Informative Prior Distributions Research Articles

Hierarchical Bayesian Small Area Estimation Using Weakly Informative Priors in Ecologically Homogeneous Areas of the Interior Western Forests

The U.S. Forest Inventory and Analysis Program (FIA) collects inventory data on and computes estimates for many forest attributes to monitor the status and trends of the nation's forests. Increasingly, FIA needs to produce estimates in small geographic and temporal regions. In this application, we implement area level hierarchical Bayesian (HB) small area estimators of several forest attributes for ecosubsections in the Interior West of the US. We use a remotely-sensed auxiliary variable, percent tree canopy cover, to predict response variables derived from ground-collected data such as basal area, biomass, tree count, and volume. We implement four area level HB estimators that borrow strength across ecological provinces and sections and consider prior information on the between-area variation of the response variables. We compare the performance of these HB estimators to the area level empirical best linear unbiased prediction (EBLUP) estimator and to the industry-standard post-stratified (PS) direct estimator. Results suggest that when borrowing strength to areas which are believed to be homogeneous (such as the ecosection level) and a weakly informative prior distribution is placed on the between-area variation parameter, we can reduce variance substantially compared the analogous EBLUP estimator and the PS estimator. Explorations of bias introduced with the HB estimators through comparison with the PS estimator indicates little to no addition of bias. These results illustrate the applicability and benefit of performing small area estimation of forest attributes in a HB framework, as they allow for more precise inference at the ecosubsection level.

Two-vehicle driver-injury severity: A multivariate random parameters logit approach

Two-vehicle crashes have been dominating all types of traffic accidents, wherein the vehicle drivers have been sustaining the highest risk of injury among all vehicle occupants. To understand the critical factors to the drivers’ injury severity of two-vehicle crashes, we employed the random parameters multinomial logit model as a data analyzing tool. To capture the unobserved heterogeneity and potential temporal instability, we combined two strategies: Bayesian random parameter logit and explicitly correlated outcomes. The random parameter logit models were validated with a nine-year large-scale dataset compiled by combining the Crash Report Sampling System (CRSS) and General Estimates Sampling (GES) databases. The results underscore the importance of explicit modeling of inter-outcome correlation, which captured the potential transition probability between adjacent levels of injury severity and improved the model’s predictability. Our model also highlighted substantial per-case and per-driver heterogeneity, which respectively explained 22.8% and 29.4% of the total variance (minor injury) and 25.4% and 24.9% of the variance (severe injury). We found that the female drivers, old (⩾65 years) drivers, unbuckled drivers, speeding drivers sustained a higher injury risk in their corresponding groups. Drivers in lighter and older vehicles suffer higher injury risks. Several other factors also considerably affect the injury severity outcomes, such as the road’s speed limit and variables that are proxies of traffic volume (intersection type, whether at the peak hours). Regarding Bayesian modeling, we observed that using weakly informative prior distribution has little effect on the parameter estimates. We also pointed to the directions to further improve the proposed modeling framework.

Deriving Priors for Bayesian Prediction of Daily Response Propensity in Responsive Survey Design: Historical Data Analysis Versus Literature Review.

Responsive survey design (RSD) aims to increase the efficiency of survey data collection via live monitoring of paradata and the introduction of protocol changes when survey errors and increased costs seem imminent. Daily predictions of response propensity for all active sampled cases are among the most important quantities for live monitoring of data collection outcomes, making sound predictions of these propensities essential for the success of RSD. Because it relies on real-time updates of prior beliefs about key design quantities, such as predicted response propensities, RSD stands to benefit from Bayesian approaches. However, empirical evidence of the merits of these approaches is lacking in the literature, and the derivation of informative prior distributions is required for these approaches to be effective. In this paper, we evaluate the ability of two approaches to deriving prior distributions for the coefficients defining daily response propensity models to improve predictions of daily response propensity in a real data collection employing RSD. The first approach involves analyses of historical data from the same survey, and the second approach involves literature review. We find that Bayesian methods based on these two approaches result in higher-quality predictions of response propensity than more standard approaches ignoring prior information. This is especially true during the early-to-middle periods of data collection, when survey managers using RSD often consider interventions.

Constrained Adjusted Maximum a Posteriori Estimation of Bayesian Network Parameters.

