# Quantifying the effect of intertrial dependence on perceptual decisions

Today we discussed a paper on sequential effects in psychophysics by Fründ et al. Although inter-trial dependencies are known to exist, psychophysical responses are typically modeled as independent Bernoulli observations. One way to account for the effect of previous trial outcomes is to use logistic regression with terms that represent previous stimuli or responses (Busse et al). Fründ and colleagues extend this approach by including a lapse rate which captures responses where the subject was not doing the task.

maximize $p(Y|x,w) = \frac{e^{Yxw}}{(1 + e^{xw})}$, where Y is the observer’s responses, x is a matrix of the stimulus (trials x stimulus vector) augmented by a column of ones (for the observer’s bias), and w is the observer’s kernel (size = [1 x(1,:)]). Using a sparse prior (L1 norm) over a set of smooth basis (defined by a laplacian pyramid) reduces the number of trials required to fit the kernel while adding only one hyperparameter. The authors use simulations and real psychophysical data to fit an observer’s psychophysical kernel and their code is available here.