitivity, and the obtained loss-aversion coefficient (...) of 1.6 is moderate but in agreement with contemporary evidence. The estimated probability weighting functions have an inverse-S shape and they imply pessimism in both domains. These results show that probability weighting is also an important phenomenon in the general population. Women and lower educated individuals are found to be more risk averse, in agreement with common findings. In contrast to previous studies that ascribed gender differences in risk attitudes solely to differences in the degree utility curvature, however, our results show that this finding is primarily driven by loss aversion and, for women, also by a more pessimistic psychological response toward the probability of obtaining the best possible outcome. (shrink)

There is ongoing debate on how to fairly allocate scarce critical care resources to patients with COVID-19. The debate revolves around two views: those who believe that priority for scarce resources should primarily aim at saving the most lives (SML) or at saving the most life-years, and those who believe that public health should focus on health equity to address health disparities and social determinants of health. I argue that maximizing medical outcomes by saving the greatest number of patients is (...) not a plausible strategy for combating COVID-19. There are reasons of fairness to give each patient who can meet general eligibility requirements a chance of being saved. Rather than focusing on outcome maximization, a better solution would be the individualist lottery that takes account of probability of survival and duration of treatment. Although the individualist lottery allocates scarce resources in a fair way that is responsive to health equity concerns, it still gives considerable weight to the concern of SML. Thus, this procedure can be reasonably accepted by all key stakeholders. (shrink)

By the time this issue of the Journal is published, the world will have moved on. More will be known, than at the time of writing this, about how medicine and societies are responding to the ethical challenges presented by the COVID-19 coronavirus pandemic. In his guest editorial,, Dominic Wilkinson writes from the perspective of a UK clinician and ethicist facing the then still impending likelihood that ‘the number of critically ill patients will overwhelm the capacity of intensive care units’ (...) and that ‘it will simply not be possible to provide mechanical ventilation to every patient who might need it’. The ‘unpalatable question’ for clinicians then will be ‘which patient to save’? In his response to this question, Wilkinson identifies benefit and fairness as the key ethical values at stake in such triage decisions: ‘how much ethical weight is given to each of these values’, he argues, will depend not only on the need to find a fair balance between them, but also on the availability of resources. ‘As resources become more limited’, he writes, ‘there is some need to temper equality with benefit’. In the limited provision of publicly funded intensive care, there already exists ’a need to decline admission to intensive care for some patients who have a low probability of survival, or of benefiting from the treatment’: but ‘in a situation where resources are overwhelmed, and choice cannot be avoided’, he argues, the ethical balance must shift to emphasizing benefit’, which in practice means prioritising ‘those patients who have the highest chance of surviving’, or ‘a shorter duration of intensive care stay’. Wilkinson does not …. (shrink)

According to the ‘Description–Experience gap’, when people are provided with the descriptions of risky prospects they make choices as if they overweight the probability of rare events; but when making decisions from experience after exploring the prospects’ properties, they behave as if they underweight such probability. This study revisits this discrepancy while focusing on information-search in decisions from experience. We report findings from a lab-experiment with three treatments: a standard version of decisions from description and two versions of (...) decisions from experience: with and without a ‘history table’ recording previously sampled events. We find that people sample more from lotteries with rarer events. The history table proved influential; in its absence search is more responsive to cues such as a lottery’s variance while in its presence the cue that stands out is the table’s maximum capacity. Our analysis of risky choices captures a significant DE gap which is mitigated by the presence of the history table. We elicit probability weighting functions at the individual level and report that subjects overweight rare events in experience but less so than in description. Finally, we report a measure that allows us to compare the type of DE gap found in studies using choice patterns with that inferred through valuation and find that the phenomenon is similar but not identical across the two methods. (shrink)