Maximum a posteriori estimation (MAP) with Dirichlet prior has been shown to be effective in improving the parameter learning of Bayesian networks when the available data are insufficient. Given no extra domain knowledge, uniform prior is often considered for regularization. However, when the underlying parameter distribution is non-uniform or skewed, uniform prior does not work well, and a more informative prior is required. In reality, unless the domain experts are extremely unfamiliar with the network, they would be able to provide some reliable knowledge on the studied network. With that knowledge, we can automatically refine informative priors and select reasonable equivalent sample size (ESS). In this paper, considering the parameter constraints that are transformed from the domain knowledge, we propose a Constrained adjusted Maximum a Posteriori (CaMAP) estimation method, which is featured by two novel techniques. First, to draw an informative prior distribution (or prior shape), we present a novel sampling method that can construct the prior distribution from the constraints. Then, to find the optimal ESS (or prior strength), we derive constraints on the ESS from the parameter constraints and select the optimal ESS by cross-validation. Numerical experiments show that the proposed method is superior to other learning algorithms.

Continuous updating of individual headache forecasting models using Bayesian methods.

To illustrate the benefits of deploying individual headache forecasting models using continuous updating with Bayesian methods. The ability to reliably forecast headache attacks within an individual over time would enhance the study of attacks and allow preemptive treatment. However, deploying a suitable forecasting model in a clinical setting will likely involve several unique challenges related to heterogeneity in the predictor weights, limited or sparse data, and the need for a quick "warm-up." The use of Bayesian methods offers solutions to each of these specific challenges. This was a post hoc analysis of a cohort study of individuals with episodic migraine attacks. Individuals completed daily diaries that allowed the estimation of several forecasting models, each using different types of ancillary information incorporated into formal prior probability distributions. An in silico analysis was conducted that mimicked the deployment of these models in a clinical-like setting where the parameters of the models were continuously updated and evaluated each day using root mean square error (RMSE). Individuals (N=95) were followed for 50days and contributed 3359days of nonmissing diary data. During the observation period, there were 1293/3359 (38.5%) days with a headache attack. Self-reported baseline headache frequency was associated with the corresponding predicted probability of future attacks, r=0.15-0.39. At Day 25, the correlation between baseline information and predicted attack likelihood was r=0.29 (95% CI: 0.09-0.47). Additionally, the use of prior probability distributions for model parameters improved the model fit, especially early in the deployment of the models (e.g., Day 5 RMSE 0.45 vs. 0.43). Models using informative prior probability distributions outperformed the models estimated without this information during the first 42days of observation, although performance became more similar as more data were collected. This analysis demonstrates the value of Bayesian methods in using additional available information to improve forecasting model performance, especially early in the deployment of a forecasting model. To obtain the full value of such models or to apply any model in clinical settings, a model with adequate discrimination and calibration will be needed.

Bayesian reasoning aimed at a prediction of failure patterns of fire induced pressure vessel explosions

The problem of assessing damage due to explosions of cylindrical pressure vessels is considered. The attention is focussed on a prediction of the arrangement of cracks in the vessel wall prior to its explosion. This arrangement of cracks is called the failure pattern. It is seen as essential information for forecasting ejection and projection of fragments generated by an explosion. Thermally induced explosions known as boiling liquid expanding vapour explosions are studied. The problem of prediction of failure patterns is formulated as a problem of estimating probabilities of these patterns. The scarcity of data on occurrences of failure patterns in the past explosion accidents was an incentive to estimate the failure pattern probabilities by means of Bayesian statistics. The main finding of the study is that the failure pattern probabilities can be handled within the Dirichlet-multinomial model and the epistemic uncertainty in these probabilities expressed by Dirichlet prior and posterior distributions. The Bayesian estimation of failure pattern probabilities is viewed as a way allowing to introduce the prediction of vessel fragmentation into the formal probabilistic risk analysis. The so-called minimally informative Dirichlet prior distribution is suggested for the probability estimation as a prior suitable to Bayesian updating with scarce data. It is stated that currently the probabilistic prediction of failure patterns on the basis of past accident data is the only practicable way to assess the potential type of vessel fragmentation. A conventional (deterministic) mechanical and/or metallurgical analysis does not provide reliable models for failure pattern prediction in case of explosions under study.

Avoiding prior–data conflict in regression models via mixture priors

The Bayesian‐80 model consists of the prior–likelihood pair. A prior–data conflict arises whenever the prior allocates most of its mass to regions of the parameter space where the likelihood is relatively low. Once a prior–data conflict is diagnosed, what to do next is a hard question to answer. We propose an automatic prior elicitation that involves a two‐component mixture of a diffuse and an informative prior distribution that favours the first component if a conflict emerges. Using various examples, we show that these mixture priors can be useful in regression models as a device for regularizing the estimates and retrieving useful inferential conclusions.

