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Statistics in Medicine Sep 2016Probabilities can be consistently estimated using random forests. It is, however, unclear how random forests should be updated to make predictions for other centers or...
Probabilities can be consistently estimated using random forests. It is, however, unclear how random forests should be updated to make predictions for other centers or at different time points. In this work, we present two approaches for updating random forests for probability estimation. The first method has been proposed by Elkan and may be used for updating any machine learning approach yielding consistent probabilities, so-called probability machines. The second approach is a new strategy specifically developed for random forests. Using the terminal nodes, which represent conditional probabilities, the random forest is first translated to logistic regression models. These are, in turn, used for re-calibration. The two updating strategies were compared in a simulation study and are illustrated with data from the German Stroke Study Collaboration. In most simulation scenarios, both methods led to similar improvements. In the simulation scenario in which the stricter assumptions of Elkan's method were not met, the logistic regression-based re-calibration approach for random forests outperformed Elkan's method. It also performed better on the stroke data than Elkan's method. The strength of Elkan's method is its general applicability to any probability machine. However, if the strict assumptions underlying this approach are not met, the logistic regression-based approach is preferable for updating random forests for probability estimation. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.
Topics: Biometry; Calibration; Humans; Logistic Models; Machine Learning; Probability
PubMed: 27074747
DOI: 10.1002/sim.6959 -
Studies in History and Philosophy of... Oct 2015This essay makes a case for regarding personal probabilities used in Bayesian analyses of confirmation as objects of acceptance and rejection. That in turn entails that...
This essay makes a case for regarding personal probabilities used in Bayesian analyses of confirmation as objects of acceptance and rejection. That in turn entails that personal probabilities are subject to the argument from inductive risk, which aims to show non-epistemic values can legitimately influence scientific decisions about which hypotheses to accept. In a Bayesian context, the argument from inductive risk suggests that value judgments can influence decisions about which probability models to accept for likelihoods and priors. As a consequence, if the argument from inductive risk is sound, then non-epistemic values can affect not only the level of evidence deemed necessary to accept a hypothesis but also degrees of confirmation themselves.
Topics: Attitude; Bayes Theorem; Cognition; Humans; Judgment; Probability
PubMed: 26386533
DOI: 10.1016/j.shpsa.2015.05.010 -
International Journal of Offender... Apr 2018Risk is the probability of an adverse event or outcome. In a previous article, I compared the Bayesian and Frequentist models of defining probability. This article...
Risk is the probability of an adverse event or outcome. In a previous article, I compared the Bayesian and Frequentist models of defining probability. This article compares the Bayesian and regression models of quantifying probability. Both approaches are widely used in the biomedical and behavioral sciences even though they yield different results. No consensus has emerged as to which is more appropriate. The choice between them remains controversial. This article concludes that the Bayesian model provides a viable alternative to logistic regression and may be more useful in quantifying the absolute recidivism risk of individual sex offenders. It shows how evaluators can easily calculate Bayesian probabilities and their associated credible intervals from an actuarial data set. Last, the article proposes a forensic practice guideline that evaluators do not conclude that an offender meets an absolute risk threshold unless the subject's risk exceeds the threshold by a credible margin of error.
Topics: Humans; Probability; Recidivism; Risk Assessment; Sex Offenses
PubMed: 27864533
DOI: 10.1177/0306624X16677784 -
Cognitive Science Jul 2022People often face the challenge of evaluating competing explanations. One approach is to assess the explanations' relative probabilities-for example, applying Bayesian...
People often face the challenge of evaluating competing explanations. One approach is to assess the explanations' relative probabilities-for example, applying Bayesian inference to compute their posterior probabilities. Another approach is to consider an explanation's qualities or "virtues," such as its relative simplicity (i.e., the number of unexplained causes it invokes). The current work investigates how these two approaches are related. Study 1 found that simplicity is used to infer the inputs to Bayesian inference (explanations' priors and likelihoods). Studies 1 and 2 found that simplicity is also used as a direct cue to the outputs of Bayesian inference (the posterior probability of an explanation), such that simplicity affects estimates of posterior probability even after controlling for elicited (Study 1) or provided (Study 2) priors and likelihoods, with simplicity having a larger effect in Study 1, where posteriors are more uncertain and difficult to compute. Comparing Studies 1 and 2 also suggested that simplicity plays additional roles unrelated to approximating probabilities, as reflected in simplicity's effect on how "satisfying" (vs. probable) an explanation is, which remained largely unaffected by the difficulty of computing posteriors. Together, these results suggest that the virtue of simplicity is used in multiple ways to approximate probabilities (i.e., serving as a cue to priors, likelihoods, and posteriors) when these probabilities are otherwise uncertain or difficult to compute, but that the influence of simplicity also goes beyond these roles.