Delineation of the subthalamic nuclei on MRI is critical for deep brain stimulation surgery in patients with Parkinson’s disease. We propose this retrospective cohort study for quantitative analysis of MR signal-to-noise ratio, contrast, and signal difference-to-noise ratio of the STN on pre-operative three-dimensional stereotactic MRI in patients with medication-refractory PD. Forty-five consecutive patients with medication-refractory PD who underwent STN-DBS surgery in our hospital from January 2018 to June 2021 were included in this study. All patients had whole-brain 3D MRI, including (...) T2-weighted imaging, T2-weighted fluid-attenuated inversion recovery, and susceptibility-weighted imaging, at 3.0 T scanner for stereotactic navigation. The signal intensities of the STN, corona radiata, and background noise were obtained after placing regions of interest on corresponding structures. Quantitative comparisons of SNR, contrast, and SDNR of the STN between MR pulse sequences, including the T2WI, FLAIR, and SWI. Subgroup analysis regarding patients’ sex, age, and duration of treatment. We used one-way repeated measures analysis of variance for quantitative comparisons of SNR, contrast, and SDNR of the STN between different MR pulse sequences, and we also used the dependent t-test for the post hoc tests. In addition, we used Mann–Whitney U test for subgroup analyses. Both the contrast and SDNR were highest on FLAIR. The SNR was highest on SWI, and both the SNR and SDNR were lowest on T2WI. Subgroup analyses demonstrated significantly lower SDNR on SWI for patients receiving medication treatment for ≥13 years. In conclusion, on 3D stereotactic MRI of medication-refractory PD patients, the contrast and SDNR for the STN are highest on FLAIR, suggesting the optimal delineation of STN on FLAIR. (shrink)

Introduction: Purpose of this essay is to draw attention to some points which are relevant to the underlying philosophy of modern statistics, but which the writer feels have been largely overlooked both by the defenders and the opponents of the classic conceptions of Laplace. There is no quarrel with methodologies as such which have found their introduction under the heads of “maximum likelihood”, “fiducial limits”, etc. But the writer cannot accept arguments ) which would make of such procedures an absolute (...) sine qua non for all decisions based on evidence, and which would relegate human judgment and all considerations of the intended use of a decision to the rubbish heap of outmoded conceptions. To assume that two rational minds, having different backgrounds and different objectives, must necessarily find themselves in agreement in their appraisal of a given objective situation, is simply absurd; yet this is the basis which underlies, so far as I can make out, all the “criticisms” of Laplace and Bayes which constitute the excuses put forward for attempting to displace those procedures in Statistics which involve “inverse probability”. Also the so-called “paradoxes” which have been invented by many writers in order to assail Laplace, contradict only this one assumption; without it they are not paradoxes. (shrink)

Causal Modeling Semantics (CMS, e.g., Galles and Pearl 1998; Pearl 2000; Halpern 2000) is a powerful framework for evaluating counterfactuals whose antecedent is a conjunction of atomic formulas. We extend CMS to an evaluation of the probability of counterfactuals with disjunctive antecedents, and more generally, to counterfactuals whose antecedent is an arbitrary Boolean combination of atomic formulas. Our main idea is to assign a probability to a counterfactual (A ∨ B) > C at a causal model M as (...) a weighted average of the probability of C in those submodels that truthmake A∨ B (Briggs 2012; Fine 2016, 2017). The weights of the submodels are given by the inverse distance to the original model M, based on a distance metric proposed by Eva, Stern, and Hartmann (2019). Apart from solving a major problem in the epistemology of counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined. (shrink)

Many philosophers argue that Keynes’s concept of the “weight of arguments” is an important aspect of argument appraisal. The weight of an argument is the quantity of relevant evidence cited in the premises. However, this dimension of argumentation does not have a received method for formalisation. Kyburg has suggested a measure of weight that uses the degree of imprecision in his system of “Evidential Probability” to quantify weight. I develop and defend this approach to measuring weight. I illustrate the (...) usefulness of this measure by employing it to develop an answer to Popper’s Paradox of Ideal Evidence. (shrink)

We consider a setting where a decision maker’s uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well known to suffer from problems. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a (...) natural approach to determining the weights. We then show how this representation can be used in decision making, by modifying a standard approach to decision making—minimizing expected regret—to obtain minimax weighted expected regret. We provide an axiomatization that characterizes preferences induced by MWER both in the static and dynamic case. (shrink)

First issued in translation as a two-volume work in 1975, this classic book provides the first complete development of the theory of probability from a subjectivist viewpoint. It proceeds from a detailed discussion of the philosophical mathematical aspects to a detailed mathematical treatment of probability and statistics. De Finetti’s theory of probability is one of the foundations of Bayesian theory. De Finetti stated that probability is nothing but a subjective analysis of the likelihood that something (...) will happen and that that probability does not exist outside the mind. It is the rate at which a person is willing to bet on something happening. This view is directly opposed to the classicist/ frequentist view of the likelihood of a particular outcome of an event, which assumes that the same event could be identically repeated many times over, and the 'probability' of a particular outcome has to do with the fraction of the time that outcome results from the repeated trials. (shrink)