Sample size determination to estimate mediation effects in cell transformation assays: A Bayesian causal model

AbstractCell transformation assays (CTAs) are in vitro methods used in the preliminary assessment of the carcinogenic potential of substances. CTAs are promising tests for cosmetic, food, and pharma companies because they are not only quick‐and‐cheap, but also able to reduce animal‐based testing. An assay has the simple structure of a randomized one‐way experiment, where the experimental factor is defined by 5 increasing concentrations. Different families of distributions have been proposed to evaluate the effect of a substance on counts of Type III foci, but all models proposed so far do not consider differences in the number of viable cells and in the total number of foci occurring among Petri dishes. In this article, a Bayesian structural causal model is proposed to distinguish total, direct, and indirect effects of a carcinogen in CTA experiments. The recommended sample size is calculated by Monte Carlo simulation given the type of effect and the magnitude to detect. An informative joint prior distribution on parameters elicited for BALB/c 3T3 CTAs is exploited to obtain the posterior distribution from each simulated dataset.

On the normalized power prior.

The power prior is a popular tool for constructing informative prior distributions based on historical data. The method consists of raising the likelihood to a discounting factor in order to control the amount of information borrowed from the historical data. However, one often wishes to assign this discounting factor a prior distribution and estimate it jointly with the parameters, which in turn necessitates the computation of a normalizing constant. In this article, we are concerned with how to approximately sample from joint posterior of the parameters and the discounting factor. We first show a few important properties of the normalizing constant and then use these results to motivate a bisection-type algorithm for computing it on a fixed budget of evaluations. We give a large array of illustrations and discuss cases where the normalizing constant is known in closed-form and where it is not. We show that the proposed method produces approximate posteriors that are very close to the exact distributions and also produces posteriors that cover the data-generating parameters with higher probability in the intractable case. Our results suggest that the proposed method is an accurate and easy to implement technique to include this normalization, being applicable to a large class of models. They also reinforce the notion that proper inclusion of the normalizing constant is crucial to the drawing of correct inferences and appropriate quantification of uncertainty.

Comparing the performance of Bayesian and least-squares approaches for inverse kinematics problems

Bayesian inference has recently been identified as an approach for estimating a subjects’ pose from noisy marker position data. Previous research suggests that Bayesian inference markedly reduces error for inverse kinematic problems relative to traditional least-squares approaches with estimators having reduced variance despite both least-squares and Bayesian estimators being unbiased. This result is surprising as Bayesian estimators are typically similar to least-squares approaches unless highly informative prior distributions are used. As a result the purpose of this work was to examine the sensitivity of Bayesian inverse kinematics solutions to the prior distribution. Our results highlight that Bayesian solutions to inverse kinematics are sensitive to the choice of prior and that the previously reported superior performance of Bayesian inference is likely due to an overly informative prior distribution which unrealistically uses knowledge of the true kinematic pose. When more realistic, ‘weakly-informative’ priors, which do not use the known kinematic pose are used then any improvements in estimator accuracy are minimal when compared to the traditional least squares approach. However, with appropriate priors, Bayesian inference can propagate uncertainties related to marker position to uncertainty in joint angles, a valuable contribution for kinematic analyses. When using Bayesian methods, we recommend researchers use weakly-informative priors and conduct a sensitivity analysis to highlight the effects of prior choice on analysis outcomes.

A re-examination of the SPYRAL HTN-OFF MED Pivotal trial with respect to the underlying model assumptions

BackgroundThe SPYRAL HTN-OFF MED Pivotal trial demonstrated that RDN was efficacious compared to a sham control. The underlying model was an extension of the analysis of covariance (ANCOVA) model, adjusted for baseline blood pressure (BP), and allowed borrowing of information from the previously reported feasibility study using a novel Bayesian method. Fundamental to the estimation of a treatment effect for efficacy are a multitude of statistical modelling assumptions, including the role of outliers, linearity of the association between baseline BP and outcome, and parallelism of the treatment effect difference over the baseline BP range. In this report, we examine the validity of these assumptions to verify the robustness of the treatment effect measured. MethodsWe examined the requisite modelling assumptions of the ANCOVA model fitted to the SPYRAL HTN-OFF MED Pivotal trial using Bayesian methods. To address outliers, we fit a robust regression model (with heavy tailed errors) to the data with diffuse weakly informative prior distributions on the parameters. To address linearity, we replaced the linear baseline term by a natural spline term with 4 degrees of freedom. To address parallelism, we refit the ANCOVA model with an interaction term for treatment arm and baseline BP. ResultsANCOVA models were fitted to the trial data (pooled across the feasibility and pivotal cohorts) using Bayesian methodology with diffuse (non-informative) prior distributions. The modelling assumptions inherent to the ANCOVA models were shown to be broadly satisfied. A robust ANCOVA model yielded a posterior treatment effect of -4.1 mmHg (95% credible interval: -6.3 to -1.9) indicating the influence of outlier values was small. There was moderate evidence of an interaction term effect between baseline BP and treatment, but no evidence of gross violation of linearity in baseline BP. ConclusionThe posterior treatment effect estimate is shown to be robust to underlying model assumptions, thus further supporting the evidence of RDN to be an efficacious treatment for resistant hypertension.

