Reinforcement learning and decision-making (RLDM) provide a quantitative framework and computational theories with which we can disentangle psychiatric conditions into the basic dimensions of neurocognitive functioning. RLDM offer a novel approach to assessing and potentially diagnosing psychiatric patients, and there is growing enthusiasm for both RLDM and computational psychiatry among clinical researchers. Such a framework can also provide insights into the brain substrates of particular RLDM processes, as exemplified by model-based analysis of data from functional magnetic resonance imaging (fMRI) or electroencephalography (EEG). However, researchers often find the approach too technical and have difficulty adopting it for their research. Thus, a critical need remains to develop a user-friendly tool for the wide dissemination of computational psychiatric methods. We introduce an R package called hBayesDM (hierarchicalBayesian modeling ofDecision-Making tasks), which offers computational modeling of an array of RLDM tasks and social exchange games. The hBayesDM package offers state-of-the-art hierarchical Bayesian modeling, in which both individual and group parameters (i.e., posterior distributions) are estimated simultaneously in a mutually constraining fashion. At the same time, the package is extremely user-friendly: users can perform computational modeling, output visualization, and Bayesian model comparisons, each with a single line of coding. Users can also extract the trial-by-trial latent variables (e.g., prediction errors) required for model-based fMRI/EEG. With the hBayesDM package, we anticipate that anyone with minimal knowledge of programming can take advantage of cutting-edge computational-modeling approaches to investigate the underlying processes of and interactions between multiple decision-making (e.g., goal-directed, habitual, and Pavlovian) systems. In this way, we expect that the hBayesDM package will contribute to the dissemination of advanced modeling approaches and enable a wide range of researchers to easily perform computational psychiatric research within different populations.

In process-tracing studies, a frequently used index describes whether information selection behavior is attribute - or alternativewise. The performance of this index is investigated under the assumption that subjects select information in a random fashion. The results show that the index may lead to inaccurate conclusions regarding the information-acquisition strategy of a subject. In addition, a Monte Carlo study is conducted that examines the sensitivity of the index to strategy changes. An alternative index is derived and a latent-class model is proposed for a parsimonious representation of individual differences in information acquisition.

Bernoulli's framework of expected utility serves as a model for various psychological processes, including motivation, moral sense, attitudes, and decision making. To account for evidence at variance with expected utility, the authors generalize the framework of fast and frugal heuristics from inferences to preferences. The priority heuristic predicts (a) the Allais paradox, (b) risk aversion for gains if probabilities are high, (c) risk seeking for gains if probabilities are low (e.g., lottery tickets), (d) risk aversion for losses if probabilities are low (e.g., buying insurance), (e) risk seeking for losses if probabilities are high, (f) the certainty effect, (g) the possibility effect, and (h) intransitivities. The authors test how accurately the heuristic predicts people's choices, compared with previously proposed heuristics and 3 modifications of expected utility theory: security-potential/aspiration theory, transfer-of-attention-exchange model, and cumulative prospect theory.

Most theoretical and empirical research on intertemporal choice assumes a deterministic and static perspective, leading to the widely adopted delay discounting models. As a form of preferential choice, however, intertemporal choice may be generated by a stochastic process that requires some deliberation time to reach a decision. We conducted 3 experiments to investigate how choice and decision time varied as a function of manipulations designed to examine the delay duration effect, the common difference effect, and the magnitude effect in intertemporal choice. The results, especially those associated with the delay duration effect, challenged the traditional deterministic and static view and called for alternative approaches. Consequently, various static or dynamic stochastic choice models were explored and fit to the choice data, including alternative-wise models derived from the traditional exponential or hyperbolic discount function and attribute-wise models built upon comparisons of direct or relative differences in money and delay. Furthermore, for the first time, dynamic diffusion models, such as those based on decision field theory, were also fit to the choice and response time data simultaneously. The results revealed that the attribute-wise diffusion model with direct differences, power transformations of objective value and time, and varied diffusion parameter performed the best and could account for all 3 intertemporal effects. In addition, the empirical relationship between choice proportions and response times was consistent with the prediction of diffusion models and thus favored a stochastic choice process for intertemporal choice that requires some deliberation time to make a decision.

