Turning up the volume to address biases in predicted healthcare-associated infections and enhance U.S. hospital rankings: A data-driven approach

ObjectivesTo examine potential biases in standardized infection ratio (SIR) metrics due to static U.S. Centers for Disease Control and Prevention (CDC) parameters and non-linearity of infection outcomes with volume. Correspondingly, to enhance the CDC predictions by incorporating additional information from volume metrics and explore an alternative approach to more fairly rank hospitals to address the SIR=0 problem.MethodsThis population-based study uses publicly available 2019 healthcare-associated infections (HAI) data from 3096 acute care U.S. hospitals. HAI-specific Poisson generalized additive models illustrate the recalibration of CDC predictions, using volume-based spline functions to adjust for biases. Implied cumulative distribution functions (CDF) were derived, and HAI-facility-specific probabilities were calculated. Hospital rankings implied from these HAI-stratified probabilities were calculated.ResultsCalibration plots demonstrate existing biases associated with CDC infection over-predictions. Volume-based spline functions were significant for all HAIs (P<.0004). CDF-based rankings resulted in larger discrimination across hospitals based on strength of evidence, especially among SIR=0 facilities. National maps depict ranking differences by HAI and state.ConclusionAdjustment of SIR biases, which differ by facility volume, is needed to produce more accurate and fairer hospital rankings.     

From the Cover: Price dynamics in political prediction markets

Prediction markets, in which contract prices are used to forecast future events, are increasingly applied to various domains ranging from political contests to scientific breakthroughs. However, the dynamics of such markets are not well understood. Here, we study the return dynamics of the oldest, most data-rich prediction markets, the Iowa Electronic Presidential Election “winner-takes-all” markets. As with other financial markets, we find uncorrelated returns, power-law decaying volatility correlations, and, usually, power-law decaying distributions of returns. However, unlike other financial markets, we find conditional diverging volatilities as the contract settlement date approaches. We propose a dynamic binary option model that captures all features of the empirical data and can potentially provide a tool with which one may extract true information events from a price time series.     

From the Cover: Using prediction markets to estimate the reproducibility of scientific research

