Dynamic Stochastic Models for Decision Making under Time Constraints

Diederich, Adele

doi:10.1006/jmps.1997.1167

Cited by 220 publications

(218 citation statements)

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“…Models based on these three plausible assumptions have been used to model choices and decision times in sensory detection (Smith, 1995), perceptual discrimination (Link & Heath, 1975;Ratcliff & Rouder, 1998), memory recognition (Ratcliff, 1978), categorization (Ashby, 2000;Nosofsky & Palmeri, 1997), risky decision making (Busemeyer & Townsend, 1993;J. G. Johnson & Busemeyer, 2005), multiattribute, multialternative decisions (Diederich, 1997;Roe, Busemeyer, & Townsend, 2001), as well as other types of response tasks like the go/no-go task (Gomez, Perea, & Ratcliff, 2007). Often, though, an alternative measure of cognitive performance in the form of confidence is collected.…”

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Two-stage dynamic signal detection: A theory of choice, decision time, and confidence.

Pleskac¹,

Busemeyer²

2010

Psychological Review

638

947

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The 3 most often-used performance measures in the cognitive and decision sciences are choice, response or decision time, and confidence. We develop a random walk/diffusion theory-2-stage dynamic signal detection (2DSD) theory-that accounts for all 3 measures using a common underlying process. The model uses a drift diffusion process to account for choice and decision time. To estimate confidence, we assume that evidence continues to accumulate after the choice. Judges then interrupt the process to categorize the accumulated evidence into a confidence rating. The model explains all known interrelationships between the 3 indices of performance. Furthermore, the model also accounts for the distributions of each variable in both a perceptual and general knowledge task. The dynamic nature of the model also reveals the moderating effects of time pressure on the accuracy of choice and confidence. Finally, the model specifies the optimal solution for giving the fastest choice and confidence rating for a given level of choice and confidence accuracy. Judges are found to act in a manner consistent with the optimal solution when making confidence judgments.

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confidence: 99%

Two-stage dynamic signal detection: A theory of choice, decision time, and confidence.

Pleskac¹,

Busemeyer²

2010

Psychological Review

638

947

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“…This situation contrasts sharply with what one finds in the literature on simple choice, where a number of detailed process models have been proposed. Although important differences exist, current models of simple choice converge on a common evidence-integration paradigm (1)(2)(3)(4)(5)(24)(25)(26). Here, each choice option is associated with a specific utility, but this quantity can only be accessed through a noisy sampling Significance Recent behavioral research has made rapid progress toward revealing the processes by which we make choices based on judgments of subjective value.…”

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Evidence integration in model-based tree search

Solway

Botvinick

2015

Proc. Natl. Acad. Sci. U.S.A.

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Research on the dynamics of reward-based, goal-directed decision making has largely focused on simple choice, where participants decide among a set of unitary, mutually exclusive options. Recent work suggests that the deliberation process underlying simple choice can be understood in terms of evidence integration: Noisy evidence in favor of each option accrues over time, until the evidence in favor of one option is significantly greater than the rest. However, real-life decisions often involve not one, but several steps of action, requiring a consideration of cumulative rewards and a sensitivity to recursive decision structure. We present results from two experiments that leveraged techniques previously applied to simple choice to shed light on the deliberation process underlying multistep choice. We interpret the results from these experiments in terms of a new computational model, which extends the evidence accumulation perspective to multiple steps of action.reward-based decision making | drift-diffusion model | reinforcement learning I magine a customer standing at the counter in an ice cream shop, deliberating among the available flavors. Such a scenario exemplifies "simple choice," a decision situation in which the objective is to select among a set of individual, immediate outcomes, each carrying a different reward. Simple choice, in this sense, has provided a convenient focus for a great deal of work in behavioral economics and decision neuroscience (1-5). However, it would be an obvious mistake to treat it as an exhaustive model of rewardbased decision making. The decisions that arise in everyday life are of course often more complicated. One important difference, among others, is that everyday decisions tend to involve sequences of actions and outcomes.As an illustration, let us return to the ice cream customer, picturing him at a point slightly earlier in the day, exiting his home in quest of something sweet. Upon reaching the sidewalk, he faces a decision between heading left toward the ice cream shop, or heading right toward a frozen yogurt shop. If he wishes to fully evaluate the relative appeal of these two options, he must answer a second set of questions: Which flavor would he choose in each shop? Furthermore, it may be relevant for him to consider more immediate consequences of the left-right decision. For example, the leftward path might pass by a bank, allowing him to deposit a check along his way, whereas the rightward path might lead by the post office, giving him the opportunity to mail a package.Rather than selecting among individual and immediate outcomes, the decision maker in this scenario finds himself at the root of a decision tree (Fig. 1A), with nodes corresponding to value-laden outcomes or states, and edges corresponding to choiceinduced state transitions. Deciding among immediate actions, even at the first branch point, requires a consideration of all of the paths that unfold below. Decision making thus assumes the form of reward-based tree search (6-10).Note that decision makin...