Heuristic models have been proposed for many domains involving choice. We conducted an out-of-sample, cross-validated comparison of heuristic models of intertemporal choice (which can account for many of the known intertemporal choice anomalies) and discounting models. Heuristic models outperformed traditional utility-discounting models, including models of exponential and hyperbolic discounting. The best-performing models predicted choices by using a weighted average of absolute differences and relative percentage differences of the attributes of the goods in a choice set. We concluded that heuristic models explain time-money trade-off choices in experiments better than do utility-discounting models.

In the last years, research on risky choice has moved beyond analyzing choices only. Models have been suggested that aim to describe the underlying cognitive processes and some studies have tested process predictions of these models. Prominent approaches are evidence accumulation models such as decision field theory (DFT), simple serial heuristic models such as the adaptive toolbox, and connectionist approaches such as the parallel constraint satisfaction (PCS) model. In two studies involving measures of attention and pupil dilation, we investigate hypotheses derived from these models in choices between two gambles with two outcomes each. We show that attention to an outcome of a gamble increases with its probability and its value and that attention shifts toward the subsequently favored gamble after about two thirds of the decision process, indicating a gaze-cascade effect. Information search occurs mostly within-gambles, and the direction of search does not change over the course of decision making. Pupil dilation, which reflects both cognitive effort and arousal, increases during the decision process and increases with mean expected value. Overall, the results support aspects of automatic integration models for risky choice such as DFT and PCS, but in their current specification none of them can account for the full pattern of results.

Disruption of function of left, but not right, lateral prefrontal cortex (LPFC) with low-frequency repetitive transcranial magnetic stimulation (rTMS) increased choices of immediate rewards over larger delayed rewards. rTMS did not change choices involving only delayed rewards or valuation judgments of immediate and delayed rewards, providing causal evidence for a neural lateral-prefrontal cortex09“based self-control mechanism in intertemporal choice.

The tendency to discount future prospects in lieu of smaller immediate outcomes is known as temporal discounting. The current work used eye‐tracking methodology to examine attentional processing to different elements of choice during an intertemporal decision task. Our findings reveal that those who tend to prefer the immediate option demonstrate attentional biases that were predictive of choice. When losses were at stake, selective attention biases also predicted unique variance in self‐report measures of risk taking, impulsivity, and self‐control beyond what was accounted for by a discounting parameter (), a typical method for summarizing intertemporal choice data. Overall, our findings suggest that eye‐tracking measures of selective attention may allow for a better theoretical understanding of the mechanisms and processes involved in intertemporal choice. Copyright 08 2015 John Wiley & Sons, Ltd.

This paper discusses the discounted utility (DU) model: its historical development, underlying assumptions, and "anomalies" - the empirical regularities that are inconsistent with its theoretical predictions. We then summarize the alternate theoretical formulations that have been advanced to address these anomalies. We also review three decades of empirical research on intertemporal choice, and discuss reasons for the spectacular variation in implicit discount rates across studies. Throughout the paper, we stress the importance of distinguishing time preference, per se, from many other considerations that also influence intertemporal choices.

The Gibbs sampler, the algorithm of Metropolis and similar iterative simulation methods are potentially very helpful for summarizing multivariate distributions. Used naively, however, iterative simulation can give misleading answers. Our methods are simple and generally applicable to the output of any iterative simulation; they are designed for researchers primarily interested in the science underlying the data and models they are analyzing, rather than for researchers interested in the probability theory underlying the iterative simulations themselves. Our recommended strategy is to use several independent sequences, with starting points sampled from an overdispersed distribution. At each step of the iterative simulation, we obtain, for each univariate estimand of interest, a distributional estimate and an estimate of how much sharper the distributional estimate might become if the simulations were continued indefinitely. Because our focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normality after transformations and marginalization, we derive our results as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations. The methods are illustrated on a random-effects mixture model applied to experimental measurements of reaction times of normal and schizophrenic patients.