Concerns about a lack of reproducibility of statistically significant results have recently been raised in many fields, and it has been argued that this lack comes at substantial economic costs. We here report the results from prediction markets set up to quantify the reproducibility of 44 studies published in prominent psychology journals and replicated in the Reproducibility Project: Psychology. The prediction markets predict the outcomes of the replications well and outperform a survey of market participants’ individual forecasts. This shows that prediction markets are a promising tool for assessing the reproducibility of published scientific results. The prediction markets also allow us to estimate probabilities for the hypotheses being true at different testing stages, which provides valuable information regarding the temporal dynamics of scientific discovery. We find that the hypotheses being tested in psychology typically have low prior probabilities of being true (median, 9%) and that a “statistically significant” finding needs to be confirmed in a well-powered replication to have a high probability of being true. We argue that prediction markets could be used to obtain speedy information about reproducibility at low cost and could potentially even be used to determine which studies to replicate to optimally allocate limited resources into replications.The process of scientific discovery centers on empirical testing of research hypotheses. A standard tool to interpret results in statistical hypothesis testing is the P value. A result associated with a P value below a predefined significance level (typically 0.05) is considered “statistically significant” and interpreted as evidence in favor of a hypothesis. However, concerns about the reproducibility of statistically significant results have recently been raised in many fields including medicine (1–3), neuroscience (4), genetics (5, 6), psychology (7–11), and economics (12, 13). For example, an industrial laboratory could only reproduce 6 out of 53 key findings from “landmark” studies in preclinical oncology (2) and it has been argued that the costs associated with irreproducible preclinical research alone are about US$28 billion a year in the United States (3). The mismatch between the interpretation of statistically significant findings and a lack of reproducibility threatens to undermine the validity of statistical hypothesis testing as it is currently practiced in many research fields (14).The problem with inference based on P values is that a P value provides only partial information about the probability of a tested hypothesis being true (14, 15). This probability also depends on the statistical power to detect a true positive effect and the prior probability that the hypothesis is true (14). Lower statistical power increases the probability that a statistically significant effect is a false positive (4, 14). Statistically significant results from small studies are therefore more likely to be false positives than statistically significant results from large studies. A lower prior probability for a hypothesis to be true similarly increases the probability that a statistically significant effect is a false positive (14). This problem is exacerbated by publication bias in favor of speculative findings and against null results (4, 16–19).Apart from rigorous replication of published studies, which is often perceived as unattractive and therefore rarely done, there are no formal mechanisms to identify irreproducible findings. Thus, it is typically left to the judgment of individual researchers to assess the credibility of published results. Prediction markets are a promising tool to fill this gap, because they can aggregate private information on reproducibility, and can generate and disseminate a consensus among market participants. Although prediction markets have been argued to be a potentially important tool for assessing scientific hypotheses (20–22)—most notably in Robin Hanson’s paper “Could Gambling Save Science? Encouraging an Honest Consensus” (20)—relatively little has been done to develop potential applications (21). Meanwhile, the potential of prediction markets has been demonstrated in a number of other domains, such as sports, entertainment, and politics (23–26).We tested the potential of using prediction markets to estimate reproducibility in conjunction with the Reproducibility Project: Psychology (RPP) (9, 10). The RPP systematically replicated studies from a sampling frame of three top journals in psychology. To investigate the performance of prediction markets in this context, a first set of prediction markets were implemented in November 2012 and included 23 replication studies scheduled to be completed in the subsequent 2 mo, and a second set of prediction markets were implemented in October 2014 and included 21 replication studies scheduled to be completed before the end of December 2014. The prediction markets were active for 2 wk at each of these occasions.For each of the replication studies, participants could bet on whether or not the key original result would be replicated. Our criterion for a successful replication was a replication result, with a P value of less than 0.05, in the same direction as the original result. In one of the studies, the original result was a negative finding, and successful replication was thus defined as obtaining a negative (i.e., statistically nonsignificant) result in the replication. Information on the original study and the setup of the replication were accessible to all participants.In the prediction markets, participants traded contracts that pay $1 if the study is replicated and $0 otherwise. This type of contract allows the price to be interpreted as the predicted probability of the outcome occurring. This interpretation of the price is not without caveats (27) but has an advantage of being simple and reasonably robust (28), especially in settings where traders’ initial endowments are the same and traders’ bets are relatively small. Invitations to participate in the prediction markets were sent to the email list of the Open Science Framework, and for the second set of markets also to the email list of the RPP collaboration. Participants were not allowed to bet in those markets where they were involved in carrying out the replication. In the first set of prediction markets, 49 individuals signed up and 47 of these actively participated; in the second set, 52 individuals signed up and 45 of these actively participated. Before the markets started, participants were asked in a survey for their subjective probability of each study being replicated. Each participant was endowed with US$100 for trading.     

The role of patient involvement in the diagnostic process in internal medicine: A cognitive approach

Much cognitive and clinical research has addressed clinical reasoning, pointing out that physicians often have difficulties in following a linear course when making accurate diagnoses. Some authors suspect that physicians make mistakes because they unknowingly fail to observe the laws of formal logic and that their reasoning becomes influenced by contextual factors.In this paper, we introduce some basic principles of the cognitive approach to medical decision making and we describe the cognitive balanced model. Then we discuss the relationship between construction of mental models, cognitive biases and patient involvement by the use of a clinical vignette.Medical decisions may be considered fundamentally biased since the use of judgment heuristics and a combination of cognitive-related and system-related factors limit physicians' rationality.While traditional understanding of clinical reasoning has failed to consider contextual factors, most techniques designed to avoid biases seem to fail in promoting sound and safer medical practice. In particular, we argue that an unbiased process requires the use of a cognitive balanced model, in which analytical and intuitive mind skills should be properly integrated.In order to improve medical decision making and thereby lessen incidence of adverse events, it is fundamental to include the patient perspective in a balanced model. Physicians and patients should improve their collective intelligence by sharing mental models within a framework of distributed intelligence.     

