Enlightenment Views of Hope

This chapter discusses accounts of hope found in the works of important Enlightenment thinkers: René Descartes, Thomas Hobbes, Baruch de Spinoza, David Hume, and Immanuel Kant. The paper’s guiding questions are: Where are discussions of hope located within these thinkers’ works? Do the authors provide an account of what hope is? Do they ascribe a certain function to hope? Most authors of the Enlightenment, with the exception of Kant, write about hope in the context of a general account of the passions. Their characterization of hope closely resembles the “standard definition” of hope in contemporary debates. According to this definition, hope consists of a desire and a belief in the possibility, but not the certainty, of the desired outcome. It turns out, however, that Descartes, Hobbes, and Hume advocate a stronger evidential condition for hope than is common today: According to their view, we do not hope for what we take to be merely possible, no matter how unlikely it is; we hope for what we take to be more likely. Kant’s account differs from the other ones in important respects: He does not treat hope as an affect and he does not require a probability estimate, but grounds hope in faith.

Performance of Traditional Pretest Probability Estimates in Stable Patients Undergoing Myocardial Perfusion Imaging

Background: The yield of myocardial perfusion imaging is low in contemporary patients with suspected coronary artery disease (CAD) selected based on American College of Cardiology Foundation/American Heart Association pretest probability estimate. We compared traditional pretest estimates of CAD probability with the prevalence of abnormal myocardial perfusion single-photon emission computed tomography (MPS). Methods: This was a cohort study from a single academic center. Consecutive stable patients without known CAD referred for stress MPS for suspected CAD between 2004 and 2011 were identified (n=15 777). Angina typicality was determined using standard criteria. Abnormal MPS perfusion was defined as a summed stress score ≥4, ischemia as summed stress score ≥4 and summed difference score ≥2, and extensive ischemia as summed difference score ≥8 using a standard, 17-segment model of the left ventricle. The pretest probability of CAD was determined using the American College of Cardiology Foundation/American Heart Association criteria. Results: Overall, 14% (n=2177) of patients had abnormal MPS of whom 11% (n=1698) had ischemia and 4% (n=684) extensive ischemia. In patients with chest pain who underwent treadmill MPS (n=4764), only 27% reported angina on the treadmill. Typical angina was associated with the highest prevalence for positive MPS (33% in men and 14% in women), ischemia (30% in men and 12% in women), and extensive ischemia (22% in men and 4% in women) when compared with other symptom categories. Prevalence of MPS abnormality was substantially lower than expected based on pretest probability estimates across most sex and age groups. In multivariable analysis, the pretest probability estimate was not an independent predictor of abnormal MPS. Conclusions: Traditional estimates of pretest probability of CAD are not predictive of MPS perfusion abnormality and overestimate its prevalence in stable patients.

Context-Dependent Probability Estimation and its Neurocomputational Substrates

ABSTRACTMany decisions rely on how we evaluate potential outcomes associated with the options under consideration and estimate their corresponding probabilities of occurrence. Outcome valuation is subjective as it requires consulting internal preferences and is sensitive to context. In contrast, probability estimation requires extracting statistics from the environment and therefore imposes unique challenges to the decision maker. Here we show that probability estimation, like outcome valuation, is subject to context effects that bias probability estimates away from other stimuli present in the same context. However, unlike valuation, these context effects appeared to be scaled by estimated uncertainty, which is largest at intermediate probabilities. BOLD imaging showed that patterns of multivoxel activity in dorsal anterior cingulate cortex (dACC) and ventromedial prefrontal cortex (VMPFC) predicted individual differences in context effects on probability estimate. These results establish VMPFC as the neurocomputational substrate shared between valuation and probability estimation and highlight the additional involvement of dACC that can be uniquely attributed to probability estimation. As probability estimation is a required component of computational accounts from sensory inference to higher cognition, the context effects found here may affect a wide array of cognitive computations.HighlightsContext impacts subjective estimates on reward probability – Stimuli carrying greater variance are more strongly affected by other stimuli present in the same contextThis phenomenon can be explained by reference-dependent computations that are gated by reward varianceMultivoxel patterns of dACC and VMPFC activity predicts individual differences in context effect on probability estimate

Estimating Physics Models and Quantifying Their Uncertainty Using Optimization With a Bayesian Objective Function

This paper reports a verification study for a method that fits functions to sets of data from several experiments simultaneously. The method finds a maximum a posteriori probability estimate of a function subject to constraints (e.g., convexity in the study), uncertainty about the estimate, and a quantitative characterization of how data from each experiment constrains that uncertainty. While this work focuses on a model of the equation of state (EOS) of gasses produced by detonating a high explosive, the method can be applied to a wide range of physics processes with either parametric or semiparametric models. As a verification exercise, a reference EOS is used and artificial experimental data sets are created using numerical integration of ordinary differential equations and pseudo-random noise. The method yields an estimate of the EOS that is close to the reference and identifies how each experiment most constrains the result.

T-Vasicek Credit Portfolio Loss Distribution

We derive and discuss a new analytical credit loss distribution. This new model, T-Vasicek, is a variant of the well-known and highly useful Vasicek distribution. We inject a t-distribution extension into Vasicek that preserves the analytical convenience of Vasicek while providing a richer credit loss framework with fat tails and an additional user-specified parameter. This additional parameter is directly tied to the t-distribution and represents the uncertainty in the default probability estimate. The classical Vasicek limit, then, is the case in which the analyst knows the pool default probability with certainty. We show how one may impose desired correlation among all debt instruments in the t-distribution framework. We derive closed-form, numerical, and analytical forms for T-Vasicek and check the numerical results with Monte Carlo simulation. We also determine suitable maximum likelihood estimators for the T-Vasicek parameters of default probability (PD), correlation (ρ), and PD-uncertainty factor (ν).

NPV Sensitivity Analysis: A Dynamic Excel Approach

Financial analysts generally create static formulas for the computation of NPV. When they do so, however, it is not readily apparent how sensitive the value of NPV is to changes in multiple interdependent and interrelated variables. It is the aim of this paper to analyze this variability by employing a dynamic, visually graphic presentation using Excel. Our approach illustrates how these variables, when increased or decreased to reflect the potential range of values in a business case, change the value of NPV, and hence affect the decision about whether to proceed with the project or to reject it. Furthermore, since sales revenue is one of the least certain elements in the business case, the presentation includes a probability estimate of whether NPV will be positive or negative, assuming that sales revenue is normally distributed with a known mean and standard deviation. The business case we have chosen for illustrative purposes is a global energy project. Nevertheless, financial analysts in any industry should be able to apply our dynamic spreadsheet approach to their projects as well.