Many everyday decisions have to be made under risk and can be interpreted as choices between gambles with different outcomes that are realized with specific probabilities. The underlying cognitive processes were investigated by testing six sets of hypotheses concerning choices, decision times, and information search derived from cumulative prospect theory, decision field theory, priority heuristic and parallel constraint satisfaction models. Our participants completed 40 decision tasks of two gambles with two non-negative outcomes each. Information search was recorded using eye-tracking technology. Results for choices, decision time, the amount of information searched for, fixation durations, the direction of the information search, and the distribution of fixations conflict with the prediction of the non-compensatory priority heuristic and indicate that individuals use compensatory strategies. Choice proportions are well in line with the predictions of cumulative prospect theory. Process measures indicate that individuals thereby do not rely on deliberate calculations of weighted sums. Information integration processes seem to be better explained by models that partially rely on automatic processes such as decision field theory or parallel constraint satisfaction models. Copyright 2010 John Wiley & Sons, Ltd.

Previous research has shown that the value of large future rewards is discounted less steeply than is the value of small future rewards. These experiments extended this line of research to probabilistic rewards. Two experiments replicated the standard findings for delayed rewards but demonstrated that amount has an opposite effect on the discounting of probabilistic rewards. That is, large probabilistic amounts were discounted at the same or higher rates than small amounts. Although amount had opposite effects on the discounting of delayed and probabilistic rewards, nevertheless, the same form of mathematical function accurately described discounting of both types of reward. The findings suggest that fundamentally similar, but not identical, processes are involved in decision making regarding delayed and probabilistic rewards. The implications of these findings for impulsivity and self-control are discussed.

In recent years, numerous studies comparing intuition and deliberation have been published. However, relatively little is known about the cognitive processes underlying the two decision modes. In two studies, we analyzed the effects of decision mode instructions on processes of information search and integration, using eye-tracking technology in a between-participants (Study 1) and a within-participants (Study 2) design. Our findings indicate that the instruction to deliberate does not necessarily lead to qualitatively different information processing compared to the instruction to decide intuitively. We found no difference in mean fixation duration and the distribution of short, medium and long fixations. Short fixations in particular prevailed under both decision mode instructions, while long fixations indicating a conscious and calculation-based information processing were rarely observed. Instruction-induced deliberation led to a higher number of fixations, a more complete information search and more repeated information inspections. We interpret our findings as support for the hypothesis that intuitive and deliberate decision modes share the same basic processes which are supplemented by additional operations in the deliberate decision mode.

统计推断在科学研究中起到关键作用,然而当前科研中最常用的经典统计方法——零假设检验(Null hypothesis significance test,NHST)却因难以理解而被部分研究者误用或滥用。有研究者提出使用贝叶斯因子(Bayes factor)作为一种替代和(或)补充的统计方法。贝叶斯因子是贝叶斯统计中用来进行模型比较和假设检验的重要方法,其可以解读为对零假设H_0或者备择假设H_1的支持程度。其与NHST相比有如下优势:同时考虑H_0和H_1并可以用来支持H_0、不"严重"地倾向于反对H_0、可以监控证据强度的变化以及不受抽样计划的影响。目前,贝叶斯因子能够很便捷地通过开放的统计软件JASP实现,本文以贝叶斯t检验进行示范。贝叶斯因子的使用对心理学研究者来说具有重要的意义,但使用时需要注意先验分布选择的合理性以及保持数据分析过程的透明与公开。

Neuroimaging studies of decision-making have generally related neural activity to objective measures (such as reward magnitude, probability or delay), despite choice preferences being subjective. However, economic theories posit that decision-makers behave as though different options have different subjective values. Here we use functional magnetic resonance imaging to show that neural activity in several brain regions--particularly the ventral striatum, medial prefrontal cortex and posterior cingulate cortex--tracks the revealed subjective value of delayed monetary rewards. This similarity provides unambiguous evidence that the subjective value of potential rewards is explicitly represented in the human brain.

Abstract090000 A basic stationarity axiom of economic theory assumes stable preference between two deferred goods separated by a fixed time. To test this assumption, we offered subjects choices between delayed rewards, while manipulating the delays to those rewards. Preferences typically reversed with changes in delay, as predicted by hyperbolic discounting models of impulsiveness. Of 36 subjects, 34 reversed preference from a larger, later reward to a smaller, earlier reward as the delays to both rewards decreased. We conclude that the stationarity axiom is not appropriate in models of human choice.