Topics: Bayes Theorem; Causality; Cues; Humans; Probability
PubMed: 35738485
DOI: 10.1111/cogs.13169 -
Trends in Cognitive Sciences Jun 2022Life in an increasingly information-rich but highly uncertain world calls for an effective means of communicating uncertainty to a range of audiences. Senders prefer to... (Review)
Review
Life in an increasingly information-rich but highly uncertain world calls for an effective means of communicating uncertainty to a range of audiences. Senders prefer to convey uncertainty using verbal (e.g., likely) rather than numeric (e.g., 75% chance) probabilities, even in consequential domains, such as climate science. However, verbal probabilities can convey something other than uncertainty, and senders may exploit this. For instance, senders can maintain credibility after making erroneous predictions. While verbal probabilities afford ease of expression, they can be easily misunderstood, and the potential for miscommunication is not effectively mitigated by assigning (imprecise) numeric probabilities to words. When making consequential decisions, recipients prefer (precise) numeric probabilities.
Topics: Communication; Humans; Probability; Uncertainty
PubMed: 35397985
DOI: 10.1016/j.tics.2022.03.002 -
Scandinavian Journal of Psychology Oct 2019Probability judgment is a vital part of many aspects of everyday life. In the present paper, we present a new theory of the way in which individuals produce probability... (Randomized Controlled Trial)
Randomized Controlled Trial
Probability judgment is a vital part of many aspects of everyday life. In the present paper, we present a new theory of the way in which individuals produce probability estimates for joint events: conjunctive and disjunctive. We propose that a majority of individuals produce conjunctive (disjunctive) estimates by making a quasi-random adjustment, positive or negative, from the less (more) likely component probability with the other component playing no obvious role. In two studies, we produce evidence supporting propositions that follow from our theory. First, the component probabilities do appear to play the distinct roles we propose in determining the joint event probabilities. Second, contrary to probability theory and other accounts of probability judgment, we show that the conjunctive-less likely probability difference is unrelated to the more likely disjunctive probability difference (in normative theory these quantities are identical). In conclusion, while violating the norms of probability judgment, we argue that estimates produced in the manner we propose will be close enough to the normative values especially given the changing nature of the external environment and the incomplete nature of available information.
Topics: Adolescent; Adult; Bias; Female; Humans; Judgment; Male; Middle Aged; Models, Psychological; Probability; Uncertainty; Young Adult
PubMed: 31242534
DOI: 10.1111/sjop.12560 -
Scientific Reports Jul 2022Empirical evidence has shown that visually enhancing the saliency of reward probabilities can ease the cognitive demands of value comparisons and improve value-based...
Empirical evidence has shown that visually enhancing the saliency of reward probabilities can ease the cognitive demands of value comparisons and improve value-based decisions in old age. In the present study, we used a time-varying drift diffusion model that includes starting time parameters to better understand (1) how increasing the saliency of reward probabilities may affect the dynamics of value-based decision-making and (2) how these effects may interact with age. We examined choices made by younger and older adults in a mixed lottery choice task. On a subset of trials, we used a color-coding scheme to highlight the saliency of reward probabilities, which served as a decision-aid. The results showed that, in control trials, older adults started to consider probability relative to magnitude information sooner than younger adults, but that their evidence accumulation processes were less sensitive to reward probabilities than that of younger adults. This may indicate a noisier and more stochastic information accumulation process during value-based decisions in old age. The decision-aid increased the influence of probability information on evidence accumulation rates in both age groups, but did not alter the relative timing of accumulation for probability versus magnitude in either group.
Topics: Cognition; Decision Making; Probability; Reward
PubMed: 35790772
DOI: 10.1038/s41598-022-15432-y -
Statistics in Medicine Apr 2020We present here a study of ordinal outcomes with a cumulative probability model. In particular, we consider the log link with the assumption of proportionality. The...
