Until recently, adaptive psychophysical estimation methods have been based on models with only few unknown variables and with the stimuli varying over one dimension only. One reason for not using more complicated models is that the straighforward grid sampling of the parameter space employed by most Bayesian estimation methods grows exponentially with the number of parameters. In some Bayesian estimation contexts, such as radar tracking, sequential Monte Carlo (SMC) algorithms have been able to overcome this curse of dimensionality. However, in psychometric measurement, the underlying model is decidedly different---the unknown parameters do not change in time, which leads to sample degeneration in most SMC algorithms. To avoid the degeneracy in static models, Chopin (2002) combines a SMC algorithm with Markov Chain Monte Carlo. In (Kujala and Lukka, JMP 2006) a similar algorithm is proposed for Bayesian adaptive estimation. The price to pay is quadratic scaling with the number of observations as opposed to the linear scaling of typical SMC algorithms or the straightforward grid sampling. However, in psychometric measurement, the number of trials is relatively small so this is generally a small price. The algorithm is applied to estimation of discrimination threshold contours around target colors in a color plane. At the four varied dimensions of this model, the SMC algorithm is on a par with a highly optimized version of the deterministic grid sampling algorithm; with more dimensions, the grid sampling is approaching its limit while the Monte Carlo approach is expected to scale much more gracefully. |