The majority consensus in the empirical literature is that probability weighting functions are typically inverse-S shaped, that is, people tend to overweight small and underweight large probabilities. A separate stream of literature has reported event-splitting effects and shown that they can explain violations of expected utility. This leads to the questions whether the observed shape of weighting functions is a mere consequence of the coalesced presentation and, more generally, whether preference elicitation should rely on presenting lotteries in a (...) canonical split form instead of the commonly used coalesced form. We analyze data from a binary choice experiment where all lottery pairs are presented in both split and coalesced forms. Our results show that the presentation in a split form leads to a better fit of expected utility theory and to probability weighting functions that are closer to linear. We thus provide some evidence that the extent of probability weighting is not an ingrained feature, but rather a result of processing difficulties. (shrink)

This case study considers the ethical defensibility of recommending weight loss as a treatment for patients with higher body mass indexes. Recommending weight loss may be motivated by clinicians’ biases toward people living in larger bodies, misperceptions about weight and its relevancy to overall health, and a failure to consider other ethical factors such as those related to equity and the social determinants of health.

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 62.1 (2001) 1-16 [Access article in PDF] The Plot of History from Antiquity to the Renaissance Eric MacPhail In the Poetics Aristotle introduced the notion of plot or mythos as a distinctly poetic form of rationality and coherence absent from history. In the course of antiquity and the Renaissance Aristotle's notion of plot underwent a curious inversion by which history came to supplant (...) poetry as the main literary form of emplotment. To account for the readjustment or even reversal of Aristotle's distinction between history and poetry, we will examine the notions of order, causality, and chance expounded by classical historians and literary theorists before tracing their influence to Renaissance writers. In the Renaissance the transmission, conflation, and distortion of Aristotelian doctrine exerted a profound influence on historiography and literary criticism, particularly in the latter part of the sixteenth century. It is even possible to understand some of the new and hybrid forms of Renaissance fiction as a reaction to this transference of the idea of plot from poetry to history. While history may indeed possess no coherent plot, as Aristotle speculated, literary history can nevertheless reconstitute the genealogy of competing notions of plot and order in Renaissance narrative.We can situate Aristotle's definition of plot in the context of his inquiry into cause and coincidence. In book two of the Physics Aristotle proposes a rigorous typology of cause, distinguishing between formal, material, efficient, and final causes, and he also considers the status of chance and fortune as accidental causes or aitia kata symbebekos (197a5-6). 1 The Metaphysics takes up the question of to kata symbebekos, translated alternately as accident or coincidence, and in doing so develops several arguments that pertain to the treatment of plot in the Poetics and to the larger issue of the coherence of fiction and history. As Richard Sorabji points out, the key to Aristotle's notion of coincidence is the [End Page 1] paradox of existence without genesis or without coming into being. 2 Metaphysics VI, 2 maintains that "of things which are in other senses there is generation and destruction [genesis kai phthora], but of things which are accidentally [kata symbebekos] there is not" (1026b24). Metaphysics VI, 3 argues that if this were not so, if nothing existed without genesis, then everything would be of necessity in the sense that every future event could be traced back to a present cause. Genesis thus seems to signify an unbroken chain of causes while to symbebekotos, the coincidental, represents a break in the causal chain. For Aristotle the coincidental or the fortuitous "goes back to some starting point (arche), which does not go back to something else" (1027b12-14). A coincidence is an uncaused cause.Aristotle's Poetics furnishes a definition of plot or mythos that provides a link between the metaphysical discussion of cause and the fictional inquiry into chance. For Aristotle the dramatic plot is the integration of various actions, or synthesis ton pragmaton (1450a5), into a whole or olon consisting of a beginning, a middle, and an end (1450b27). The unity of action does not admit of any accidents within the plot as it moves continuously from beginning to middle to end, and yet the plot as a whole exemplifies the metaphysical notion of a coincidence. Aristotle defines the beginning of the plot or the arche as "that which does not itself follow anything by causal necessity but after which something naturally is or comes to be" (1450b28-29). Thus the mythos, like the coincidence, originates in an uncaused cause, that scandal abhorred by rationalism. Aristotle further complicates the question of causality when he denies to historical events the type of probability or necessity that he associates with dramatic actions. Chapter 23 of the Poetics exhorts the epic poet to emulate tragedy and shun the example of histories (1459a17-22), for while historical events may possess a chronological unity, they do not form any causal chain and thus do not exhibit any unity of action.In chapter 9 of the Poetics Aristotle... (shrink)