Diabetes,diabetic complications,and blood pressure targets

Association of diabetes with hypertension is frequent and it well known that high blood pressure potentiates the probability of diabetic patients to develop macrovascularand microvascular complications. Strong evidence obtained in a number of large scale prospective studies indicates that adequate blood pressure control in diabetic patients is highly beneficial for prevention of cardiovascular events. Nonetheless, only a limited proportion of hypertensive-diabetic individuals included in studies on anti-hypertensive treatment has met the predefined blood pressure goal. The optimal blood pressure goal to be pursued in diabetic patients with hypertension to guarantee effective protection from cardiovascular outcomes is still under intense debate and recommendations of current guidelines on hypertension treatment are still inconsistent. We comment here on the most important studies and conclude that current evidence does not conclusively support the need to reach a blood pressure target in hypertensive patients with diabetes different from nondiabetic hypertensive individuals.     

Effect of marital quality on eight-year survival of patients with heart failure

Recent evidence suggests that psychosocial factors such as self-efficacy, psychological distress, perceived social support, and marital quality have prognostic significance for morbidity and mortality after heart failure. Previously, we reported that interview and observational measures of marital quality obtained from 189 patients with heart failure (139 men and 50 women) and their spouses predicted all-cause patient mortality during the next 4 years, independent of the baseline illness severity (New York Heart Association class). We present additional follow-up results for this sample, with Cox regression analyses showing that a couple-level composite measure of marital quality continued to predict survival during an 8-year period (p <0.001), especially when the patient was a woman, and did so substantially better than individual (patient-level) risk and protective factors, such as psychological distress, hostility, neuroticism, self-efficacy, optimism, and breadth of perceived emotional support. In conclusion, relationship factors may be especially relevant in managing a difficult chronic condition such as heart failure, which makes stringent and complex demands on patients and their families.     

Bayesian motion estimation accounts for a surprising bias in 3D vision

Determining the approach of a moving object is a vital survival skill that depends on the brain combining information about lateral translation and motion-in-depth. Given the importance of sensing motion for obstacle avoidance, it is surprising that humans make errors, reporting an object will miss them when it is on a collision course with their head. Here we provide evidence that biases observed when participants estimate movement in depth result from the brain's use of a “prior” favoring slow velocity. We formulate a Bayesian model for computing 3D motion using independently estimated parameters for the shape of the visual system's slow velocity prior. We demonstrate the success of this model in accounting for human behavior in separate experiments that assess both sensitivity and bias in 3D motion estimation. Our results show that a surprising perceptual error in 3D motion perception reflects the importance of prior probabilities when estimating environmental properties.     

Attitudes and Experiences With Older Adults: A Case for Service Learning for Undergraduates

The current study examined whether relationship quality with older adults currently and in childhood, as well as experience with older adults, was associated with biases toward older adults and interest in working with older adults as a possible career area. The authors sampled undergraduate students (N = 753, M = 18.97 years, SD = 2.11 years) from a Northern California university. In hierarchical regression analyses, higher perceived quality of relationships with older adult family members, higher perceived social support, and lower perceived conflict from relationships with older adults was significantly associated with positive attitudes toward older adults. Interest in working with older adults was significantly associated with taking courses in aging, providing care to an older adult, and volunteering with older adults. These results suggest that positive relationships with older adults are useful in reducing biases, though student interactions with older adults are key in helping to promote interest in working with older adults.     

B-type natriuretic peptide (BNP) levels and ethnic disparities in perceived severity of heart failure: results from the Rapid Emergency Department Heart Failure Outpatient Trial (REDHOT) multicenter study of BNP levels and emergency department decision making in patients presenting with shortness of breath

BackgroundPrevious studies have shown that in patients presenting to the emergency department (ED) with heart failure, there is a disconnect between the perceived severity of congestive heart failure (CHF) by physicians and the severity as determined by B-type natriuretic peptide (BNP) levels. Whether ethnicity plays a role in this discrepancy is unknown.Methods and ResultsThe Rapid Emergency Department Heart Failure Outpatient Trial (REDHOT) was a 10-center trial of 464 patients seen in the ED with acute dyspnea and BNP level higher than 100 pg/mL on arrival. Physicians were blinded to BNP levels. Patients were followed for 90 days after discharge. A total of 151 patients identified themselves as white (32.5%) and 294 as black (63.4%). Of these, 90% were hospitalized. African Americans were more likely to be perceived as New York Heart Association class I or II than whites (P = .01). Blacks who were discharged from the ED had higher median BNP levels than whites who were discharged (1293 vs. 533, P = .004). The median BNP of blacks who were discharged was actually higher than the median BNP of blacks who were admitted (1293 vs. 769, P = .04); the same did not hold true for whites. BNP was predictive of 90-day outcome in both blacks and whites; however, perceived severity of CHF, race, and ED disposition did not contribute to the prediction of events.ConclusionIn patients presenting to the ED with heart failure, the disconnect between perceived severity of CHF and severity as determined by BNP levels is most pronounced in African Americans.     

