A martingale analysis of first passage times of time-dependent Wiener diffusion models

Randomness accelerates the dynamic clearing process of the COVID-19 outbreaks in China

During the implementation of strong non-pharmaceutical interventions (NPIs), more than one hundred COVID-19 outbreaks induced by different strains in China were dynamically cleared in about 40 days, which presented the characteristics of small scale clustered outbreaks with low peak levels. To address how did randomness affect the dynamic clearing process, we derived an iterative stochastic difference equation for the number of newly reported cases based on the classical stochastic SIR model and calculate the stochastic control reproduction number (SCRN). Further, by employing the Bayesian technique, the change points of SCRNs have been estimated, which is an important prerequisite for determining the lengths of the exponential growth and decline phases. To reveal the influence of randomness on the dynamic zeroing process, we calculated the explicit expression of the mean first passage time (MFPT) during the decreasing phase using the relevant theory of first passage time (FPT), and the main results indicate that random noise can accelerate the dynamic zeroing process. This demonstrates that powerful NPI measures can rapidly reduce the number of infected people during the exponential decline phase, and enhanced randomness is conducive to dynamic zeroing, i.e. the greater the random noise, the shorter the average clearing time is. To confirm this, we chose 26 COVID-19 outbreaks in various provinces in China and fitted the data by estimating the parameters and change points. We then calculated the MFPTs, which were consistent with the actual duration of dynamic zeroing interventions.

Associative memory retrieval modulates upcoming perceptual decisions

Expectations can inform fast, accurate decisions. But what informs expectations? Here we test the hypothesis that expectations are set by dynamic inference from memory. Participants performed a cue-guided perceptual decision task with independently-varying memory and sensory evidence. Cues established expectations by reminding participants of past stimulus-stimulus pairings, which predicted the likely target in a subsequent noisy image stream. Participant's responses used both memory and sensory information, in accordance to their relative reliability. Formal model comparison showed that the sensory inference was best explained when its parameters were set dynamically at each trial by evidence sampled from memory. Supporting this model, neural pattern analysis revealed that responses to the probe were modulated by the specific content and fidelity of memory reinstatement that occurred before the probe appeared. Together, these results suggest that perceptual decisions arise from the continuous sampling of memory and sensory evidence.

Asynchrony rescues statistically optimal group decisions from information cascades through emergent leaders

It is usually assumed that information cascades are most likely to occur when an early but incorrect opinion spreads through the group. Here, we analyse models of confidence-sharing in groups and reveal the opposite result: simple but plausible models of naive-Bayesian decision-making exhibit information cascades when group decisions are synchronous; however, when group decisions are asynchronous, the early decisions reached by Bayesian decision-makers tend to be correct and dominate the group consensus dynamics. Thus early decisions actually rescue the group from making errors, rather than contribute to it. We explore the likely realism of our assumed decision-making rule with reference to the evolution of mechanisms for aggregating social information, and known psychological and neuroscientific mechanisms.

Mixing memory and desire: How memory reactivation supports deliberative decision-making

Memories affect nearly every aspect of our mental life. They allow us to both resolve uncertainty in the present and to construct plans for the future. Recently, renewed interest in the role memory plays in adaptive behavior has led to new theoretical advances and empirical observations. We review key findings, with particular emphasis on how the retrieval of many kinds of memories affects deliberative action selection. These results are interpreted in a sequential inference framework, in which reinstatements from memory serve as "samples" of potential action outcomes. The resulting model suggests a central role for the dynamics of memory reactivation in determining the influence of different kinds of memory in decisions. We propose that representation-specific dynamics can implement a bottom-up "product of experts" rule that integrates multiple sets of action-outcome predictions weighted based on their uncertainty. We close by reviewing related findings and identifying areas for further research. This article is categorized under: Psychology > Reasoning and Decision Making Neuroscience > Cognition Neuroscience > Computation.