A Bayesian inverse dynamic approach for impulsive wave loading reconstruction: Theory, laboratory and field application

The measurement of wave forces acting on marine structures is a complicated task, both during physical experiments and, even more so, in the field. Force transducers adopted in laboratory experiments require a minimum level of structural movement, thus violating the main assumption of fully rigid structure and introducing a dynamic response of the system. Sometimes the induced vibrations are so intense that they completely nullify the reliability of the experiments. On-site, it is even more complex, since there are no force transducers of the size and capacity able to measure such massive force intensity acting over the very large domain of a marine structure. To this end, this investigation proposes a Bayesian methodology aimed to remove the undesired effects from the directly (laboratory applications) or indirectly (field applications) measured wave forces. The paper presents three applications of the method: i) a theoretical application on a synthetic signal for which MATLAB® procedures are provided, ii) an experimental application on laboratory data collected during experiments aimed to model broken wave loading on a cylinder upon a shoal and iii) a field application designed to reconstruct the wave force that generated recorded vibrations on the Wolf Rock lighthouse during Hurricane Ophelia. The proposed methodology allows the inclusion of existing information on breaking and broken wave forces through the process-based informative prior distributions, while it also provides the formal framework for uncertainty quantification of the results through the posterior distribution.Notable findings are that the broken wave loading shows similar features for both laboratory and field data. The load time series is characterised by an initial impulsive component constituted by two peaks and followed by a delayed smoother one. The first two peaks are due to the initial impact of the aerated front and to the sudden deceleration of the falling water mass previously upward accelerated by the initial impact. The third, less intense peak, is due to the interaction between the cylinder and remaining water mass carried by the individual wave.Finally, the method allows to properly identify the length of the impulsive loading component. The implications of this length on the use of the impulse theory for the assessment or design of marine structures are discussed.

Oral steroids for reducing kidney scarring in young children with febrile urinary tract infections: the contribution of Bayesian analysis to a randomized trial not reaching its intended sample size

BackgroundThis study aimed to evaluate the effect of oral dexamethasone in reducing kidney scars in infants with a first febrile urinary tract infection (UTI).MethodsChildren aged between 2 and 24 months with their first presumed UTI, at high risk for kidney scarring based on procalcitonin levels (≥1 ng/mL), were randomly assigned to receive dexamethasone in addition to routine care or routine care only. Kidney scars were identified by kidney scan at 6 months after initial UTI. Projections of enrollment and follow-up completion showed that the intended sample size could not be reached before funding and time to complete the study ran out. An amendment to the protocol was approved to conduct a Bayesian analysis.ResultsWe randomized 48 children, of whom 42 had a UTI and 18 had outcome kidney scans (instead of 128 planned). Kidney scars were found in 0/7 and 2/11 patients in the treatment and control groups respectively. The probability that dexamethasone could prevent kidney scarring was 99% in the setting of an informative prior probability distribution (which fully incorporated in the final inference the information on treatment effect provided by previous studies) and 98% in the low-informative scenario (which discounted the prior literature information by 50%). The probabilities that dexamethasone could reduce kidney scar formation by up to 20% were 61% and 53% in the informative and low-informative scenario, respectively.ConclusionsDexamethasone is highly likely to reduce kidney scarring, with a more than 50% probability to reduce kidney scars by up to 20%.Trial registration numberEudraCT number: 2013-000388-10; registered in 2013 (prospectively registered)Graphical A higher resolution version of the Graphical abstract is available as Supplementary information

Seroprevalence of SARS-CoV-2 antibodies in South Korea.