Gender bias in clinical decision making emerges when patients with coronary heart disease symptoms also have psychological symptoms

BackgroundDelayed treatment may contribute to women's relatively higher morbidity and mortality from coronary heart disease (CHD). We tested whether disparities in treatment may be due to bias in diagnosis and treatment recommendations for women with psychological symptoms.MethodsFourth year medical students (N = 225) from 13 U.S. medical schools were randomly assigned to make clinical decisions (CHD risk judgments, diagnosis, treatment recommendations) about one of four experimental vignette patients (male or female; with symptoms of depression and anxiety or without). Vignettes were presented as text via an online survey platform.ResultsThe female patient with psychological symptoms was perceived to be at lowest risk for CHD. Perceptions of risk partly mediated lower likelihood of recommending the female patient with psychological symptoms be seen in an emergency department, take medication, or receive nutrition or exercise advice relative to the male patient with psychological symptoms.ConclusionsThere was a gender bias in CHD clinical decision-making when patients had concurrent psychological symptoms.     

Appraisal of caregiving burden,expressed emotion and psychological distress in families of people with eating disorders: A systematic review

The purpose of this review is to appraise the literature regarding psychological distress, burden and expressed emotion (EE) in caregivers of people with eating disorders (EDs). Electronic databases were searched up until October 2008. Selected studies contained carers of people with ED and employed one measure of burden, EE or psychological distress. Twenty studies were identified measuring psychological distress burden and EE. Most of the studies examined these features in families of anorexic patients. The majority of the studies found high levels of psychological distress, burden and EE in this population. Only few studies included a control group. Carers of people with ED presented high levels of psychological distress and burden. ED carers tend to have levels of EE resembling that found in families of depressed patients, rather than schizophrenic patients. There is some evidence (particularly for EE) that these factors can impact the outcome of ED. Copyright © 2009 John Wiley & Sons, Ltd and Eating Disorders Association.     

Live well and die with inner peace: The importance of retrospective need-based experiences,ego integrity and despair for late adults’ death attitudes

Given that prior research has provided evidence for the role of late adults’ attitudes towards death in their mental health, we sought to understand its underlying sources. Guided by Self-Determination Theory and Erikson’s theory of psychosocial development, two cross-sectional studies examined whether older individuals’ psychological need-based experiences, as accumulated during life, relate to their death attitudes and whether their experienced ego integrity and despair play an intervening role in these associations. Whereas Study 1 (N = 394 late adults; Mage = 75.14; SD = 6.52; 62.9 % female) involved an assessment of need satisfaction only, in Study 2 (N = 126 late adults; Mage = 78.09; SD = 7.17; 61.9 % female) both need satisfaction and need frustration were assessed. Structural equation modeling showed that, across studies, experienced need satisfaction related positively to ego integrity and negatively to despair. Need frustration was related to despair only. In turn, ego integrity related positively to death acceptance and negatively to death anxiety, while despair related positively to death anxiety. Finally, the contribution of need satisfaction to death attitudes was mostly mediated by individuals’ ego integrity. Theoretical and practical implications of these results are discussed.     

Multi-state analysis illustrates treatment success after stem cell transplantation for acute myeloid leukemia followed by donor lymphocyte infusion

In the field of hematopoietic stem cell transplantation, the common approach is to focus outcome analyses on time to relapse and death, without assessing the impact of post-transplant interventions. We investigated whether a multi-state model would give insight into the events after transplantation in a cohort of patients who were transplanted using a strategy including scheduled donor lymphocyte infusions. Seventy-eight consecutive patients who underwent myeloablative T-cell depleted allogeneic stem cell transplantation for acute myeloid leukemia or myelodysplastic syndrome were studied. We constructed a multi-state model to analyze the impact of donor lymphocyte infusion and graft-versus-host disease on the probabilities of relapse and non-relapse mortality over time. Based on this model we introduced a new measure for outcome after transplantation which we called ‘treatment success’: being alive without relapse and immunosuppression for graft-versus-host disease. All relevant clinical events were implemented into the multi-state model and were denoted treatment success or failure (either transient or permanent). Both relapse and non-relapse mortality were causes of failure of comparable magnitude. Whereas relapse was the dominant cause of failure from the transplantation state, its rate was reduced after graft-versus-host disease, and especially after donor lymphocyte infusion. The long-term probability of treatment success was approximately 40%. This probability was increased after donor lymphocyte infusion. Our multi-state model helps to interpret the impact of post-transplantation interventions and clinical events on failure and treatment success, thus extracting more information from observational data.     

