Modeling across-trial variability in the Wald drift rate parameter

The millisecond component of the Jovian decameter emission has been studied at high resolution, in order to examine the short‐term behavior of the S‐burst drift rates and to define the drift rate spectrum at high frequencies. By using dynamic spectra having 300‐µs and 3.3‐kHz resolution and covering discrete frequency bands in the range 26–33 MHz, large systematic changes in the magnitude of the S‐burst drift rates are observed to take place on a time scale of seconds to minutes. It is noted that the drift rate variability is of sufficient magnitude to prevent reliable evaluation of the drift rate dependence on frequency, unless simultaneous or near‐simultaneous multifrequency measurements are made. In presenting such observations we fail to observe the predicted drift rate turnover in the spectrum, in spite of measurements made at frequencies within 0.6 to 4.4 MHz of the electron gyrofrequency at the Jovian foot of the Io flux tube. This result is interpreted in terms of an ionospheric electron source, rather than within the conventional theoretical framework of trapped particles initially accelerated at Io. Low‐resolution intensity‐time tracings reveal a characteristic organization of S bursts into groups, each of several seconds duration and consisting of tens to hundreds of bursts. Abrupt changes in mean drift rates from group to group suggest that some of the group structuring may be a source‐related rather than a scintillation‐related phenomenon. Finally, some evidence exists for systematic variations in the group‐to‐group mean drift rates, which may be due to predictiable temporal changes in the magnetic field gradient on the Io flux tube. These temporal changes are due to motion of the Io‐associated magnetic flux tube in the Jovian magnetosphere.

A single trial analysis of EEG in recognition memory: Tracking the neural correlates of memory strength

A circular analogue of the diffusion model adapted for continuous response tasks is applied to a continuous-outcome source memory task. In contrast to existing models of source retrieval that attribute all of the variability in responding to memory, the circular diffusion model decomposes noise into variability arising from memory and from decision processes. We compared three models: (1) a single diffusion process with trial-to-trial variability in drift rate, (2) a mixture of two diffusion processes, one with positive drift that does not vary from trial-to-trial, and a second zero-drift process that represents discrete guessing, and (3) a hybrid model that mixed positive and zero-drift processes with trial-to-trial variability in the positive drift process. Comparison of model fits to joint response error and response-time (RT) data suggest that a memory strength threshold under which no information is retrieved appears to underlie responding in a continuous-report source memory task. Additionally, we also conditioned participants' source responding on their confidence in an old/new recognition task, ruling out the possibility that participant guessing was only due to unrecognized items. Overall, our findings support an all-or-none or some-or none view of source memory retrieval and pose a challenge to continuous models of source memory.

The diffusion model (Ratcliff, 1978) takes into account the reaction time distributions of both correct and erroneous responses from binary decision tasks. This high degree of information usage allows the estimation of different parameters mapping cognitive components such as speed of information accumulation or decision bias. For three of the four main parameters (drift rate, starting point, and non-decision time) trial-to-trial variability is allowed. We investigated the influence of these variability parameters both drawing on simulation studies and on data from an empirical test-retest study using different optimization criteria and different trial numbers. Our results suggest that less complex models (fixing intertrial variabilities of the drift rate and the starting point at zero) can improve the estimation of the psychologically most interesting parameters (drift rate, threshold separation, starting point, and non-decision time).

A note on decomposition of sources of variability in perceptual decision-making

Linking the diffusion model and general recognition theory: Circular diffusion with bivariate-normally distributed drift rates

The flanker task is a widely used measure of cognitive control abilities. Drift-diffusion modeling of flanker task behavior can yield separable parameters of cognitive control-related subprocesses, but the parameters' psychometrics are not well-established. We examined the reliability and validity of four behavioral measures: (1) raw accuracy, (2) reaction time (RT) interference, (3) NIH Toolbox flanker score, and (4) two drift-diffusion model (DDM) parameters-drift rate and boundary separation-capturing evidence accumulation efficiency and speed-accuracy trade-off, respectively. Participants from two independent studies - one cross-sectional (N = 381) and one with three timepoints (N = 83) - completed the flanker task while electroencephalography data were collected. Across both studies, drift rate and boundary separation demonstrated comparable split-half and test-retest reliability to accuracy, RT interference, and NIH Toolbox flanker score, but better incremental convergent validity with psychophysiological measures (i.e., the error-related negativity; ERN) and neuropsychological measures of cognitive control than the other behavioral indices. Greater drift rate (i.e., faster and more accurate responses) to congruent and incongruent stimuli, and smaller boundary separation to incongruent stimuli were related to 1) larger ERN amplitudes (in both studies) and 2) faster and more accurate inhibition and set-shifting over and above raw accuracy, reaction time, and NIH Toolbox flanker scores (in Study 1). Computational models, such as DDM, can parse behavioral performance into subprocesses that exhibit comparable reliability to other scoring approaches, but more meaningful relationships with other measures of cognitive control. The application of these computational models may be applied to existing data and enhance the identification of cognitive control deficits in psychiatric disorders.