The principle that causes always render their effects more likely is fundamental to the enterprise of reducing facts of causation to facts about (objective) chances. This reductionist enterprise faces famous difficulties in accommodating common-sense intuitions about causal processes, if it insists on cashing out causal processes in terms of streams of events in which every event that belongs to the stream is a cause of the adjoining event downstream of it. I shall propose modifications to this way of cashing out (...) causal processes, still well within the reductionist faith. These modifications will allow the reductionist to handle processes successfully, on the assumption that the reductionist proposal is itself otherwise satisfactory. I shall then argue that the reductionist enterprise lies squarely behind the Theory of Relativity, and so has all the confirmatory weight of Relativity behind it. However this is not all good news for reductionists. For throughout I shall simply assume that the reductionist proposal, to the effect that causes are just chance-raisers, is correct. And I shall sidestep problems with that proposal as such. And so I shall show that, if in the end we find the reductionist proposal unsatisfactory, it cannot be on grounds of its treatment of causal processes as such. Thus, while I shall argue that causal processes pose no extra trouble for reductionists, I shall be making a case that all the action between reductionists and their opponents should be focused upon the proposal to reduce the two-term causal relation itself to relations amongst probabilities. (shrink)

About one third of patients with epilepsy have seizures refractory to the medical treatment. Electrical stimulation mapping is the gold standard for the identification of “eloquent” areas prior to resection of epileptogenic tissue. However, it is time-consuming and may cause undesired side effects. Broadband gamma activity recorded with extraoperative electrocorticography during cognitive tasks may be an alternative to ESM but until now has not proven of definitive clinical value. Considering their role in cognition, the alpha and beta bands could (...) further improve the identification of eloquent cortex. We compared gamma, alpha and beta activity, and their combinations for the identification of eloquent cortical areas defined by ESM. Ten patients with intractable focal epilepsy participated in a delayed-match-to-sample task, where syllable sounds were compared to visually presented letters. We used a generalized linear model approach to find the optimal weighting of each band for predicting ESM-defined categories and estimated the diagnostic ability by calculating the area under the receiver operating characteristic curve. Gamma activity increased more in eloquent than in non-eloquent areas, whereas alpha and beta power decreased more in eloquent areas. Diagnostic ability of each band was close to 0.7 for all bands but depended on multiple factors including the time period of the cognitive task, the location of the electrodes and the patient’s degree of attention to the stimulus. We show that diagnostic ability can be increased by 3–5% by combining gamma and alpha and by 7.5–11% when gamma and beta were combined. We then show how ECoG power modulation from cognitive testing can be used to map the probability of eloquence in individual patients and how this probability map can be used in clinical settings to optimize ESM planning. We conclude that the combination of gamma and beta power modulation during cognitive testing can contribute to the identification of eloquent areas prior to ESM in patients with refractory focal epilepsy. (shrink)

