has proposed the diffusion model as a form of data analysis for speeded binary decisions. The diffusion model assumes that binary decisions are based on a continuous process that fluctuates between two possible outcomes ( Figure 1). As soon as the process reaches a critical upper or lower value, a decision is made, and the corresponding response is executed. One main advantage of the diffusion model is that different components of the decision process (rate of information uptake, bias, conservatism, and motor component) are represented by different parameters of the model. Theoretically, distinct aspects of the decision process can be separated statistically. In a sense, the model allows inferences regarding hidden cognitive processes. Another advantage of the diffusion model data analysis is the high degree of information utilization. In contrast to conventional forms of data analysis, the diffusion model incorporates response times (RTs) for correct responses and errors, as well as the ratio of correct and erroneous responses.The diffusion model thus provides a powerful statistical tool that allows a very fine-grained analysis of the cognitive processes underlying simple response tasks. Previous applications of the diffusion model have included, for example, the analysis of retrieval processes (Ratcliff, 1978(Ratcliff, , 1988 and the identification of the factors underlying age-related slowing (Ratcliff, Spieler, & McKoon, 2000;Ratcliff, Thapar, & McKoon, 2001, 2003. These examples reveal that the diffusion model has a wide range of possible applications and can be used to decide between competing theoretical interpretations of experimental findings. However, although interpretations of the different parameters of the diffusion model seem fairly straightforward, it should be kept in mind that these interpretations are based mainly on theoretical reflections and presuppose the validity of the diffusion model as an adequate representation of the underlying cognitive processes. 1 The main aim of the present article, therefore, is to provide an empirical validation of the theoretical interpretation of the parameters of the diffusion model. To this end, we investigated the effects of different experimental manipulations on the parameter set in a diffusion model data analysis. The experimental manipulations were intended to specifically affect the different processing components of the model (rate of information uptake, setting of response criteria, duration of the motor response and bias; see Ratcliff, 2002;Ratcliff & Rouder, 1998;Ratcliff et al., 2001). Analyzing whether experimental manipulations of the different processing components that are specified in the model map uniquely onto the corresponding parameters of the model (and not Correspondence concerning this article should be addressed to A. Voss, Institut für Psychologie, Albert-Ludwigs-Universistät Freiburg, Engelbergstr. 41, D-79085 Freiburg im Breisgau, Germany (e-mail: andreas. voss@psychologie.uni-freiburg.de) or to K. Rothermund, Institut für Psy...

In the present paper a flexible and fast computer program, called fast-dm, for diffusion model data analysis is introduced. Fast-dm is free software and can be obtained from the authors of this paper. The program allows estimating all parameters of Ratcliff's (1978) diffusion model from the empiric response time distributions of any binary classification task. Fast-dm is easy to use: it reads input data from simple text files, while program settings are specified by commands in a control file. The program allows to estimate even complex, hierarchical models and to fix individual parameters to given values. Detailed directions for use of fast-dm are presented, as well as results from three short simulation studies exemplifying the utility of fast-dm.

We present and study a Langevin MCMC approach for sampling nonlinear diffusion bridges. The method is based on recent theory concerning stochastic partial differential equations (SPDEs) reversible with respect to the target bridge, derived by applying the Langevin idea on the bridge pathspace. In the process, a Random-Walk Metropolis algorithm and an Independence Sampler are also obtained. The novel algorithmic idea of the paper is that proposed moves for the MCMC algorithm are determined by discretising the SPDEs in the time direction using an implicit scheme, parameterised by θ ∈ [0, 1]. We show that the resulting infinite-dimensional MCMC sampler is well defined only if θ = 1/2, when the MCMC proposals have the correct quadratic variation. Previous Langevin-based MCMC methods used explicit schemes, corresponding to θ = 0. The significance of the choice θ = 1/2 is inherited by the finite-dimensional approximation of the algorithm used in practice. We present numerical results illustrating the phenomenon and the theory that explains it. Diffusion bridges (with additive noise) are representative of the family of laws defined as a change of measure from Gaussian distributions on arbitrary separable Hilbert spaces; the analysis in this paper can be readily extended to target laws from this family and an example from signal processing illustrates this fact.