Irrational exuberance and neural crash warning signals during endogenous experimental market bubbles

Groups of humans routinely misassign value to complex future events, especially in settings involving the exchange of resources. If properly structured, experimental markets can act as excellent probes of human group-level valuation mechanisms during pathological overvaluations—price bubbles. The connection between the behavioral and neural underpinnings of such phenomena has been absent, in part due to a lack of enabling technology. We used a multisubject functional MRI paradigm to measure neural activity in human subjects participating in experimental asset markets in which endogenous price bubbles formed and crashed. Although many ideas exist about how and why such bubbles may form and how to identify them, our experiment provided a window on the connection between neural responses and behavioral acts (buying and selling) that created the bubbles. We show that aggregate neural activity in the nucleus accumbens (NAcc) tracks the price bubble and that NAcc activity aggregated within a market predicts future price changes and crashes. Furthermore, the lowest-earning subjects express a stronger tendency to buy as a function of measured NAcc activity. Conversely, we report a signal in the anterior insular cortex in the highest earners that precedes the impending price peak, is associated with a higher propensity to sell in high earners, and that may represent a neural early warning signal in these subjects. Such markets could be a model system to understand neural and behavior mechanisms in other settings where emergent group-level activity exhibits mistaken belief or valuation.Asset price bubbles are extended periods in which prices rise well above fundamental values. Identifying bubbles and predicting crashes from price data alone is a notoriously difficult problem (1). However, prices are created by the collective behavior of the market participants, so neural activity could offer biomarkers for the evolution of price bubbles. Studies of asset price bubbles indicate a role for psychological factors such as “euphoria” (2), “irrational exuberance” (3), “mania” (4), “animal spirits” (5), and “sentiment” (6). We sought neural data supporting such psychological constructs that might help to identify price bubbles.We observed the formation and crash of endogenous bubbles in experimental asset markets (7, 8) using multisubject neuroimaging. In each of 16 market sessions, consisting of an average of 20 traders (range, 11–23), we measured the neural activity of 2–3 participants (n = 44 total) using functional magnetic resonance imaging (fMRI). Our market design is based upon ref. 9. Traders could buy or sell one risky asset unit in each period. Fig. 1A illustrates the sequence of experimental events. Each market had 50 trading periods. All subjects began with 100 units of experimental currency (a risk-free asset) and 6 units of a risky asset. Each period, the risky asset paid a currency dividend d of either 0.40 or 1.00 per unit (with equal probability), creating an expected dividend E[d] = 0.70. Currency earned a fixed interest rate r of 5% each period. After all 50 rounds of trading were completed, the risky asset was redeemed for 14 units of the risk-free currency.Open in a separate windowFig. 1.Asset market experiment. (A) Each period subjects viewed the following screens, in order: Positions, Order Entry (×5), Trading Results, and Dividends and Interest. (B) Order elicitation procedure. Subjects responded Buy, Sell, or Hold to a random (uniform) price draw from each of five bins, each of width equal to 10% of the last period’s price. The middle bin was centered on the last period’s price. (C) How the price is chosen (=market clearing). The highest price at which subjects responded Buy, and the lowest price at which subjects responded Sell, were entered into a closed book call market. Prices and trading outcomes were reported on the Trading Results screen.These parameters defined an unambiguous fundamental value for the risky asset. Buying the risky asset in period t at price P_t and selling it one period later leads to the expected net gain E_t[P_t+1] ? P_t? + ?E[d]. The same investment of P_t in the risk-free asset yields a sure net gain of rP_t. If these two amounts are equal—in economic terms, if asset prices are “in equilibrium”—then there is a stationary price equal to a constant fundamental value F defined by F = E[d]/r = 0.70/0.05 = 14. Prices persistently above F = 14 indicate a bubble; such a clear bubble measure is rarely available in field data. Fig. 2A illustrates the price paths for all 16 markets in this experiment. Bubbles are typical and large: the median price peak was 64.30 (range, 19.68–156.01). The bubble paths always result in a crash, and prices in the final period are near the fundamental F = 14 (median, 14.13). Fig. 2B illustrates a typical experimental session. This market bubble crashed after period 30. Trading volume is substantial, which means that prices do not result from a few extreme traders.Open in a separate windowFig. 2.Endogenous market bubbles. (A) Price paths in16 different experimental market sessions. The dark line shows the average price in each period over the 16 sessions. Plotted below the prices is the normalized per-subject volume for each period; error bars are SEs. (B) Single-session prices (Top) and trading volume (Middle) from one statistically typical experimental session. At Bottom is shown the risky asset holdings; each subject is indicated by a different color. MRI subjects are shown with thicker lines. The dashed line is the “clairvoyant” profit-maximizing share path (assuming subjects could somehow correctly anticipate all future prices).     