Investors systematically deviate from rationality when making financial decisions, yet the mechanisms responsible for these deviations have not been identified. Using event-related fMRI, we examined whether anticipatory neural activity would predict optimal and suboptimal choices in a financial decision-making task. We characterized two types of deviations from the optimal investment strategy of a rational risk-neutral agent as risk-seeking mistakes and risk-aversion mistakes. Nucleus accumbens activation preceded risky choices as well as risk-seeking mistakes, while anterior insula activation preceded riskless choices as well as risk-aversion mistakes. These findings suggest that distinct neural circuits linked to anticipatory affect promote different types of financial choices and indicate that excessive activation of these circuits may lead to investing mistakes. Thus, consideration of anticipatory neural mechanisms may add predictive power to the rational actor model of economic decision making.

This paper presents a model of how humans choose between mutually exclusive alternatives. The model is based on the observation that human decision makers are unable or unwilling to compute the overall worth of the offered alternatives. This approach models much human choice behavior as a process in which people seek to equate a less significant difference between alternatives on one dimension, thus leaving the greater one-dimensional difference to be differentiated as the determinant of the final choice. These aspects of the equate-to-differentiate model are shown to be able to provide an alternative and seemingly better account of the prominence effect. The model is also able to provide an explanation and prediction regarding the empirical violation of independence and transitivity axioms. It is suggested that the model allows understanding perplexing decision phenomena better than alternative models.

An interesting phenomenon, which we dub the ‘pseudo‐immediacy effect’, was detected in intertemporal choices. The majority of our participants preferred the smaller but sooner (SS) outcome to the larger but later (LL) outcome when a pseudo‐immediacy reward was framed, but a higher proportion of participants preferred the LL outcome to the SS outcome when the pseudo‐immediate format was removed. Such a shift violated the invariance principle which requires that the preference order between options does not depend on the manner in which they are described. With reference to the pseudo‐certainty effect reported by Kahneman and Tversky in 1984, our findings typically support the notion that risk and delay are psychologically equivalent and that the same psychological process underlies risk and intertemporal choice.

There is growing interest in modelling how people make choices that involve both risks and delays, i.e., risky inter-temporal choices. We investigated an untested assumption underlying several proposed risky inter-temporal choice models: that pure risky choices and pure inter-temporal choices are special cases of risky inter-temporal choice. We tested this assumption by presenting a single group of participants with risky choices and inter-temporal choices. We then compared the performance of a model that is fit to both choice types simultaneously, with the performance of separate models fit to the risky choice and inter-temporal choice data. We find, using Bayesian model comparison, that the majority of participants are best fit by a single model that incorporates both risky and inter-temporal choices. This result supports the assumption that risky choices and inter-temporal choices may be special cases of risky inter-temporal choice. Our results also suggest that, under the conditions of our experiment, interpretation of monetary value is very similar in risky choices and inter-temporal choices.

Research on decision making under uncertainty has been strongly influenced by the documentation of numerous expected utility (EU) anomalies--behaviors that violate the expected utility axioms. The relative lack of progress on the closely related topic of intertemporal choice is partly due to the absence of an analogous set of discounted utility (DU) anomalies. We enumerate a set of DU anomalies analogous to the EU anomalies and propose a model that accounts for the anomalies, as well as other intertemporal choice phenomena incompatible with DU. We discuss implications for savings behavior, estimation of discount rates, and choice framing effects.

61Reply to Robert (2016) The expected demise of the Bayes factor.61Reply to Chandramouli and Shiffrin (2016) Extending Bayesian induction.61Further elaboration on Jeffreys’s Bayes factors.

61The Bayes factor follows logically from Jeffreys’s philosophy of model selection.61The ideas are illustrated with two examples: the Bayesian t-test and correlation test.61The Bayes factors are adapted to one-sided tests.61The Bayes factors are illustrated with various applications in psychological research.