In 2020, Korea Disease Control and Prevention Agency reported three rounds of surveys on seroprevalence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) antibodies in South Korea. SARS-CoV-2 is the virus which inflicts the coronavirus disease 2019 (COVID-19). We analyze the seroprevalence surveys using a Bayesian method with an informative prior distribution on the seroprevalence parameter, and the sensitivity and specificity of the diagnostic test. We construct the informative prior of the sensitivity and specificity of the diagnostic test using the posterior distribution obtained from the clinical evaluation data. The constraint of the seroprevalence parameter induced from the known confirmed coronavirus 2019 cases can be imposed naturally in the proposed Bayesian model. We also prove that the confidence interval of the seroprevalence parameter based on the Rao’s test can be the empty set, while the Bayesian method renders interval estimators with coverage probability close to the nominal level. As of the 30th of October 2020, the ,,,,,,95%,,,,,, credible interval of the estimated SARS-CoV-2 positive population does not exceed 318, 685, approximately 0.62% of the Korean population.Supplementary InformationThe online version contains supplementary material available at 10.1007/s42952-021-00131-7.

A Similarity-Weighted Informative Prior Distribution for Bayesian Multiple Regression Models.

Specifying accurate informative prior distributions is a question of carefully selecting studies that comprise the body of comparable background knowledge. Psychological research, however, consists of studies that are being conducted under different circumstances, with different samples and varying instruments. Thus, results of previous studies are heterogeneous, and not all available results can and should contribute equally to an informative prior distribution. This implies a necessary weighting of background information based on the similarity of the previous studies to the focal study at hand. Current approaches to account for heterogeneity by weighting informative prior distributions, such as the power prior and the meta-analytic predictive prior are either not easily accessible or incomplete. To complicate matters further, in the context of Bayesian multiple regression models there are no methods available for quantifying the similarity of a given body of background knowledge to the focal study at hand. Consequently, the purpose of this study is threefold. We first present a novel method to combine the aforementioned sources of heterogeneity in the similarity measure ω. This method is based on a combination of a propensity-score approach to assess the similarity of samples with random- and mixed-effects meta-analytic models to quantify the heterogeneity in outcomes and study characteristics. Second, we show how to use the similarity measure ωas a weight for informative prior distributions for the substantial parameters (regression coefficients) in Bayesian multiple regression models. Third, we investigate the performance and the behavior of the similarity-weighted informative prior distribution in a comprehensive simulation study, where it is compared to the normalized power prior and the meta-analytic predictive prior. The similarity measure ω and the similarity-weighted informative prior distribution as the primary results of this study provide applied researchers with means to specify accurate informative prior distributions.

Robust Bayesian estimator for S-wave spectra, using a combined empirical Green’s function

Summary We propose a new fully automatic and robust Bayesian method to estimate precise and reliable model parameters describing the observed S-wave spectra. All the spectra associated with each event are modelled jointly, using a t-distribution as likelihood function together with informative prior distributions for increased robustness against outliers and extreme values. The model includes the observed noise and a combined empirical Green’s function. It captures source-, receiver-, and path-dependent terms in the description of the observed spectra by combining a physical source and attenuation model with a spatially and event-size dependent empirical compensation. The proposed method propagates estimation uncertainties along the entire processing chain starting from the hypocentre location and delivers reliable uncertainty description of the estimands. The objective is to automatically provide robust and valid descriptions of the observed S-wave spectra generated from an earthquake source in a noisy and heterogeneous environment. The efficiency of the method is tested with synthetic seismograms, and the model is calibrated and cross-validated using 31 640 mining induced seismic events in a iron ore mine (in north of Sweden) with an comprehensive seismic network. The model is evaluated using both posterior predictive checks and residual analysis and we found no evidence that indicates any model deficiencies with respect to central tendency, dispersion, and residual trends.

Bayes analysis of some important lifetime models using MCMC based approaches when the observations are left truncated and right censored

The paper considers the Bayes analysis of important lifetime models such as the Weibull, the gamma, and the lognormal distributions when the available data are left truncated and right-censored. Weakly informative prior distributions are employed for the purpose. Two well-known Markov chain Monte Carlo based approaches, namely, the Metropolis algorithm and the Hamiltonian Monte Carlo technique are used to draw samples from analytically intractable posterior distributions. Besides, the paper does a comparative study of the three entertained models using Bayes factor. The paper has considered calculating the marginal likelihood using bridge sampler algorithm for evaluating the necessary Bayes factor. Finally, a numerical illustration based on a real dataset compares the two algorithms and draws relevant conclusions appropriately.