Medical, scientific and societal progress has been such that, in a universalist humanist perspective such as the WHO’s, it has become an ethical imperative for the primary endpoints in evidence based health care research to be expressed in e.g. Quality Adjusted Life Years (QALYs). The classical endpoints of discrete health‐related functions and duration of survival are increasingly perceived as unacceptably reductionistic. The major problem in ‘felicitometrics’ is the measurement of the ‘quality’ term in QALYs. That the mental, physical and social (...) domains, each containing many dimensions and items, all contribute to QOL is uncontroversial. What is controversial, is the weight of the different dimensions in overall QOL. It has been shown to be very different between different patient populations. In human individuals, assuredly complex systems, the many dimensions and items of QOL observably interact, probably sometimes also in chaotic ways. In these conditions, the weights of isolated items in individuals become for all practical purposes meaningless. Therefore, the much used multi‐item questionnaires at best describe, but do not evaluate QOL, neither in individuals, nor in populations. For example, allergic patients treated with cetirizine scored better than those a placebo on all dimensions of the SF‐36, a standard QOL questionnaire. Here there is no serious doubt that the treatment improved QOL, because it is highly unlikely that any important dimension on which the patient groups would have scored otherwise is missing in the SF‐36. However, whether piracetam treatment of acute stroke, which improved the surrogate endpoints neurological and functional scores, also improved QOL is plausible, but will be proven only when comprehensive QOL measurement will have been done. And suppose in randomised populations of end‐stage metastatic solid cancer patients, one would compare palliative last‐line chemotherapy with only palliative care, and one would, as can be expected, find no significant differences in average survival, and chemotherapy superior for the mental domain, but inferior for the physical comfort domain: we would not know which treatment, on aggregate, would be the better. The problem is that QOL is an individual and emergent construct, the resultant of a great many intractions, and of a different order than its contributing components. Overall QOL can therefore best be captured only as the Gestalt of a global self‐assessment. Just as people in everyday life, while acting under uncertainty, make global assessments all the time, so they can seriously answer the serious question: ‘How have you been?’ A solemn, practical, non peer‐relativistic, non‐cultural, experiential, and well tolerated way to obtain such responses is Anamnestic Comparative Self Assessment (ACSA), in which the subjects' memories of the best and the worst times in their life experience define their individual scale of QOL. ACSA is thus both exquisitely idiosyncratic, and yet can in a universalist humanistic perspective be considered generic. Using both a multi‐item questionnaire and a global assessment allows by one logistic regression, to estimate the weights of the dimensions and items in populations, and thus identify those whose improvement would most contribute to the QOL of the greatest number. A combined approach to measurement of QOL is necessary to maximise the utility of QOL interventions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Under the Floorboards:Examining the Foundations of Mild Cognitive ImpairmentMichael Bavidge (bio)KeywordsAlzheimer’s disease, culture, dementia, normal aging, science"Building a mystery: Alzheimer disease, mild cognitive impairment, and beyond" (Gaines and Whitehouse 2006) is an absorbing and important case study of how Alzheimer's disease (AD) came to be seen as a disease and how mild cognitive impairment (MCI) has been constructed in recent years as a related incipient condition.The interdisciplinary approach taken (...) in the article produces findings of very different sorts, which are then marshaled to challenge the status of AD and MCI. The factors identified as contributing to the emergence of dementia as a disease include the inconclusive nature of the empirical evidence relating to the causes of dementia, the divergence in the paradigms of the biological sciences, the social pressures resulting from the aging of the population, consumerism in medicine, research funding, the profit motive in the pharmaceutical industries, and our "hypercognitive culture."There is a danger in a short article drawing on detailed work in different disciplines that no single argument is conclusive and the combination of inconclusive arguments remains unsatisfactory. Nevertheless, the picture that emerges is convincing. It is interesting to follow the details of a particular case history to track the intricate interlacing of clinical findings and social decision making that enter into the construction of a disease. The article traces the factors that encouraged the identification of dementia as a widespread, treatable condition and the diagnostic techniques and treatments that determined the delineation of the disease.In the case of AD and MCI, the implications of this process of construction extend beyond taxonomy. They call into question our attitude to aging. Do we see aging as itself a pathology? When Professor Tom Kirkwood writes "from a biological point of view, there is nothing necessary or inevitable about aging" (2001, xi), he does not mean to deny that as the years pass people get older (inevitably); he means that the deteriorations that at present we cannot but see as normal features of aging, are not inevitable. Do we have a spurious ideal of competence based on a time-slice taken from what we like to think of the prime of our lives? Why do we not think of the "cognitive [End Page 75] impairments" of childhood and adolescence as pathological? These are fundamental questions about our experience and understanding of living, aging and dying and they add layers of significance to the topic of the paper (Bavidge 2006).The main focus of the article is to expose the complex process involved in the classification of dementia as "a degenerative, biological, clinical entity" (Gaines and Whitehouse 2006, XX) and to raise doubts about its distinction from normal aging. Not everyone will be happy that so much weight is placed on disease as a dysfunctional clinical entity. Nor will everyone think that so much hangs on the disease status of dementia and MCI. However, on any account, the contrast between disease and normal aging has become less clear because our understanding of both terms of the comparison has become less secure. The question "Is dementia a disease?" is matched by the question "Is aging normal?"Many of the disabilities or degenerations associated with aging are now understood to be conditions that could be avoided, cured, or controlled. So although the article raises doubts about the stability of the category of AD, parallel problems have arisen about normal aging. If important elements of what we classify as dementia should be seen as normal human development, it is equally the case that some aspects of what we accept as part of the normal aging experience should be seen as pathological. The authors assert "we have not argued that there is no 'there' there. Rather, we suggest that the mystery of the 'there' (i.e., AD, MCI) may not be much different (if at all) from, and probably is, the mystery of the 'everywhere' (i.e., aging)" (Gaines and Whitehouse 2006, 61).The article is an exercise in the sociology of knowledge. This will be enough in itself to raise some hackles. It is interesting how an historical and sociological approach to the sciences has... (shrink)