Abstract [3] experiments showed that an adjusting procedure can provide useful information about choice between reinforcers, especially when delayed reinforcers are involved pigeon (PsycINFO Database Record (c) 2012 APA, all rights reserved)

Subjects learned and recognized patterns which were marginally visible, requiring them to fixate directly each feature to which they wished to attend. Fixed "scanpaths," specific to subject and pattern, appeared in their saccadic eye movements, both intermittently during learning and in initial eye movements during recognition. A proposed theory of pattern perception explains these results.

People prefer to receive good outcomes immediately rather than wait, and they must be compensated for waiting. But what influences their decision about how much compensation is required for a given wait? To give a partial answer to this question, we develop the DRIFT model, a heuristic description of how framing influences intertemporal choice. We describe 4 experiments showing the implications of this model. In the experiments, we vary how the difference between a smaller sooner outcome and a larger later outcome is framed-either as total interest earned, as an interest rate, or as total amount earned (the conventional frame in studies of intertemporal choice)-and whether the larger later outcome is described as resulting from the investment of the smaller sooner one. These alternate frames have several effects. First, the investment language increases patience. Second, the explicit provision of the (otherwise implicit) experimental interest rate sharply reduces the magnitude effect. Correspondingly, we find that interest frames increase patience when the rewards are small, but they decrease patience when they are large. Third, the interest-rate frame induces somewhat greater discounting for longer time periods and, thus, reverses the common finding of "hyperbolic" discounting. Thus, many of the "stylized facts" implied by studies involving choices between a smaller sooner and a larger later amount are eliminated or reverse under alternate outcome frames.

People often make decisions with consequences that unfold over time. When facing such intertemporal choices, people use different search strategies. We examine how these search strategies differ and how they relate to patience in intertemporal choice. We demonstrate that search varies substantially across individuals and identify two main search strategies omparative or integrative search. Importantly, comparative search correlates with greater patience and higher susceptibility to contextual influences on choice. We manipulated search using an unobtrusive technique, revealing a causal relationship between strategy and choice. Comparative searchers make more patient choices and exhibit larger framing effects than integrative searchers. An understanding of how differences in psychological processes change discounting can inform the design of behavioral interventions to improve consumer welfare. Intertemporal choice impacts many important outcomes, such as decisions about health, education, wealth, and the environment. However, the psychological processes underlying decisions involving outcomes at different points in time remain unclear, limiting opportunities to intervene and improve people patience. This research examines information-search strategies used during intertemporal choice and their impact on decisions. In experiment 1, we demonstrate that search strategies vary substantially across individuals. We subsequently identify two distinct search strategies across individuals. Comparative searchers, who compare features across options, discount future options less and are more susceptible to acceleration versus delay framing than integrative searchers, who integrate the features of an option. Experiment 2 manipulates search using an unobtrusive method to establish a causal relationship between strategy and choice, randomly assigning participants to conditions promoting either comparative or integrative search. Again, comparative search promotes greater patience than integrative search. Additionally, when participants adopt a comparative search strategy, they also exhibit greater effects of acceleration versus delay framing. Although most participants reported that the manipulation did not change their behavior, promoting comparative search decreased discounting of future rewards substantially and speeded patient choices. These findings highlight the central role that heterogeneity in psychological processes plays in shaping intertemporal choice. Importantly, these results indicate that theories that ignore variability in search strategies may be inadvertently aggregating over different subpopulations that use very different processes. The findings also inform interventions in choice architecture to increase patience and improve consumer welfare.

Progress in science often comes from discovering invariances in relationships among variables; these invariances often correspond to null hypotheses. As is commonly known, it is not possible to state evidence for the null hypothesis in conventional significance testing. Here we highlight a Bayes factor alternative to the conventional t test that will allow researchers to express preference for either the null hypothesis or the alternative. The Bayes factor has a natural and straightforward interpretation, is based on reasonable assumptions, and has better properties than other methods of inference that have been advocated in the psychological literature. To facilitate use of the Bayes factor, we provide an easy-to-use, Web-based program that performs the necessary calculations.

No abstract is available for this item.