Accelerated degradation is a pivotal section for lithium cells for a long cycle life. Wiener process as an important part of stochastic process, plays a key role for the accelerated degradation analysis. In general, the basic Wiener process is modeled with the constant drift rate and diffusion parameter. That indicates the lithium-ion batteries have the same degradation process for the same stress and the complexity of the algorithm is reduced. However, due to the differences in production processes and materials, the individual variations exist. The general Wiener process ignores the individual variations. That leads to reduction of algorithm accuracy. To improve the algorithm accuracy, this paper proposes a Wiener model for the accelerated degradation analysis, considering individual variation. The accelerated model with individual variation is modeled. First, degradation model parameters for each sample are estimated separately. Then, the varieties in the estimation results of each sample parameters are analyzed. That provides the theoretical reference for the parameters of Wiener process. In addition, the coefficient of variation is used as a measure of drift rate and diffusion parameters. Meanwhile, combining with the Wiener process and accelerated model, parameters are optimized by the `maximum likelihood estimation (MLE). Finally, the proposed model is demonstrated for the effectiveness by a practical example.

Convertible bonds are crucial derivatives in quantitative finance. Their complex terms like automatic redemption and barrier prices, coupled with stocks’ dynamic pricing features, pose precise pricing challenges. Traditional analytical methods struggle to capture the interactions among multiple factors. Thus, this study develops a quantitative pricing framework for complex convertible bonds by integrating the geometric Brownian motion (GBM) model with Monte Carlo simulation. Using Tesla’s closing prices from January 6, 2020, to January 11, 2022, as the sample, this article estimated the GBM parameters (drift rate is 0.4428 and volatility is 1.2866) via log returns. Finally, this paper simulated 10,000 future one-year stock price paths and retained 4,895 valid paths after normal distribution filtering. Based on risk-neutral pricing theory, this paper priced a 13.25% p.a. USD Autocallable Barrier Reverse Convertible issued by Credit Suisse London Branch (face value USD 5,000). The theoretical price was USD 3,593.87, and repeated simulations show the price stabilizes above USD 3,500. Risk analysis reveals that 72.54% of valid paths indicate a stock price decline after one year, and 37.4% of valid paths trigger barrier clauses (consistent with 2022-2023 actual trends), validating the framework’s feasibility.

Evidence-accumulation models are a useful tool for investigating the cognitive processes that give rise to behavioural data patterns in reaction times (RTs) and error rates. In their simplest form, evidence-accumulation models include three parameters: The average rate of evidence accumulation over time (drift rate) and the amount of evidence that needs to be accumulated before a response becomes selected (boundary) both characterise the response-selection process; a third parameter summarises all processes before and after the response-selection process (non-decision time). Researchers often compute experimental effects as simple difference scores between two within-subject conditions and such difference scores can also be computed on model parameters. In the present paper, we report spurious correlations between such model parameter difference scores, both in empirical data and in computer simulations. The most pronounced spurious effect is a negative correlation between boundary difference and non-decision difference, which amounts to r = - .70 or larger. In the simulations, we only observed this spurious negative correlation when either (a) there was no true difference in model parameters between simulated experimental conditions, or (b) only drift rate was manipulated between simulated experimental conditions; when a true difference existed in boundary separation, non-decision time, or all three main parameters, the correlation disappeared. We suggest that care should be taken when using evidence-accumulation model difference scores for correlational approaches because the parameter difference scores can correlate in the absence of any true inter-individual differences at the population level.

