In W. Batchelder, H. Colonius, E. Dzhafarov, & J. Myung (Eds.), New handbook of mathematical psychology, Volume 2 (pp. 223-270). New York: Cambridge University Press. Computational Cognitive Neuroscience F. Gregory Ashby University of California, Santa Barbara Contents 6.1 Introduction 6.1.1 A Brief History 6.1.2 Organization of the Chapter 6.2 Advantages of CCN Modeling 6.2.1 Testing Against Many Different Data Types 6.2.2 Model Inflexibility 6.2.3 Model Convergence 6.2.4 Ability to Unite Seemingly Disparate Fields 6.3 CCN Modeling Principles 6.3.1 The Neuroscience Ideal 6.3.2 The Simplicity Heuristic 6.3.3 The Set-in-Stone Ideal 6.4 Models of Single Spiking Neurons 6.4.1 The Leaky Integrate-and-Fire Model 6.4.2 The Quadratic Integrate-and-Fire Model 6.4.3 The Izhikevich Model 6.4.4 Modeling Synaptic Delays 6.4.5 Noise 6.5 Firing-Rate Models 6.6 Learning 6.6.1 Synaptic Plasticity 6.6.2 Models of Learning in the Striatum and Cortex 6.6.2.1 Discrete-time models of learning at synapses that lack fast DA reuptake 6.6.2.2 Discrete-time models of learning at synapses with fast DA reuptake 6.6.2.3 Modeling DA Release 6.6.2.4 Continuous-time models of Hebbian learning 6.7 Testing CCN Models 6.7.1 Single-Unit Recording Data 6.7.2 Behavioral Data 6.7.3 FMRI Data 6.7.4 TMS Data 6.7.5 Pharmacological and Neuropsychological Patient Data 6.8 Parameter Estimation and Model Evaluation 6.9 Conclusions References 6.1 Introduction Cognitive neuroscience was born in the 1990’s amid a technological explosion that produced powerful new meth- ods for noninvasively studying the human brain, including functional magnetic resonance imaging (fMRI) and transcra- nial magnetic stimulation (TMS). These exciting new tech- nologies revolutionized the scientific study of the mind, giv- ing unprecedented observability into the neural processes that mediate human thought and action. With the new data came a growing need for new kinds of theories that could simultaneously account for the behavioral data that are the bread and butter of traditional mathematical psychology as well as the brain-related measures coming from the new tech- nologies. Computational Cognitive Neuroscience (CCN) was created to fill this void. CCN evolved from computational neuroscience on one side and connectionism, neural network theory, and machine learning on the other. Like computational neuroscience, CCN strives for neurobiological accuracy and like connec- 1