Hierarchical Bayesian parameter estimation for cumulative prospect theory

Nilsson, Håkan; Rieskamp, Jörg; Wagenmakers, Eric‐Jan

doi:10.1016/j.jmp.2010.08.006

Cited by 185 publications

(187 citation statements)

References 58 publications

(70 reference statements)

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“…In a second step, these independent estimates can then be aggregated across participants to make inferences about the population from which the individuals were drawn (Gelman & Hill, 2007). As an alternative to this "independence" approach, hierarchical Bayesian procedures have recently grown in popularity (e.g., Gelman & Hill, 2007;Lee & Wagenmakers, 2013;Lee & Webb, 2005;Nilsson, Rieskamp, & Wagenmakers, 2011;Scheibehenne, Rieskamp, & Wagenmakers, 2013). A key characteristic of hierarchical procedures is that they exploit group-level distributions to inform individual-level estimations.…”

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confidence: 99%

Using Bayesian hierarchical parameter estimation to assess the generalizability of cognitive models of choice

2014

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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 choicecumulative 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.

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Using Bayesian hierarchical parameter estimation to assess the generalizability of cognitive models of choice

2014

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“…An empirical study of Guo's model is beyond the aim of the present paper. However, we refer the interested reader to papers that have estimated similar models, finding values of λ either in the range of 1.4-5 (see Table 1 in Abdellaoui et al (2007)) or slightly above 1 Murphy and ten Brincke (2018); Nilsson et al (2011). For a careful and critical review, see, e.g., Harrison and Swarthout (2016).…”

Section: Proportional Insurancementioning

confidence: 99%

Risk Aversion, Loss Aversion, and the Demand for Insurance

Eeckhoudt

Fiori

Gianin

2018

Risks

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Abstract:In this paper we analyze insurance demand when the utility function depends both upon final wealth and the level of losses or gains relative to a reference point. Besides some comparative statics results, we discuss the links with first-order risk aversion, with the Omega measure, and with a tendency to over-insure modest risks that has been been extensively documented in real insurance markets.

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“…Often this process can be completely automated with recognized mathematical packages or through accepted machine learning algorithms (Azaria, Rabinovich, Kraus, Goldman, & Tsimhoni, 2012;Ratcliff & Smith, 2004;Nilsson, Rieskamp, & Wagenmakers, 2011). For example, within computer science Azaria et.…”

Section: Introductionmentioning

confidence: 99%

“…Within psychology and behaviorial economics, Ratcliff and Smith used the Simplex algorithm to fit parameters within a 2-choice decision model (Ratcliff & Smith, 2004) and Nilsson et. al contrasted how Bayesian and maximum likelihood approaches could be used to set parameters within prospect theory (Nilsson et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

“…However, these approaches (Azaria et al, 2012;Ratcliff & Smith, 2004;Nilsson et al, 2011) are not appropriate for domains that are simply too complex to understand which behavior model should be applied or how parameters within a given model can be tuned. These domains suffer from a phenomenon often known as the "curse of dimensionality" (Evangelista, Embrechts, & Szymanski, 2006;Bengio, Delalleau, & Roux, 2005).…”

Section: Introductionmentioning

confidence: 99%

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Combining psychological models with machine learning to better predict people’s decisions

et al. 2012

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Creating agents that proficiently interact with people is critical for many applications. Towards creating these agents, models are needed that effectively predict people's decisions in a variety of problems. To date, two approaches have been suggested to generally describe people's decision behavior. One approach creates a-priori predictions about people's behavior, either based on theoretical rational behavior or based on psychological models, including bounded rationality. A second type of approach focuses on creating models based exclusively on observations of people's behavior. At the forefront of these types of methods are various machine learning algorithms. This paper explores how these two approaches can be compared and combined in different types of domains. In relatively simple domains, both psychological models and machine learning yield clear prediction models with nearly identical results. In more complex domains, the exact action predicted by psychological models is not even clear, and machine learning models are even less accurate. Nonetheless, we present a novel approach of creating hybrid methods that incorporate features from psychological models in conjunction with machine learning in order to create significantly improved models for predicting people's decisions. To demonstrate these claims, we present an overview of previous and new results, taken from representative domains ranging from a relatively simple optimization problem and complex domains such as negotiation and coordination without communication.

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Hierarchical Bayesian parameter estimation for cumulative prospect theory

Cited by 185 publications

References 58 publications

Using Bayesian hierarchical parameter estimation to assess the generalizability of cognitive models of choice

Using Bayesian hierarchical parameter estimation to assess the generalizability of cognitive models of choice

Risk Aversion, Loss Aversion, and the Demand for Insurance

Combining psychological models with machine learning to better predict people’s decisions

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