To be useful, cognitive models with fitted parameters should show generalizability across time and allow accurate predictions of future observations. It has been proposed that hierarchical procedures yield better estimates of model parameters than do nonhierarchical, independent approaches, because the formers’ estimates for individuals within a group can mutually inform each other. Here, we examine Bayesian hierarchical approaches to evaluating model generalizability in the context of two prominent models of risky choice—cumulative prospect theory (Tversky & Kahneman, 1992 ) and the transfer-of-attention-exchange model (Birnbaum & Chavez, 1997 ). Using empirical data of risky choices collected for each individual at two time points, we compared the use of hierarchical versus independent, nonhierarchical Bayesian estimation techniques to assess two aspects of model generalizability: parameter stability (across time) and predictive accuracy. The relative performance of hierarchical versus independent estimation varied across the different measures of generalizability. The hierarchical approach improved parameter stability (in terms of a lower absolute discrepancy of parameter values across time) and predictive accuracy (in terms of deviance; i.e., likelihood). With respect to test–retest correlations and posterior predictive accuracy, however, the hierarchical approach did not outperform the independent approach. Further analyses suggested that this was due to strong correlations between some parameters within both models. Such intercorrelations make it difficult to identify and interpret single parameters and can induce high degrees of shrinkage in hierarchical models. Similar findings may also occur in the context of other cognitive models of choice.

Decision research has experienced a shift from simple algebraic theories of choice to an appreciation of mental processes underlying choice. A variety of process-tracing methods has helped researchers test these process explanations. Here, we provide a survey of these methods, including specific examples for subject reports, movement-based measures, peripheral psychophysiology, and neural techniques. We show how these methods can inform phenomena as varied as attention, emotion, strategy use, and understanding neural correlates. Two important future developments are identified: broadening the number of explicit tests of proposed processes through formal modeling and determining standards and best practices for data collection.

The challenge in inferring cognitive processes from observational data is to correctly matrix overt behavior with its covert cognitive process. To improve our understanding of the overt-covert mapping in the domain of decision making, we collected eye-movement data during decisions between gamble-problems. Participants were either free to choose or instructed to use a specific choice strategy (maximizing expected value or a choice heuristic). We found large differences in looking patterns between free and instructed choices. Looking patterns provided no support for the common assumption that attention is equally distributed between outcomes and probabilities, even when participants were instructed to maximize expected value. Eye-movement data are to some extent ambiguous with respect to underlying cognitive processes. Copyright (c) 2017 John Wiley & Sons, Ltd.

Abstract It is commonly assumed that people make intertemporal choices by "discounting" the value of delayed outcomes, assigning discounted values independently to all options, and comparing the discounted values. We identify a class of anomalies to this assumption of alternative-based discounting, which collectively shows that options are not treated independently but rather comparatively: The time difference, or interval, between the options sometimes counts more and sometimes counts less if it is taken as a whole than if it is divided into shorter subintervals (superadditivity and subadditivity, respectively), and whether the interval counts more or less depends on the money difference, or compensation, involved (inseparability). We develop a model that replaces alternative-based discounting with attribute-based tradeoffs. In our model, people make intertemporal choices by weighing how much more they will receive or pay if they wait longer against how much longer the wait will be, or, conversely, how much less they will receive or pay if they do not wait longer against how much shorter the wait will be. This model, called the tradeoff model, accommodates, in a psychologically plausible way, all anomalies that the discounting approach can and cannot address. (c) 2010 APA, all rights reserved.

We asked participants to make simple risky choices while we recorded their eye movements. We built a complete statistical model of the eye movements and found very little systematic variation in eye movements over the time course of a choice or across the different choices. The only exceptions were finding more (of the same) eye movements when choice options were similar, and an emerging gaze bias in which people looked more at the gamble they ultimately chose. These findings are inconsistent with prospect theory, the priority heuristic, or decision field theory. However, the eye movements made during a choice have a large relationship with the final choice, and this is mostly independent from the contribution of the actual attribute values in the choice options. That is, eye movements tell us not just about the processing of attribute values but also are independently associated with choice. The pattern is simple—people choose the gamble they look at more often, independently of the actual numbers they see—and this pattern is simpler than predicted by decision field theory, decision by sampling, and the parallel constraint satisfaction model. 08 2015 The Authors.Journal of Behavioral Decision Makingpublished by John Wiley & Sons Ltd.