Selecting the highest of three binomial probabilities

A sequential elimination procedure for selecting the highest probability in binomial trials, proposed by Levin and Robbins [Levin, B. & Robbins, H. (1981) Proc. Natl. Acad. Sci. USA 78, 4663-4666], is examined further in the special case of trials involving three probabilities. A conjectured inequality relating ratios of selection probabilities to odds ratios is shown to hold only under certain necessary and sufficient conditions. Weaker conjectured inequalities involving the probability of correct selection are shown to hold without restriction.     

Associations Between Prognostic Awareness,Acceptance of Illness,and Psychological and Spiritual Well-being Among Patients With Heart Failure

BackgroundThis study aimed to (1) investigate the association of prognostic awareness with psychological (distress level and emotional well-being) and spiritual well-being among patients with heart failure, and (2) assess the main and moderating effects of illness acceptance on the relationship between prognostic awareness and psychological and spiritual well-being.Methods and ResultsThis study used baseline data of a Singapore cohort of patients with heart failure (N = 245) who had New York Heart Association class 3 or 4 symptoms. Patients reported their awareness of prognosis and extent of illness acceptance. Multivariable linear regressions were used to investigate the associations. Prognostic awareness was not significantly associated with psychological and spiritual well-being. Illness acceptance was associated with lower levels of distress (β [SE] = –0.9 [0.2], P < .001), higher emotional well-being (β [SE] = 2.2 [0.4], P < .001), and higher spiritual well-being (β [SE] = 5.4 [0.7], P < .001). Illness acceptance did not moderate the associations of prognostic awareness with psychological and spiritual well-being.ConclusionsThis study suggests that illness acceptance could be a key factor in improving patient well-being. Illness acceptance should be regularly assessed and interventions to enhance illness acceptance should be considered for those with poor acceptance.     

Robust identification of investor beliefs

This paper develops a method informed by data and models to recover information about investor beliefs. Our approach uses information embedded in forward-looking asset prices in conjunction with asset pricing models. We step back from presuming rational expectations and entertain potential belief distortions bounded by a statistical measure of discrepancy. Additionally, our method allows for the direct use of sparse survey evidence to make these bounds more informative. Within our framework, market-implied beliefs may differ from those implied by rational expectations due to behavioral/psychological biases of investors, ambiguity aversion, or omitted permanent components to valuation. Formally, we represent evidence about investor beliefs using a nonlinear expectation function deduced using model-implied moment conditions and bounds on statistical divergence. We illustrate our method with a prototypical example from macrofinance using asset market data to infer belief restrictions for macroeconomic growth rates.

