Multi-step look-ahead adaptive designs for the estimation of sensory thresholds : a thesis presented in partial fulfilment of the requirements for the degree of Master of Applied Statistics at Massey University, Albany, New Zealand
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2013
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Massey University
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Abstract
The estimation of sensory thresholds is an important part of the psychophysics field.
The point at which a physical stimulus becomes detectable can vary from trial to trial
within as well as between subjects. Often the probability of detection is modelled over
a range of stimulus intensities using an assumed psychometric curve which has the
threshold as a parameter. To estimate the threshold with a reasonable accuracy often
requires careful placement of the stimulus levels when the total number of trials are
limited. There have been a number of design schemes proposed over the years to find
the optimum placement strategy to minimise a given loss function. Some of the most
successful have been Bayesian adaptive designs which select the next signal intensity
based on prior knowledge and the responses observed up until that point. A critical
step in the adaptive designs is the choice of threshold estimator and error term, also
known as the loss function, to be minimised by the design scheme. A sub-class of these
look-ahead a short number of trials to calculate the expected loss function given the
current posterior distribution. However sometimes it is not possible to adjust the
signal after every test. Olfactory sensory threshold tests, for example, can require a
large setup time. In this situation a number of sensory tests may be grouped into
sessions, with any design alterations occurring between these. However this would
require a look-ahead design with a number of steps equal to the number of samples in
a session.
Most of the look-ahead designs have been restricted to one or two steps due to the
little performance increase gained by increasing them and the computational
limitations at the time they were suggested. The first point is not relevant to situations
where the step size must be larger, and the second point may be less true today due to
advances in computer power. This investigation demonstrates that it is possible to
implement multi-step look-ahead adaptive designs in a computationally efficient
manner for sessions up to sizes of twelve samples. Based on Monte-Carlo simulations,
these multi-step look-ahead designs also provide encouraging results in terms of
performance in minimising a number of loss functions.
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Keywords
Sensory thresholds, Psychophysics, Sensory trials, Loss function, Adaptive designs, Sensory evaluation, Sensory threshold tests