Multi-fidelity Bayesian neural networks: Algorithms and applications

We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs). These multi-fidelity BNNs consist of three neural networks: The first is a fully connected neural network, which is trained following the maximum a posteriori probability (MAP) method to fit the low-fidelity data; the second is a Bayesian neural network employed to capture the cross-correlation with uncertainty quantification between the low- and high-fidelity data; and the last one is the physics-informed neural network, which encodes the physical laws described by PDEs. For the training of the last two neural networks, we first employ the mean-field variational inference (VI) to maximize the evidence lower bound (ELBO) to obtain informative prior distributions for the hyperparameters in the BNNs, and subsequently we use the Hamiltonian Monte Carlo (HMC) method to estimate accurately the posterior distributions for the corresponding hyperparameters. We demonstrate the accuracy of the present method using synthetic data as well as real measurements. Specifically, we first approximate a one- and four-dimensional function, and then infer the reaction rates in one- and two-dimensional diffusion-reaction systems. Moreover, we infer the sea surface temperature (SST) in the Massachusetts and Cape Cod Bays using satellite images and in-situ measurements. Taken together, our results demonstrate that the present method can capture both linear and nonlinear correlation between the low- and high-fidelity data adaptively, identify unknown parameters in PDEs, and quantify uncertainties in predictions, given a few scattered noisy high-fidelity data. Finally, we demonstrate that we can effectively and efficiently reduce the uncertainties and hence enhance the prediction accuracy with an active learning approach, using as examples a specific one-dimensional function approximation and an inverse PDE problem.

Optimal Localization With Sequential Pseudorange Measurements for Moving Users in a Time-Division Broadcast Positioning System

In a time division broadcast positioning system (TDBPS), a user device (UD) determines its position by obtaining sequential time-of-arrival (TOA) or pseudorange measurements from signals broadcast by multiple synchronized base stations (BSs). The existing localization method using sequential pseudorange measurements and a linear clock drift model for the TDPBS, namely LSPM-D, does not compensate the position displacement caused by the UD movement and will result in position error. In this paper, depending on the knowledge of the UD velocity, we develop a set of optimal localization methods for different cases. First, for known UD velocity, we develop the optimal localization method, namely LSPM-KVD, to compensate the movement-caused position error. We show that the LSPM-D is a special case of the LSPM-KVD when the UD is stationary with zero velocity. Second, for the case with unknown UD velocity, we develop a maximum likelihood (ML) method to jointly estimate the UD position and velocity, namely LSPM-UVD. Third, in the case that we have prior distribution information of the UD velocity, we present a maximum a posteriori (MAP) estimator for localization, namely LSPM-PVD. We derive the Cramer-Rao lower bound (CRLB) for all three estimators and analyze their localization error performance. We show that the position error of the LSPM-KVD increases as the assumed known velocity deviates from the true value. As expected, the LSPM-KVD has the smallest position error while the LSPM-PVD and the LSPM-UVD are more robust when the prior knowledge of the UD velocity is limited. Numerical results verify the theoretical analysis on the optimality and the positioning accuracy of the proposed methods.

Systematic Parameter Reviews in Cognitive Modeling: Towards a Robust and Cumulative Characterization of Psychological Processes in the Diffusion Decision Model.

Parametric cognitive models are increasingly popular tools for analyzing data obtained from psychological experiments. One of the main goals of such models is to formalize psychological theories using parameters that represent distinct psychological processes. We argue that systematic quantitative reviews of parameter estimates can make an important contribution to robust and cumulative cognitive modeling. Parameter reviews can benefit model development and model assessment by providing valuable information about the expected parameter space, and can facilitate the more efficient design of experiments. Importantly, parameter reviews provide crucial—if not indispensable—information for the specification of informative prior distributions in Bayesian cognitive modeling. From the Bayesian perspective, prior distributions are an integral part of a model, reflecting cumulative theoretical knowledge about plausible values of the model's parameters (Lee, 2018). In this paper we illustrate how systematic parameter reviews can be implemented to generate informed prior distributions for the Diffusion Decision Model (DDM; Ratcliff and McKoon, 2008), the most widely used model of speeded decision making. We surveyed the published literature on empirical applications of the DDM, extracted the reported parameter estimates, and synthesized this information in the form of prior distributions. Our parameter review establishes a comprehensive reference resource for plausible DDM parameter values in various experimental paradigms that can guide future applications of the model. Based on the challenges we faced during the parameter review, we formulate a set of general and DDM-specific suggestions aiming to increase reproducibility and the information gained from the review process.