Improving memory for studied items (targets) often helps participants reject nonstudied items (lures), a pattern referred to as the strength-based mirror effect (SBME). Criss (2010) demonstrated the SBME in diffusion model drift rates; that is, the target drift rate was higher and the lure drift rate was lower for lists of words studied 5 times versus lists of words studied once. She interpreted the drift rate effect for lures as evidence for the differentiation process, whereby strong memory traces produce a poorer match to lure items than do weak memory traces. However, she noted that strength may have also affected a model parameter called the drift criterion-a participant-controlled decision parameter that defines the zero point in drift rate. We directly contrasted the differentiation and drift-criterion accounts by manipulating list strength either at both encoding and retrieval (which produces a differentiation difference in the studied traces) or at retrieval only (which equates differentiation from the study list but provides the opportunity to change decision processes based on strength). Across 3 experiments, results showed that drift rates for lures were lower on strong tests than on weak tests, and this effect was observed even when strength was varied at retrieval alone. Therefore, results provided evidence that the SBME is produced by changes in decision processes, not by differentiation of memory traces.

Modeling reaction time data using diffusion models comes with the advantage of separating different processes involved in decision making. Each parameter of the diffusion model is assumed to translate into one (or more) process(es). If this assumption holds true, selective manipulations of specific processes involved in decision making should selectively influence the related parameter, but not any other parameter (high convergent and discriminant validities). We present two experiments (total N = 104) and one simulation study that-using a manipulation of the difficulty of encoding in a lexical decision task-tested the convergent validity of the nondecision time t₀. As hypothesized, we found large effects on t₀ in both experiments but also medium to large effects on the drift rate v as well as on the starting point z. Our simulation study suggests that the effects on the drift rate, but not on the starting point, might be explained by incorrect assumptions about the intertrial variability of the nondecision time. Our results speak in favor of a high convergent validity of t₀ but question the discriminant validities of v and z, at least under the assumption that our manipulation affected encoding selectively. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

Diffusion models of decision making, in which successive samples of noisy evidence are accumulated to decision criteria, provide a theoretical solution to von Neumann’s (1956) problem of how to increase the reliability of neural computation in the presence of noise. I introduce and evaluate a new neurally-inspired dual diffusion model, the linear drift, linear infinitesimal variance (LDLIV) model, which embodies three features often thought to characterize neural mechanisms of decision making. The accumulating evidence is intrinsically positively-valued, saturates at high intensities, and is accumulated for each alternative separately. I present explicit integral-equation predictions for the response time distribution and choice probabilities for the LDLIV model and compare its performance on two benchmark sets of data to three other models: the standard diffusion model and two dual diffusion model composed of racing Wiener processes, one between absorbing and reflecting boundaries and one with absorbing boundaries only. The LDLIV model and the standard diffusion model performed similarly to one another, although the standard diffusion model is more parsimonious, and both performed appreciably better than the other two dual diffusion models. I argue that accumulation of noisy evidence by a diffusion process and drift rate variability are both expressions of how the cognitive system solves von Neumann’s problem, by aggregating noisy representations over time and over elements of a neural population. I also argue that models that do not solve von Neumann’s problem do not address the main theoretical question that historically motivated research in this area.

The relationship between baseline EEG spectra power and memory performance in older African Americans endorsing cognitive concerns in a community setting

In conflict tasks like the Simon task, participants are instructed to respond to a task-relevant target dimension while ignoring additional distracting information. In the Simon task the distracting spatial information can be congruent or incongruent with the task-relevant target information, causing a congruency effect. As seen in the proportion congruency effect and the congruency sequence effect, this congruency effect is larger in mostly congruent blocks and following congruent trials, respectively. Common theories suggest that when the proportion of incongruent trials is high or after an incongruent trial, focus on the task-relevant target information is increased and distracting information is inhibited. In two experiments, we investigated how reward modulates these phenomena. Specifically, performance-contingent reward – but not non-contingent reward – increased the usage of the distracting information in mostly congruent blocks or following congruent trials, while the adaptation to incongruency (i.e., mostly incongruent blocks or preceding incongruent trials) was the same in all conditions. Additional diffusion model analyses found that this effect of performance-contingent reward was captured by the drift rate parameter. These results suggest an increased focus on the target information by incongruent trials independent from reward, while the adaptation to (mostly) congruent trials characterized by increased usage of distracting information can be motivationally boosted. That is, performance-contingent reward increases the use of congruent distracting information beyond a mere relaxation of the increased target-focus following (mostly) congruent trials.