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1、Chapter 3A New Theory of Trial-by-Trial P300Amplitude FluctuationsThischapterreviewsstate-of-the-artobservermodelsoftheP300event-relatedpoten-tial and introduces a new digital filtering (DIF) model. It starts with a brief overviewof the models known from literature and of the approach proposed in th
2、is work.After a description of the employed variant of the oddball task and specific methodsfor capturing trial-by-trial fluctuations in the P300 amplitudes y(n), the models andresponse functions constituting the model space M are presented in detail and thetwo most renowned ones are integrated into
3、 the digital filtering model. Next, theparameter optimization schemes as well as the composition of the design matricesfor model estimation and selection (see Chap.2) are specified. Results and conclu-sions complete this chapter, which was adapted and extended from Kolossa et al.(2013).3.1OverviewIn
4、 the following, the oddball task and the four observer models investigated in thischapterarebrieflydescribed.Thesubjectsperformedanoddballtask,whichisasim-ple two-choice response time task: Frequent and rare events are sequentially shownto the subjects who have to respond to the event type by pressi
5、ng the correspondingkey on a keyboard. The trial-by-trial P300 amplitudes were derived from the EEGsignal at electrode Pz and used for Bayesian model estimation and selection (seeSect.2 for details).Table3.1presentsallobservermodels:ThefirstmodeliscalledhereSQUandgoesbacktoSquiresetal.(1976),whoshow
6、edandmodeleddependenciesofP300ampli-tude fluctuations from observable events based on the concept of expectancy, whichwas thought to be determined by three factors: “(i) the memory for event frequencywithin the prior stimulus sequence, (ii) the specific structure of the prior sequence,and (iii) the
7、global probability of the event.” (p. 1144). Note that as expectancy isnot a probability, it is not linked to the P300 amplitudes via a response functionbut used to predict the amplitudes directly. Although Squires et al.s model offers Springer International Publishing Switzerland 2016A. Kolossa, Co
8、mputational Modeling of Neural Activitiesfor Statistical Inference, DOI 10.1007/978-3-319-32285-8_341423A New Theory of Trial-by-Trial P300 Amplitude FluctuationsTable 3.1 Overview and short description of the observer modelsModelDescriptionSQUObserver model based on memory with exponential forgetti
9、ng, alternationexpectation, and prior knowledge (Squires et al. 1976)MARObserver model based on memory with no forgetting (Mars et al. 2008)OSTObserver model based on memory with exponential forgetting (Mars et al. 2008)DIFObserver model which fuses properties of the SQU and MAR models using a digit
10、alfiltering approach (Kolossa et al. 2013)a good explanation of the measured data, it remained descriptive and not plausible.Specifically, Squires et al. (1976) incorporated a lookup table instead of a formalcalculus for alternation expectation as well as knowledge which was not available tothe subj
11、ects. In order to make the SQU model accessible to model selection, it willbe reformulated in a completely computational way in Sect.3.3.1.ThesecondinvestigatedmodeliscalledMARandgoesbacktoMarsetal.(2008),who proposed a computational model of processes underlying the generation ofthe P300 amplitudes
12、 in which trial-by-trial amplitude fluctuations are explained byan observer keeping track of the global probability distribution over events. Thisdistribution is linked to the P300 amplitudes via predictive surprise (see Sect.1.4.2),but postdictive surprise (see Sect.1.4.1) is alternatively tested a
13、s a response functionin this work. The subjective estimates of statistical regularities in the environmentare modeled to depend solely on the integration of observations over infinitely longperiods of time. This is similar to factor (iii) of the SQU model, but in contrast to theSQU model the statist
14、ical regularities are learned from observations with uniforminitial prior probabilities and are not assumed to be known a priori. However, theexplanatorypowerofthisobservermodelislimited,becauseitcannotaccountfortheeffects of the recent stimulus sequence on the P300 amplitudes, which were alreadywel
15、l-documented decades earlier (e.g., Squires et al. 1976; Leuthold and Sommer1993).The third investigated model is called OST in this work and goes back to Ostwaldet al. (2012), who proposed a computational model that treats the event probabilityitself as a hidden random variable. They used Bayesian
16、surprise as response function(see Sect.1.4.1) to link the trial-by-trial evolution of the distribution over the hiddenvariabletoneuralactivities.Theirmodelisbasedonexponentiallyforgettingmemorytraces similar to factor (i) of the SQU model, but with a uniform initial prior such asthe MAR model. But as the MAR model, this model cannot account appropriatelyfor the influence of the structure of the recent stimulus sequence on P300 amplitudefluctuations.This chapter also introduces a computational di
