models & measurements
Chapter 5
There are two main analyses performed in a scientific context: measurement and model selection.
Here, we explore the topic of measurement. We see that models of the data are always a part of measurement, although we show that the presence of a model is sometimes 'transparent' to our calculations. We then develop a measurement algorithm that allows measurements to be made for a wide range of models. The utility of this algorithm is demonstrated in a series of worked examples, such as measuring rates (death rates, recovery rates, etc.), rate differences (differential recovery), times and time intervals (reaction time and qrs duration), means, variances, straight-line slopes, exponential decay, and stimulus detectability (d-prime).
Programming Asides:
-
computing confidence intervals [p281]
-
body temperature measurement [p285]
-
temperature measurement with multiplicative noise [p289]
-
binomial rate measurement [p294]
-
multinomial rate measurement [p295]
-
measuring the qrs duration [p300]
-
measuring saccade latency [p303]
-
straight-line model i [p306]
-
priors in slope and angle [p309]
-
straight-line model ii [p309]
-
d-prime [p316]
-
complex observation functions in threshold detection [p323]
-
measuring exponentially decaying sensory-motor error [p328]
-
dark adaptation [p336]
-
multiple-source transparent measurement [p342]
-
temperature from multiple thermometers [p346]
-
measuring multiple-source slope parameter [p351]