A flexible framework for simulating and fitting generalized drift-diffusion models

The drift-diffusion model (DDM) is an important decision-making model in cognitive neuroscience. However, innovations in model form have been limited by methodological challenges. Here, we introduce the generalized drift-diffusion model (GDDM) framework for building and fitting DDM extensions, and provide a software package which implements the framework. The GDDM framework augments traditional DDM parameters through arbitrary user-defined functions. Models are solved numerically by directly solving the Fokker-Planck equation using efficient numerical methods, yielding a 100-fold or greater speedup over standard methodology. This speed allows GDDMs to be fit to data using maximum likelihood on the full response time (RT) distribution. We demonstrate fitting of GDDMs within our framework to both animal and human datasets from perceptual decision-making tasks, with better accuracy and fewer parameters than several DDMs implemented using the latest methodology, to test hypothesized decision-making mechanisms. Overall, our framework will allow for decision-making model innovation and novel experimental designs.

Audiovisual detection at different intensities and delays

In the redundant signals task, two target stimuli are associated with the same response. If both targets are presented together, redundancy gains are observed, as compared with single-target presentation. Different models explain these redundancy gains, including race and coactivation models (e.g., the Wiener diffusion superposition model, Schwarz, 1994, Journal of Mathematical Psychology, and the Ornstein Uhlenbeck diffusion superposition model, Diederich, 1995, Journal of Mathematical Psychology). In the present study, two monkeys performed a simple detection task with auditory, visual and audiovisual stimuli of different intensities and onset asynchronies. In its basic form, a Wiener diffusion superposition model provided only a poor description of the observed data, especially of the detection rate (i.e., accuracy or hit rate) for low stimulus intensity. We expanded the model in two ways, by (A) adding a temporal deadline, that is, restricting the evidence accumulation process to a stopping time, and (B) adding a second "nogo" barrier representing target absence. We present closed-form solutions for the mean absorption times and absorption probabilities for a Wiener diffusion process with a drift towards a single barrier in the presence of a temporal deadline (A), and numerically improved solutions for the two-barrier model (B). The best description of the data was obtained from the deadline model and substantially outperformed the two-barrier approach.

Amount and time exert independent influences on intertemporal choice

Intertemporal choices involve trade-offs between the value of rewards and the delay before those rewards are experienced. Canonical intertemporal choice models such as hyperbolic discounting assume that reward amount and time until delivery are integrated within each option prior to comparison1,2. An alternative view posits that intertemporal choice reflects attribute-wise processes in which amount and time attributes are compared separately3-6. Here, we use multi-attribute drift diffusion modelling (DDM) to show that attribute-wise comparison represents the choice process better than option-wise comparison for intertemporal choice in a young adult population. We find that, while accumulation rates for amount and time information are uncorrelated, the difference between those rates predicts individual differences in patience. Moreover, patient individuals incorporate amount earlier than time into the decision process. Using eye tracking, we link these modelling results to attention, showing that patience results from a rapid, attribute-wise process that prioritizes amount over time information. Thus, we find converging evidence that distinct evaluation processes for amount and time determine intertemporal financial choices. Because intertemporal decisions in the lab have been linked to failures of patience ranging from insufficient saving to addiction7-13, understanding individual differences in the choice process is important for developing more effective interventions.

Information Processing: The Language and Analytical Tools for Cognitive Psychology in the Information Age

The information age can be dated to the work of Norbert Wiener and Claude Shannon in the 1940s. Their work on cybernetics and information theory, and many subsequent developments, had a profound influence on reshaping the field of psychology from what it was prior to the 1950s. Contemporaneously, advances also occurred in experimental design and inferential statistical testing stemming from the work of Ronald Fisher, Jerzy Neyman, and Egon Pearson. These interdisciplinary advances from outside of psychology provided the conceptual and methodological tools for what is often called the cognitive revolution but is more accurately described as the information-processing revolution. Cybernetics set the stage with the idea that everything ranging from neurophysiological mechanisms to societal activities can be modeled as structured control systems with feedforward and feedback loops. Information theory offered a way to quantify entropy and information, and promoted theorizing in terms of information flow. Statistical theory provided means for making scientific inferences from the results of controlled experiments and for conceptualizing human decision making. With those three pillars, a cognitive psychology adapted to the information age evolved. The growth of technology in the information age has resulted in human lives being increasingly interweaved with the cyber environment, making cognitive psychology an essential part of interdisciplinary research on such interweaving. Continued engagement in interdisciplinary research at the forefront of technology development provides a chance for psychologists not only to refine their theories but also to play a major role in the advent of a new age of science.