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Cognitive Psychology Sep 2020Causal judgements in explaining-away situations, where multiple independent causes compete to account for a common effect, are ubiquitous in both everyday and...
Causal judgements in explaining-away situations, where multiple independent causes compete to account for a common effect, are ubiquitous in both everyday and specialised contexts. Despite their ubiquity, cognitive psychologists still struggle to understand how people reason in these contexts. Empirical studies have repeatedly found that people tend to 'insufficiently' explain away: that is, when one cause explains the presence of an effect, people do not sufficiently reduce the probability of other competing causes. However, the diverse accounts that researchers have proposed to explain this insufficiency suggest we are yet to find a compelling account of these results. In the current research we explored the novel possibility that insufficiency in explaining away is driven by: (i) some people interpreting probabilities as propensities, i.e. as tendencies of a physical system to produce an outcome and (ii) some people splitting the probability space among the causes in diagnostic reasoning, i.e. by following a strategy we call 'the diagnostic split'. We tested these two hypotheses by manipulating (a) the characteristics of cover stories to reflect different degrees to which the propensity interpretation of probability was pronounced, and (b) the prior probabilities of the causes which entailed different normative amounts of explaining away. Our results were in line with the extant literature as we found insufficient explaining away. However, we also found empirical support for our two hypotheses, suggesting that they are a driving force behind the reported insufficiency.
Topics: Adult; Bayes Theorem; Female; Humans; Judgment; Male; Models, Psychological; Probability
PubMed: 32388007
DOI: 10.1016/j.cogpsych.2020.101293 -
PloS One 2017Probability matching occurs when the behavior of an agent matches the likelihood of occurrence of events in the agent's environment. For instance, when artificial neural...
Probability matching occurs when the behavior of an agent matches the likelihood of occurrence of events in the agent's environment. For instance, when artificial neural networks match probability, the activity in their output unit equals the past probability of reward in the presence of a stimulus. Our previous research demonstrated that simple artificial neural networks (perceptrons, which consist of a set of input units directly connected to a single output unit) learn to match probability when presented different cues in isolation. The current paper extends this research by showing that perceptrons can match probabilities when presented simultaneous cues, with each cue signaling different reward likelihoods. In our first simulation, we presented up to four different cues simultaneously; the likelihood of reward signaled by the presence of one cue was independent of the likelihood of reward signaled by other cues. Perceptrons learned to match reward probabilities by treating each cue as an independent source of information about the likelihood of reward. In a second simulation, we violated the independence between cues by making some reward probabilities depend upon cue interactions. We did so by basing reward probabilities on a logical combination (AND or XOR) of two of the four possible cues. We also varied the size of the reward associated with the logical combination. We discovered that this latter manipulation was a much better predictor of perceptron performance than was the logical structure of the interaction between cues. This indicates that when perceptrons learn to match probabilities, they do so by assuming that each signal of a reward is independent of any other; the best predictor of perceptron performance is a quantitative measure of the independence of these input signals, and not the logical structure of the problem being learned.
Topics: Cues; Humans; Neural Networks, Computer; Perception; Probability; Reinforcement, Psychology
PubMed: 28212422
DOI: 10.1371/journal.pone.0172431 -
Journal of the Royal Society, Interface Nov 2023Symmetry arguments are frequently used-often implicitly-in mathematical modelling of natural selection. Symmetry simplifies the analysis of models and reduces the number...
Symmetry arguments are frequently used-often implicitly-in mathematical modelling of natural selection. Symmetry simplifies the analysis of models and reduces the number of distinct population states to be considered. Here, I introduce a formal definition of symmetry in mathematical models of natural selection. This definition applies to a broad class of models that satisfy a minimal set of assumptions, using a framework developed in previous works. In this framework, population structure is represented by a set of sites at which alleles can live, and transitions occur via replacement of some alleles by copies of others. A symmetry is defined as a permutation of sites that preserves probabilities of replacement and mutation. The symmetries of a given selection process form a group, which acts on population states in a way that preserves the Markov chain representing selection. Applying classical results on group actions, I formally characterize the use of symmetry to reduce the states of this Markov chain, and obtain bounds on the number of states in the reduced chain.
Topics: Models, Genetic; Selection, Genetic; Markov Chains; Probability; Mutation
PubMed: 37963562
DOI: 10.1098/rsif.2023.0306 -
The Journal of General Psychology 2020In social and economic interactions, people often decide differently for others, as against for themselves, under situations involving risks. This sometimes leads to...