The debate about whether making a risky choice is based on a weighting and adding process has a long history and is still unresolved. To address this long-standing controversy, we developed a comparative paradigm. Participants' eye movements in 2 risky choice tasks that required participants to choose between risky options in single-play and multiple-play conditions were separately compared with those in a baseline task in which participants naturally performed a deliberate calculation following a weighting and adding process. The results showed that, when participants performed the multiple-play risky choice task, their eye movements were similar to those in the baseline task, suggesting that participants may use a weighting and adding process to make risky choices in multiple-play conditions. In contrast, participants' eye movements were different in the single-play risky choice task versus the baseline task, suggesting that participants were not likely to use a weighting and adding process to make risky choices in single-play conditions and were more likely to use a heuristic process. We concluded that an expectation-based index for predicting risk preferences is applicable in multiple-play conditions but not in single-play conditions, implying the need to improve current theories that postulate the use of a heuristic process.

Leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC) are methods for estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model using the log-likelihood evaluated at the posterior simulations of the parameter values. LOO and WAIC have various advantages over simpler estimates of predictive error such as AIC and DIC but are less used in practice because they involve additional computational steps. Here we lay out fast and stable computations for LOO and WAIC that can be performed using existing simulation draws. We compute LOO using Pareto smoothed importance sampling (PSIS), a new procedure for regularizing importance weights. As a byproduct of our calculations, we also obtain approximate standard errors for estimated predictive errors and for comparing of predictive errors between two models. We implement the computations in an R package called 'loo' and demonstrate using models fit with the Bayesian inference package Stan.

A state-of-the-art data analysis procedure is presented to conduct hierarchical Bayesian inference and hypothesis testing on delay discounting data. The delay discounting task is a key experimental paradigm used across a wide range of disciplines from economics, cognitive science, and neuroscience, all of which seek to understand how humans or animals trade off the immediacy verses the magnitude of a reward. Bayesian estimation allows rich inferences to be drawn, along with measures of confidence, based upon limited and noisy behavioural data. Hierarchical modelling allows more precise inferences to be made, thus using sometimes expensive or difficult to obtain data in the most efficient way. The proposed probabilistic generative model describes how participants compare the present subjective value of reward choices on a trial-to-trial basis, estimates participant- and group-level parameters. We infer discount rate as a function of reward size, allowing the magnitude effect to be measured. Demonstrations are provided to show how this analysis approach can aid hypothesis testing. The analysis is demonstrated on data from the popular 27-item monetary choice questionnaire (Kirby, Psychonomic Bulletin & Review, 16 (3), 457 462 2009 ), but will accept data from a range of protocols, including adaptive procedures. The software is made freely available to researchers.

Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t -test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP ( http://www.jasp-stats.org ), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder 檚 BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.

Bayesian parameter estimation and Bayesian hypothesis testing present attractive alternatives to classical inference using confidence intervals and p values. In part I of this series we outline ten prominent advantages of the Bayesian approach. Many of these advantages translate to concrete opportunities for pragmatic researchers. For instance, Bayesian hypothesis testing allows researchers to quantify evidence and monitor its progression as data come in, without needing to know the intention with which the data were collected. We end by countering several objections to Bayesian hypothesis testing. Part II of this series discusses JASP, a free and open source software program that makes it easy to conduct Bayesian estimation and testing for a range of popular statistical scenarios (Wagenmakers et al. this issue ).

基于信息加工过程视角,本研究采用眼动技术检验风险决策整合模型和占优启发式模型。结果表明,自主决策任务条件下决策过程反应时及信息搜索模式均不同于期望价值(EV)迫选任务条件下的决策过程反应时及信息搜索模式;自主决策任务条件下决策过程反应时并未随着选项间整体值(CPT值)差值的变大而变快,且基于特征(attribute-based)的信息搜索多于基于选项(option-based)的信息搜索,不符合整合模型预期。此外,决策者亦未按照占优启发式模型所假定的决策步骤进行决策。基于信息加工过程的检验结果既不利于以累积预期理论为代表的整合模型,亦不利于占优启发式模型。文章建议从决策过程视角检验已有决策模型及建立新的启发式决策过程模型(processmodel)。

No abstract is available for this item.