This paper shows that expected utility belongs to the intersection of models satisfying betweenness and a homotheticity condition for risky choice. Betweenness models can accommodate variable risk attitudes, originally highlighted by the Allais paradox, by restricting indifference curves to be linear while allowing non-parallelism. Homotheticity, in contrast, restricts indifference curves to be parallel while permitting non-linearities, such as those highlighted by inverse-S probability weighting. Data from an experiment indicate that approximately 2/3s of participants satisfied homotheticity. Of this group, (...) about half satisfied the expected utility hypothesis. The other half violated expected utility and therefore betweenness. These results indicate that homothetic preferences, and in particular those violating betweenness, can be empirically relevant for decision making under risk. (shrink)

Although Bayesian methods are widely used in phylogenetic systematics today, the foundations of this methodology are still debated among both biologists and philosophers. The Bayesian approach to phylogenetic inference requires the assignment of prior probabilities to phylogenetic trees. As in other applications of Bayesian epistemology, the question of whether there is an objective way to assign these prior probabilities is a contested issue. This paper discusses the strategy of constraining the prior probabilities of phylogenetic trees by means of the Principal (...) Principle. In particular, I discuss a proposal due to Velasco (Biol Philos 23:455–473, 2008) of assigning prior probabilities to tree topologies based on the Yule process. By invoking the Principal Principle I argue that prior probabilities of tree topologies should rather be assigned a weighted mixture of probability distributions based on Pinelis’ (P Roy Soc Lond B Bio 270:1425–1431, 2003) multi-rate branching process including both the Yule distribution and the uniform distribution. However, I argue that this solves the problem of the priors of phylogenetic trees only in a weak form. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:David Hume and the Probability of Miracles Barry Gower 1. Introduction Oflate there have been published several discussions ofDavid Hume's famous essay "Of Miracles" which attempt to make precise the reasoning it contains. This, it turns out, requires the use of certain mathematical rules and theorems of the probability calculus which were unknown to Hume or, indeed, to anyone else when the essay was first published. It (...) is suggested, in particular, that the claims he made can best be understood in the light of a theorem of the probability calculus which we now name after a celebrated eighteenth century probabilist, Thomas Bayes. However, the so-called "Bayesian" interpretation of the argument against miracles misrepresents Hume's reasoning in that the manner in which he expressed his thinking does not fit such an interpretation. Moreover, this error needs to be rectified, not just because it involves a mistaken view about the past but, more importantly, because it obscures the legacy of a different mode of thinking evident in Hume's writing about probabilistic inference which deserves to be recovered. Our thinkingisimpoverishedifcertain presumptions aboutprobability become so entrenched that we have great difficulty in seeing them as anything other than obvious. By imputing them to Hume we overlook their contestability and so lose an opportunity to recapture an alternative way of understanding probabilistic reasoning. As is well known, the argument against miracles, though not published until 1748, had been worked out some twelve or thirteen years earlier during Hume's stay at the Jesuit college of La Fleche, where he wrote most of A Treatise of Human Nature. A chapter entitled "Reasonings concerning Miracles" had been written but, at the last moment, it was suppressed for fear that such an explicit attack on religion would give offence and thus deflect attention from the book's main philosophical aim which was to put an end to controversy. On the other hand, Thomas Bayes's famous memoir on probability was not published until 1764, andit is unlikely that Hume knew ofits existence until Richard Price mentionedit, though without identifyingits author, in an elaborate mathematical footnote to a dissertation containing remarks on the probability of miracles, published in 1767. Had Hume taken the trouble to follow up this reference, he would almost certainly Volume XVI Number 1 17 BARRY GOWER have been either baffled by its mathematics or discouraged by its lack of practical advice. That, at least, seems to have been the reaction of Hume's contemporaries, for apart from Price none of them seems to have paid any attention to the memoir. Even today, when anyone with the slightest acquaintance with probability can recite a version of Bayes's theorem, it is hard to follow the reasoning of the memoir and to appreciate the significance of the ideas it contains. As an historian of statistics has recently said, "Bayes's contemporaries were stymied by the work, and modern readers unwilling to devote many hours to it are likely to gain only a superficial understanding ofit." One paradoxical feature of attributing Bayesianism to Hume concerns the role of Richard Price. His dissertation, which had, it seems, been written some years before it was published — perhaps in the early 1750's — is sharply critical of Hume's argument against miracles. Yet it was Price himself who was responsible for the posthumous publication of Bayes's memoir, and his introduction and commentary clearly express approval of its methods and conclusions. We are, then, faced with the suggestion that Hume, not having heard of Bayes, was applying Bayesian ideas about "inverse" inference to miraculous events, whereas Price, who was not only familiar with but also endorsed Bayes's ideas, preferred a quite different approach to reasoning about miracles and about the credibility of testimony generally. Can Hume really be described as a "better intuitive Bayesian" than Price? Before embracing such aparadoxical conclusion we should consider whether it is really justified by what Hume said about the probability ofmiracles. First, though, some attention needs to be paid to a way ofthinking about probable arguments which does not conform to convention, and which implies a non-Bayesian interpretation of the question about miracles. 2. Jakob Bernoulli and the Combination... (shrink)