In social and economic interactions, people often decide differently for others, as against for themselves, under situations involving risks. This sometimes leads to conflicts or contradictions. Although previous studies have explored such contradictions, the findings have been inconsistent. To reconcile these inconsistencies, this paper investigates the role played by the different domains and probabilities in the self-other differences under risk. Two groups of participants completed a gambling task combining different domains (gain vs. loss) and probabilities (small vs. large). One group made decisions for others and the other group made decisions for themselves. The results revealed a four pattern of discrepancy: the ones who made decisions for others were less risk-seeking than those who made decisions for themselves over the small probability gains. This was reversed over the large probability gains. Conversely, the participants who made decisions for others were more risk-seeking than those who made decisions for themselves over the small probability losses. The results were reversed over the large probability losses. These results reconcile the contradictory findings of the previous studies and suggest the significant role played by contextual factors in such discrepancies.
Topics: Decision Making; Female; Humans; Male; Probability; Risk Assessment; Risk-Taking; Young Adult
PubMed: 31530234
DOI: 10.1080/00221309.2019.1664388 -
Archives of Osteoporosis Jun 2021Hip fracture rates in Botswana were used to create a FRAX® model for fracture risk assessment.
INTRODUCTION
Hip fracture rates in Botswana were used to create a FRAX® model for fracture risk assessment.
OBJECTIVE
This paper describes the development and characteristics of a country-specific FRAX model for Botswana.
METHODS
Age-specific and sex-specific incidence of hip fracture and national mortality rates was incorporated into a FRAX model for Botswana. Ten-year fracture probabilities were compared with those from African countries having a FRAX model and African Americans from the USA.
RESULTS
The probabilities of hip fracture and major osteoporotic fracture were low compared with those from South Africa (Black and Coloured) and US Blacks. Probabilities were marginally higher than for Tunisia.
CONCLUSION
The creation of a FRAX model is expected to help guide decisions about the prevention and treatment of fragility fractures in Botswana.
Topics: Botswana; Female; Hip Fractures; Humans; Male; Osteoporotic Fractures; Risk Assessment; Risk Factors; South Africa
PubMed: 34100118
DOI: 10.1007/s11657-021-00965-y -
Risk Analysis : An Official Publication... Oct 2015Wildfires present a complex applied risk management environment, but relatively little attention has been paid to behavioral and cognitive responses to risk among public...
Wildfires present a complex applied risk management environment, but relatively little attention has been paid to behavioral and cognitive responses to risk among public agency wildfire managers. This study investigates responses to risk, including probability weighting and risk aversion, in a wildfire management context using a survey-based experiment administered to federal wildfire managers. Respondents were presented with a multiattribute lottery-choice experiment where each lottery is defined by three outcome attributes: expenditures for fire suppression, damage to private property, and exposure of firefighters to the risk of aviation-related fatalities. Respondents choose one of two strategies, each of which includes "good" (low cost/low damage) and "bad" (high cost/high damage) outcomes that occur with varying probabilities. The choice task also incorporates an information framing experiment to test whether information about fatality risk to firefighters alters managers' responses to risk. Results suggest that managers exhibit risk aversion and nonlinear probability weighting, which can result in choices that do not minimize expected expenditures, property damage, or firefighter exposure. Information framing tends to result in choices that reduce the risk of aviation fatalities, but exacerbates nonlinear probability weighting.
Topics: Decision Making; Empirical Research; Fires; Humans; Probability; Risk Assessment
PubMed: 26269258
DOI: 10.1111/risa.12457 -
Lifetime Data Analysis Oct 2022Multi-state models are frequently used when data come from subjects observed over time and where focus is on the occurrence of events that the subjects may experience. A... (Review)
Review
Multi-state models are frequently used when data come from subjects observed over time and where focus is on the occurrence of events that the subjects may experience. A convenient modeling assumption is that the multi-state stochastic process is Markovian, in which case a number of methods are available when doing inference for both transition intensities and transition probabilities. The Markov assumption, however, is quite strict and may not fit actual data in a satisfactory way. Therefore, inference methods for non-Markov models are needed. In this paper, we review methods for estimating transition probabilities in such models and suggest ways of doing regression analysis based on pseudo observations. In particular, we will compare methods using land-marking with methods using plug-in. The methods are illustrated using simulations and practical examples from medical research.