Many important decisions involve outcomes that are either probabilistic or delayed. Based on similarities in decision preferences, models of decision making have postulated that the same psychological processes may underlie decisions involving probabilities (i.e., risky choice) and decisions involving delay (i.e., intertemporal choice). Equivocal behavioral evidence has made this hypothesis difficult to evaluate. However, a combination of functional neuroimaging and behavioral data may allow identification of differences between these forms of decision making. Here, we used functional magnetic resonance imaging (fMRI) to examine brain activation in subjects making a series of choices between pairs of real monetary rewards that differed either in their relative risk or their relative delay. While both sorts of choices evoked activation in brain systems previously implicated in executive control, we observed clear distinctions between these forms of decision making. Notably, choices involving risk evoked greater activation in posterior parietal and lateral prefrontal cortices, whereas choices involving delay evoked greater activation in the posterior cingulate cortex and the striatum. Moreover, activation of regions associated with reward evaluation predicted choices of a more-risky option, whereas activation of control regions predicted choices of more-delayed or less-risky options. These results indicate that there are differences in the patterns of brain activation evoked by risky and intertemporal choices, suggesting that the two domains utilize at least partially distinct sets of cognitive processes.

利用过程追踪技术实现对“决策过程”的追踪，或能真正解答“人类是如何做出决策”这一科学问题。在各种过程追踪技术中，眼动技术由于具有无干扰性、适用范围广泛、采集信息多样等独一无二的优势，已被广泛应用于各种决策研究中，为验证和比较不同决策理论的不同假设和预测做出了贡献。本文介绍了眼动技术如何被应用于验证补偿性决策理论与非补偿性决策理论对风险决策过程的不同假设，眼动技术如何用于检验多次决策与单次决策的决策过程差异，以及眼动技术如何用于检验“剔除-关注模型”与“齐当别决策模型”对多属性决策中共享信息发挥作用机制的不同预测。

近年来，心理学研究者逐渐认识到假设检验这一推论统计方法在理论与实践中的不足。在心理学研究面对日益严重的“可重复危机”、急需更优良的验证手段时，贝叶斯因子分析在众多统计方法中脱颖而出。相比传统的假设检验方法，贝叶斯因子具有诸多优势，能够揭示备择假设与虚无假设发生概率的高低，因此心理学界也出现了以贝叶斯因子分析取代传统假设检验的呼声。本文列举了贝叶斯因子相对于假设检验的主要优势，并重点介绍了贝叶斯因子在常规心理学研究中的计算方法及应用，同时说明了运用贝叶斯因子进行统计分析时需注意的问题。

Economic decision-making consists of two traditional problems: Intertemporal choices and Decision-making under risk and uncertainty. Intertemporal choice is divided into impulsivity and self-control. Paralimbic cortex, are preferentially activated by decisions involving impulsivity, including nucleus accumbens, orbitofrontal cortex in the central and middle prefrontal cortex; and regions of the lateral prefrontal cortex and posterior parietal cortex show enhanced changes in activity by self-controlled decisions. Cerebral cortex and amygdala are associated with the deciong-making under risk and uncertainty.

Gain-loss asymmetry in temporal discounting (i.e., when individuals discount gains more than losses) has been implicated in numerous problematic and addictive behaviors, resulting in enormous personal and societal costs. On the basis of findings from a previous study, we speculated that approach-avoidance motivation would modulate gain-loss asymmetry. To test this speculation, we examined the effects of motivation on gain-loss asymmetry by analyzing functional connectivity. We found that approach and avoidance motivation were negatively associated with functional connectivity between the medial orbitofrontal cortex (MOFC) and the dorsolateral prefrontal cortex and functional connectivity between the MOFC and the posterior parietal cortex (PPC) in the gain domain. Only avoidance motivation was found to be positively associated with functional connectivity between the medial prefrontal cortex (MPFC) and the posterior cingulate cortex (PCC) as well as between the MPFC and the insula in the loss domain. Our findings suggest that the relationships of approach-avoidance motivation and neural correlates yielded an asymmetrical pattern between the gain and loss domains in temporal discounting. Thus, we provide new insight into understanding gain-loss asymmetry in temporal discounting.

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