BackgroundWhether patients in the vegetative state (VS), minimally conscious state (MCS) or the clinically related locked-in syndrome (LIS) should be kept alive is a matter of intense controversy. This study aimed to examine the moral attitudes of lay people to these questions, and the values and other factors that underlie these attitudes.MethodOne hundred ninety-nine US residents completed a survey using the online platform Mechanical Turk, comprising demographic questions, agreement with treatment withdrawal from each of the conditions, agreement with a (...) series of ethical principles and three personality tests.ResultsMore supported treatment withdrawal from VS (40.2 % agreed, 17.6 % disagreed) than MCS (20.6 %, 41.2 %) or LIS (25.3 %, 35.8 %). Agreement with treatment withdrawal was negatively correlated with religiosity (r = −0.272, P < 0.001), though showed no significant relationship with need for cognition or empathy, and only a partial association with utilitarian judgment in a standard moral dilemma. Support for treatment withdrawal was most strongly associated with endorsement of the importance of patient autonomy, dignity, suffering, best interests. Distributive justice was not given significant weight by most. Importantly, agreement with treatment withdrawal was noticeably higher when considered from a first as opposed to third person perspective for VS (Z = −6.056, P < 0.001), MCS (Z = −6.746, P < 0.001) and LIS (Z = −6.681, P < 0.001).ConclusionLay attitudes to withdrawal of treatment in brain damaged patients are largely shaped by values similar to those central to the secular ethical debate. Neither traditional values such as the sanctity of life nor utilitarian values relating to resource allocation seem to play a central role. Far greater weight is given to autonomy, which may explain why participants were far more willing to endorse withdrawal of treatment when the issue was presented in the first person, or in relation to a concrete case involving a patient’s explicit wishes. Surveys focusing on abstract cases presented in the third person may not provide an accurate picture of lay attitudes to these critical ethical questions. (shrink)

In comparing different risk elicitation methods under the assumptions of expected utility theory, previous studies have found significant differences in the elicited risk attitudes. This paper extends this line of research to consider cumulative prospect theory by comparing risk attitudes and probability weightings determined using two elicitation methods: the method by Tanaka et al. :557–571, 2010; TCN method) and the method by Wakker and Deneffe :1131–1150, 1996; WD method). We demonstrate that the two methods reveal significantly different mean values (...) for the measured risk attitudes. Participants are classified on average as moderately risk-averse using the TCN method, whereas the same individuals are classified as nearly risk-neutral using the WD method. Moreover, we find that on average, participants overweight low probabilities and underweight high probabilities to a greater extent with the WD method than with the TCN method. Therefore, the different elicitation methods, that both consider probability weighting, can lead to different measured values of risk attitude and probability weighting. (shrink)