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“…The accuracy of all methods depended critically on the size of the approximating time step. The large (∼10 ms) step sizes often used by psychological researchers resulted in large and systematic errors in evaluating RT distributions.Over the past 40 years, models of response time (RT) for simple decision making have become very successful at capturing the details of observed data (Audley & Pike, 1965;Brown & Heathcote, 2005;Busemeyer & Townsend, 1993;Diederich, 1997;Heath, 1981;LaBerge, 1962;Lacouture and Marley, 1991;Laming, 1966;Link & Heath, 1975;Ratcliff, 1978; Ratcliff & Smith, 2004, Appendix;Ratcliff, Van Zandt, & McKoon, 1999;Smith, 1995;Vickers, 1970;Vickers & Lee, 2000). More recently, the same models have also become quite successful at explaining decision making at a neural level (Carpenter & Reddi, 2001;Cook & Maunsell, 2002;Glimcher 2003;Gold & Shadlen, 2001;Ratcliff, Cherian & Seagraves, 2003;Reddi & Carpenter, 2000;Roitman & Shadlen, 2002;Sato, Murthy, Thompson & Schall, 2001;Sato & Schall, 2003;Shadlen, Britten, Newsome & Movshon, 1996;Wang, 2002).…”

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Evaluating methods for approximating stochastic differential equations

Brown

Ratcliff

Smith

2006

Journal of Mathematical Psychology

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Models of decision making and response time (RT) are often formulated using stochastic differential equations (SDEs). Researchers often investigate these models using a simple Monte Carlo method based on Euler's method for solving ordinary differential equations. The accuracy of Euler's method is investigated and compared to the performance of more complex simulation methods. The more complex methods for solving SDEs yielded no improvement in accuracy over the Euler method. However, the matrix method proposed by Diederich and Busemeyer (2003) yielded significant improvements. The accuracy of all methods depended critically on the size of the approximating time step. The large (∼10 ms) step sizes often used by psychological researchers resulted in large and systematic errors in evaluating RT distributions.Over the past 40 years, models of response time (RT) for simple decision making have become very successful at capturing the details of observed data (Audley & Pike, 1965;Brown & Heathcote, 2005;Busemeyer & Townsend, 1993;Diederich, 1997;Heath, 1981;LaBerge, 1962;Lacouture and Marley, 1991;Laming, 1966;Link & Heath, 1975;Ratcliff, 1978; Ratcliff & Smith, 2004, Appendix;Ratcliff, Van Zandt, & McKoon, 1999;Smith, 1995;Vickers, 1970;Vickers & Lee, 2000). More recently, the same models have also become quite successful at explaining decision making at a neural level (Carpenter & Reddi, 2001;Cook & Maunsell, 2002;Glimcher 2003;Gold & Shadlen, 2001;Ratcliff, Cherian & Seagraves, 2003;Reddi & Carpenter, 2000;Roitman & Shadlen, 2002;Sato, Murthy, Thompson & Schall, 2001;Sato & Schall, 2003;Shadlen, Britten, Newsome & Movshon, 1996;Wang, 2002). The most successful models of decision making in both cognitive and neural domains are the sequential sampling models. These models are based on the idea that noisy stimulus information is accumulated progressively over time until sufficient information for one of the response alternatives has been obtained. The predicted decision time in such models is obtained mathematically by solving a first-passage-time (FPT) problem, that is, the time taken for the accumulated information to reach a criterion and trigger a response. For some models, there exist explicit analytic methods or highly accurate numerical methods for solving the FPT problem (see Ratcliff & Smith, Appendix, for a survey). For other models, this problem may be complex or intractable. In such situations, researchers must resort to Monte Carlo simulation techniques to obtain predicted RT distributions and choice probabilities. We investigate the properties of such simulation techniques in this article.One of the best-known sequential sampling models, and one that has been applied to a wide range of experimental data, is the diffusion model of Ratcliff (1978;Ratcliff & Rouder, 1998). This model assumes that evidence accumulation begins at some initial value (z) and

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Dynamic Stochastic Models for Decision Making under Time Constraints

Cited by 220 publications

References 15 publications

Two-stage dynamic signal detection: A theory of choice, decision time, and confidence.

Two-stage dynamic signal detection: A theory of choice, decision time, and confidence.

Evidence integration in model-based tree search

Evaluating methods for approximating stochastic differential equations

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