The judgments that people make are not independent –initial decisions can bias later perception. This has beenshown in tasks in which participants first decide whetherthe direction of moving dots is to one side or the otherof a reference line: their subsequent estimates are biasedaway from this reference line. This interesting bias has beenexplained in past work as either a consequence of weightingsensory neurons, or as a consequence of participants adjustingtheir estimate to match their decision. We propose anew explanation: that people sequentially sample evidenceto make their decision, and reuse these samples to maketheir estimate (i.e., amortised inference). Because optimalstopping leads to samples that strongly favor one or anotherdecision alternative, the subsequent estimates are also biasedaway from the reference line. We introduce a sequentialsampling model for posterior samples that does not assumeconstant thresholds, and provide evidence for our explanationin a new experiment that generalizes the perceptual bias to anew domain.

With the explosion of "big data," digital repositories of texts and images are growing rapidly. These datasets present new opportunities for psychological research, but they require new methodologies before researchers can use these datasets to yield insights into human cognition. We present a new method that allows psychological researchers to take advantage of text and image databases: a procedure for measuring human categorical representations over large datasets of items, such as arbitrary words or pictures. We call this method discrete Markov chain Monte Carlo with people (d-MCMCP). We illustrate our method by evaluating the following categories over datasets: emotions as represented by facial images, moral concepts as represented by relevant words, and seasons as represented by images drawn from large online databases. Three experiments demonstrate that d-MCMCP is powerful and flexible enough to work with complex, naturalistic stimuli drawn from large online databases.