We present here a study of ordinal outcomes with a cumulative probability model. In particular, we consider the log link with the assumption of proportionality. The logit link is currently the most widely used link with ordinal outcomes in the health research literature. With the logit link, one obtains regression coefficients that are functions of odds. When the log link is used, one obtains regression coefficients that are functions of probabilities. While odds might be preferred with certain studies that are retrospective, many health researchers may prefer to have direct statements about probabilities. There are two classes of models with the log link analogous to those with the logit link. We will call these two classes the Proportional Probability Model (PPM) and the Log Cumulative Probability Model (LCPM). These models introduce a challenge not seen with the logit link models. The log link models have constraints on the parameter space. We must insist that the maximum likelihood estimate (MLE) satisfy these constraints. We present conditions for the uniqueness of the MLE and we present other features of the MLE. Several examples and several closed form expressions for the MLE are presented. While this paper is primarily about the PPM, our R package lcpm contains functions to fit both the PPM and the LCPM.
Topics: Humans; Likelihood Functions; Logistic Models; Models, Statistical; Probability; Retrospective Studies
PubMed: 32020671
DOI: 10.1002/sim.8479 -
Journal of Personality and Social... Aug 1991People commonly violate a basic rule of probability, judging a conjunction of events to be more probable than at least 1 of its component events. Many manifestations of...
People commonly violate a basic rule of probability, judging a conjunction of events to be more probable than at least 1 of its component events. Many manifestations of this conjunction fallacy have been ascribed to people's reliance on the representativeness heuristic for judging probability. Some conjunction fallacies, however, have been ascribed to the incorrect rules people use to combine probabilities. In 2 experiments, representativeness was pitted against probability combination to determine the contributions of each to the fallacy. Even for exemplar representativeness problems, the fallacy stemmed primarily from the application of incorrect combination rules. Representativeness seemed to be involved only insofar as it influenced the probabilities of a conjunction's component events. Implications of these findings are discussed for the representativeness account of judgmental errors and the relation between similarity and probability.
Topics: Humans; Judgment; Probability; Surveys and Questionnaires
PubMed: 1920061
DOI: 10.1037//0022-3514.61.2.181 -
Osteoporosis International : a Journal... Mar 2023A greater propensity to falling is associated with higher fracture risk. This study provides adjustments to FRAX-based fracture probabilities accounting for the number...
UNLABELLED
A greater propensity to falling is associated with higher fracture risk. This study provides adjustments to FRAX-based fracture probabilities accounting for the number of prior falls.
INTRODUCTION
Prior falls increase subsequent fracture risk but are not currently directly included in the FRAX tool. The aim of this study was to quantify the effect of the number of prior falls on the 10-year probability of fracture determined with FRAX®.
METHODS
We studied 21,116 women and men age 40 years or older (mean age 65.7 ± 10.1 years) with fracture probability assessment (FRAX®), self-reported falls for the previous year, and subsequent fracture outcomes in a registry-based cohort. The risks of death, hip fracture, and non-hip major osteoporotic fracture (MOF-NH) were determined by Cox proportional hazards regression for fall number category versus the whole population (i.e., an average number of falls). Ten-year probabilities of hip fracture and major osteoporotic fracture (MOF) were determined according to the number of falls from the hazards of death and fracture incorporated into the FRAX model for the UK. The probability ratios (number of falls vs. average number of falls) provided adjustments to conventional FRAX estimates of fracture probability according to the number of falls.
RESULTS
Compared with the average number of falls, the hazard ratios for hip fracture, MOF-NH and death were lower than unity in the absence of a fall history. Hazard ratios increased progressively with an increasing number of reported falls. The probability ratio rose progressively as the number of reported falls increased. Probability ratios decreased with age, an effect that was more marked the greater the number of prior falls.
CONCLUSION
The probability ratios provide adjustments to conventional FRAX estimates of fracture probability according to the number of prior falls.
Topics: Male; Humans; Female; Middle Aged; Aged; Adult; Osteoporotic Fractures; Bone Density; Risk Assessment; Hip Fractures; Probability; Risk Factors
PubMed: 36562788
DOI: 10.1007/s00198-022-06633-2