We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal treatment (...) introduced here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context---a stimulus or another concept---to `collapse' to observable form as an exemplar, prototype, or other (possibly imaginary) instance. The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance---one using collapse probabilities and the other weighted properties---and show how they can be applied to conjunctions using the pet fish problem. (shrink)

Women are commonly stereotyped as more risk averse than men in financial decision making. In this paper we examine whether this stereotype reflects gender differences in actual risk-taking behavior by means of a laboratory experiment with monetary incentives. Gender differences in risk taking may be due to differences in valuations of outcomes or in probability weights. The results of our experiment indicate that value functions do not differ significantly between men and women. Men and women differ in their (...) probability weighting schemes, however. In general, women tend to be less sensitive to probability changes. They also tend to underestimate large probabilities of gains more strongly than do men. This effect is particularly pronounced when the decisions are framed in investment terms. As a result, women appear to be more risk averse than men in specific circumstances. (shrink)

Our understanding of the decisions made under scenarios where both descriptive and experience-based information are available is very limited. Underweighting of small probabilities was observed in the gain domain when both description and experience were provided. The divergence observed from the prospect theory suggests a need for a separate or modified theory of decision making under risk. Recent studies suggest a possible role of probability weighting in the choice behaviour under risk. We investigated both gain and loss domains with (...) and without feedback for small and large probability conditions. We characterized the shape of the probability weighting function by a two-parameter functional form representing discriminability (concave-convex shape) and attractiveness (level of absolute weights relative to objective probability). We replicated four-fold pattern of risk attitude on non-WEIRD population. We find that feedback leads to underweighting of small probabilities and overweighting of large probabilities in the gain domain and overall underweighting of probabilities in the loss domain. We find that underweighting of small probabilities is driven by changes in discriminability and attractiveness components in the gain domain and changes in the attractiveness component in the loss domain. We have interpreted the results by proposing an updated belief-based account of decisions under uncertainty in which feedback, when available, influences the probability weighting mediating the choice behaviour. (shrink)

I examine Hume’s proposal about rationally considering testimonial evidence for miracles. He proposes that we compare the probability of the miracle (independently of the testimony) with the probability that the testimony is false, rejecting whichever has the lower probability. However, this superficially plausible proposal is massively ignored in our treatment of testimonial evidence in nonreligious contexts. I argue that it should be ignored, because in many cases, including the resurrection of Jesus, neither we nor Hume have (...) any experience which is at all relevant to assigning a prior probability to the alleged event. (shrink)

Abstract.This paper is devoted to a logical and algebraic treatment of conditional probability. The main ideas are the use of non-standard probabilities and of some kind of standard part function in order to deal with the case where the conditioning event has probability zero, and the use of a many-valued modal logic in order to deal probability of an event φ as the truth value of the sentence φ is probable, along the lines of Hájek’s book (...) [H98] and of [EGH96]. To this purpose, we introduce a probabilistic many-valued logic, called FP(SŁΠ), which is sound and complete with respect a class of structures having a non-standard extension [0,1]⋆ of [0,1] as set of truth values. We also prove that the coherence of an assessment of conditional probabilities is equivalent to the coherence of a suitably defined theory over FP(SŁΠ) whose proper axioms reflect the assessment itself. (shrink)

The “reproductive suppression hypothesis” states that the strong desire of adolescent girls in our culture to control their weight may reflect the operation of an adaptive mechanism by which ancestral women controlled the timing of their sexual maturation and hence first reproduction, in response to cues about the probable success of reproduction in the current situation. We develop a model based on this hypothesis and explore its behavior and evolutionary and psychological implications across a range of parameter values. We use (...) the process of model development to identify assumptions implicit in the reproductive suppression hypothesis and variables that need to be measured in order to investigate it more fully. In addition, because costs were probably associated with weight control, an important part of this analysis is the specification of situations in which the benefits of adaptive adjustment of the maturation schedule could have outweighed the costs of achieving that adjustment by slowing adolescent weight gain. (shrink)