Prices in asset markets reflect a combination of investor beliefs and their risk preferences. Researchers, as well as policymakers, look to asset market data as a barometer of public beliefs. Derivative claims prices potentially enrich what we can infer about conditional probability distributions of future events, but events of interest often entail components of macroeconomic uncertainty for which there will be a paucity of information along some dimensions. Moreover, since a central tenet of asset pricing is that investors must be compensated for exposure to macroeconomic shocks that are not diversifiable, beliefs about future macroeconomic performance are of paramount importance to understanding asset prices.To disentangle the contributions of risk aversion from beliefs, many empirical approaches in the last few decades have focused on models of investor preferences by assuming rational expectations. Using the implied moment conditions of the investor’s portfolio choice problem in conjunction with this restriction gives a directly applicable and tractable approach for estimating and testing alternative model specifications. This approach, however, often leads to risk prices in some time periods that are attributed to an arguably extreme level of investor risk aversion or a rejection of the model. Risk aversion and belief formulation are intertwined. Rational expectation as a model of belief formation is meant to be a simplifying approximation. It can serve as an elegant and powerful modeling choice when appropriate. In a complex environment, however, it can be challenging to make statistical inferences pertinent to forward-looking decision making. In such settings, we find the presumption that model-dwelling investors and entrepreneurs know the true data-generating process to be tenuous and worthy of relaxation. We are not alone in this view.Some researchers have explored mechanisms that could account for this evidence via a different channel, namely beliefs which differ from rational expectations. It is sometimes argued, but typically not justified formally, that these alternatives are small departures from rational expectations. These “belief distortions” relative to rational expectations alternatively could reflect the lack of investor confidence about the assignment of probabilities to future events. This has been modeled and captured formally as ambiguity aversion or concerns about model misspecification.This paper proposes a formal methodology for analyzing models that imply conditional moment restrictions where the restrictions are presumed to hold under a distorted probability measure. It extends a previous econometrics literature that represents the statistical implications of asset pricing implications as conditional moment restrictions under rational expectations. Rational expectations on the part of individuals or enterprises can be motivated by a law of large numbers approximation used to pin down the beliefs of these economic agents “inside the model.” Once we relax the rational expectations, there are typically many choices of investor beliefs that satisfy the conditional moment restrictions. Rather than imposing a specific alternative to rational expectations, we restrict the family of investor probabilities to satisfy discrepancy bounds, which gives us a way of relaxing the rational expectations hypothesis based on pushing back from a law of large numbers approximation. We then use the conditional moment restrictions along with statistical discrepancy bounds, to characterize families of probabilities that satisfy the conditional moment restrictions.Our approach provides a version of “bounded rationality” when assessing empirical evidence. Not only are the bounds we deduce of direct interest; they also can be used as diagnostics for specific models of belief distortions. Additionally, we show how to include survey data on subjective beliefs. Such data are typically sparse and not sufficient to pin down full probabilistic characterizations of beliefs. Given these data limitations, we bound probabilities even when certain features of the data may be known through direct evidence.A common way to represent a probability distribution of a random vector is through how it assigns expectations to functions of that random vector. Since we have multiple probability distributions in play, we represent our bounds by building what is called a “nonlinear expectation” that minimizes expectations over members of the family of probability distortions that we identify. This gives us a formal way to characterize properties of probability distributions that are consistent with model-implied conditional moment restrictions. The choice of minimization is essentially a normalization as we bound expectations of functions of observable variables as well as the negative of such functions. Given the flexibility in our choice of what functions of observables we use when forming expectation bounds, our analysis provides a rich characterization of implications for the belief distortions.While we use asset pricing applications for motivation, our analysis is more generally applicable to economic models with forward-looking agents. These agents may be groups of individuals making investment or portfolio choices when facing production or financial opportunities that are exposed to uncertainty in different ways. Alternatively, they may be forward-looking enterprises, making decisions today that have important consequences for the future.In summary, our methodology gives a way to extract information on investor beliefs from asset market and survey data pertinent for both external analysts and policymakers who are looking for evidence to gauge private sector sentiments. In addition, our computations provide revealing diagnostics for model builders that embrace specific formulations of belief distortions as is common in the behavioral economics and finance literatures.Literature Review.There is a long intellectual history exploring the impact of expectations on investment decisions. As was well appreciated by economists such as in refs. (1–3), investment decisions are in part based on people’s views of the future. Alternative approaches for modeling expectations of economic actors were suggested including static expectations, ref. 4’s extrapolative expectations, ref. 5’s adaptive expectations, or appeals to data on beliefs; but these approaches leave open how to proceed when using dynamic economic models to assess hypothetical policy interventions. A productive approach to this modeling challenge has been to add the hypothesis of rational expectations. Motivated by long histories of data, this hypothesis pins down beliefs by equating the expectations of agents inside the model to those implied by the data-generating distribution. This approach to completing the specification of a stochastic equilibrium model was initiated by ref. 6 and developed fully in ref. 7.Recently there has been a renewed interest in alternative belief distortions within the asset pricing literature. See, for example, refs. 8–12. Relatedly, since survey evidence on investor beliefs is typically rather sparse and not able to produce entire predictive distributions, refs. 13 and 14 fitted time series models to the observed beliefs that can be distinct from the actual data evolution. Our approach is different from these literatures, but complementary to them. We focus on the construction of the implied bounds for expectations for functions of the stochastic process of interest that could provide empirical targets of tests of parametric models of subjective beliefs fitted to time series.There is similarity in motivation and overlaps in the methods we use to the study of robust optimization (see, for instance, refs. 15 and 16) and robust Markov chain modeling (see, for instance, ref. 17). But our is aim different. While the robust optimization research features decision makers that confront multiple probabilities, our perspective is that of analyst seeking information about the beliefs of economic decision makers from observed financial market data or survey data through the lens of a dynamic economic model.Refs. 18 and 19 describe and implement econometric methods for confronting conditioning information under correct model specification under rational expectations, within a generalized method of moments framework. Refs. 20 and 21 give extensions of the measure of model misspecification proposed by ref. 22 to accommodate conditioning information. Similarly, the models we consider are misspecified under rational expectations. This misspecification is induced as it is in precursors (23, 24) by investor belief distortions (these two papers abstract from the role of conditioning information). Our innovation is to propose and justify a dynamic formulation with belief uncertainty that 1) accommodates conditioning and 2) uses the recursive structure of multiperiod likelihoods to characterize families of beliefs that are consistent with alternative divergence thresholds.Outline of the Paper. 1. Asset Pricing with Distorted Beliefs introduces the framework we use for moment restrictions implied by an asset pricing model. 2. Data Generation and Probability Divergence specifies the probabilistic environment that underlies our computations and gives a dynamic version of the divergence with a built-in recursive structure. 3. Moment Bounds presents and justifies our recursive formulation of the functional equation used to compute the bounds along with some special cases that are of particular interest. This section provides a more complete characterization of the solution for the familiar relative entropy divergence and discusses the relation to results from large deviation theory. Finally, 3. Moment Bounds characterizes a nonlinear expectation as a way to represent the bounds on the subjective probabilities. 4. Illustration presents an empirical illustration of our methodology. 5. Bounding Other Probabilities shows how to apply our approach to extract information about the one-period, risk neutral measure and the long-term counterpart without assuming the existence of data on a complete set of Arrow–Debreu securities. Both of these probability measures are of interest in their own right. 6. Conclusions concludes.     