Topics: Humans; Markov Chains; Probability; Stochastic Processes; Survival Analysis
PubMed: 35764854
DOI: 10.1007/s10985-022-09560-w -
Otolaryngology--head and Neck Surgery :... Dec 2017In biomedical research, it is imperative to differentiate chance variation from truth before we generalize what we see in a sample of subjects to the wider population.... (Review)
Review
In biomedical research, it is imperative to differentiate chance variation from truth before we generalize what we see in a sample of subjects to the wider population. For decades, we have relied on null hypothesis significance testing, where we calculate P values for our data to decide whether to reject a null hypothesis. This methodology is subject to substantial misinterpretation and errant conclusions. Instead of working backward by calculating the probability of our data if the null hypothesis were true, Bayesian statistics allow us instead to work forward, calculating the probability of our hypothesis given the available data. This methodology gives us a mathematical means of incorporating our "prior probabilities" from previous study data (if any) to produce new "posterior probabilities." Bayesian statistics tell us how confidently we should believe what we believe. It is time to embrace and encourage their use in our otolaryngology research.
Topics: Bayes Theorem; Biomedical Research; Data Interpretation, Statistical; Humans; Otolaryngology; Probability; Research Design
PubMed: 29192853
DOI: 10.1177/0194599817739260 -
Risk Analysis : An Official Publication... Aug 2008This article reports on a study to quantify expert beliefs about the explosion probability of unexploded ordnance (UXO). Some 1,976 sites at closed military bases in the...
This article reports on a study to quantify expert beliefs about the explosion probability of unexploded ordnance (UXO). Some 1,976 sites at closed military bases in the United States are contaminated with UXO and are slated for cleanup, at an estimated cost of $15-140 billion. Because no available technology can guarantee 100% removal of UXO, information about explosion probability is needed to assess the residual risks of civilian reuse of closed military bases and to make decisions about how much to invest in cleanup. This study elicited probability distributions for the chance of UXO explosion from 25 experts in explosive ordnance disposal, all of whom have had field experience in UXO identification and deactivation. The study considered six different scenarios: three different types of UXO handled in two different ways (one involving children and the other involving construction workers). We also asked the experts to rank by sensitivity to explosion 20 different kinds of UXO found at a case study site at Fort Ord, California. We found that the experts do not agree about the probability of UXO explosion, with significant differences among experts in their mean estimates of explosion probabilities and in the amount of uncertainty that they express in their estimates. In three of the six scenarios, the divergence was so great that the average of all the expert probability distributions was statistically indistinguishable from a uniform (0, 1) distribution-suggesting that the sum of expert opinion provides no information at all about the explosion risk. The experts' opinions on the relative sensitivity to explosion of the 20 UXO items also diverged. The average correlation between rankings of any pair of experts was 0.41, which, statistically, is barely significant (p= 0.049) at the 95% confidence level. Thus, one expert's rankings provide little predictive information about another's rankings. The lack of consensus among experts suggests that empirical studies are needed to better understand the explosion risks of UXO.
Topics: California; Explosions; Explosive Agents; Probability; Risk Assessment
PubMed: 18627542
DOI: 10.1111/j.1539-6924.2008.01068.x -
European Journal of Anaesthesiology Jan 2012Prognosis is a forecast, based on present observations in a patient, of their probable outcome from disease, surgery and so on. Research methods for the development of... (Review)
Review
Prognosis is a forecast, based on present observations in a patient, of their probable outcome from disease, surgery and so on. Research methods for the development of risk probabilities may not be familiar to some anaesthesiologists. We briefly describe methods for identifying risk factors and risk scores. A probability prediction rule assigns a risk probability to a patient for the occurrence of a specific event. Probability reflects the continuum between absolute certainty (Pi = 1) and certified impossibility (Pi = 0). Biomarkers and clinical covariates that modify risk are known as risk factors. The Pi as modified by risk factors can be estimated by identifying the risk factors and their weighting; these are usually obtained by stepwise logistic regression. The accuracy of probabilistic predictors can be separated into the concepts of 'overall performance', 'discrimination' and 'calibration'. Overall performance is the mathematical distance between predictions and outcomes. Discrimination is the ability of the predictor to rank order observations with different outcomes. Calibration is the correctness of prediction probabilities on an absolute scale. Statistical methods include the Brier score, coefficient of determination (Nagelkerke R2), C-statistic and regression calibration. External validation is the comparison of the actual outcomes to the predicted outcomes in a new and independent patient sample. External validation uses the statistical methods of overall performance, discrimination and calibration and is uniformly recommended before acceptance of the prediction model. Evidence from randomised controlled clinical trials should be obtained to show the effectiveness of risk scores for altering patient management and patient outcomes.
Topics: Decision Support Techniques; Discriminant Analysis; Health Status Indicators; Humans; Logistic Models; Models, Statistical; Probability; Prognosis; Reproducibility of Results; Risk Assessment; Risk Factors; Time Factors
PubMed: 22089517
DOI: 10.1097/EJA.0b013e32834d9474