Significant structure theory applied to liquid helium-3

The significant structure theory of liquids is successfully applied to the quantum liquid ³He. The partition function uses the Debye partition function for the solid-like molecules and the Fermi-Dirac partition function for the gas-like degrees of freedom. To evaluate the gas-like partition function, numerical calculations are performed and some integral functions appearing in the equation of state of the ideal Fermi-Dirac gas are tabulated. In the solid-like molecules, the molar volume V_s depends on the temperature, and a linear dependence is used.     

Psychological cue use and implications for a clinical decision support system

Effective clinical decision making depends upon identifying possible outcomes for a patient, selecting relevant cues, and processing the cues to arrive at accurate judgements of each outcome's probability of occurrence. These activities can be considered as classification tasks. This paper describes a new model of psychological classification that explains how people use cues to determine class or outcome likelihoods. It proposes that clinicians respond to conditional probabilities of outcomes given cues and that these probabilities compete with each other for influence on classification. The model explains why people appear to respond to base rates inappropriately, thereby overestimating the occurrence of rare categories, and a clinical example is provided for predicting suicide risk. The model makes an effective representation for expert clinical judgements and its psychological validity enables it to generate explanations in a form that is comprehensible to clinicians. It is a strong candidate for incorporation within a decision support system for mental-health risk assessment, where it can link with statistical and pattern recognition tools applied to a database of patients. The symbiotic combination of empirical evidence and clinical expertise can provide an important web-based resource for risk assessment, including multi-disciplinary education and training.