A Bayesian approach can contribute to an understanding of the brain on multiple levels, by giving normative predictions about how an ideal sensory system should combine prior knowledge and observation, by providing mechanistic interpretation of the dynamic functioning of the brain circuit, and by suggesting optimal ways of deciphering experimental data. Bayesian Brain brings together contributions from both experimental and theoretical neuroscientists that examine the brain mechanisms of perception, decision making, and motor control according to the concepts of Bayesian estimation.After an overview of the mathematical concepts, including Bayes' theorem, that are basic to understanding the approaches discussed, contributors discuss how Bayesian concepts can be used for interpretation of such neurobiological data as neural spikes and functional brain imaging. Next, contributors examine the modeling of sensory processing, including the neural coding of information about the outside world. Finally, contributors explore dynamic processes for proper behaviors, including the mathematics of the speed and accuracy of perceptual decisions and neural models of belief propagation.
Author(s): Kenji Doya, Shin Ishii, Alexandre Pouget, Rajesh P. N. Rao
Edition: 1
Publisher: The MIT Press
Year: 2007
Language: English
Pages: 327
Contents......Page 6
Series Foreword......Page 10
Preface......Page 11
I Introduction......Page 14
1.1 What Is Probability?......Page 15
1.3 Measuring Information......Page 18
1.4 Making an Inference......Page 20
1.5 Learning from Data......Page 22
1.6 Graphical Models and Other Bayesian Algorithms......Page 25
II Reading Neural Codes......Page 26
2.1 Spikes: What Kind of Code?......Page 27
2.2 Encoding and Decoding......Page 35
2.3 Adaptive Spike Coding......Page 52
2.5 Recommended Reading......Page 57
3.1 The Neural Coding Problem......Page 63
3.2 Model Fitting with Maximum Likelihood......Page 65
3.3 Model Validation......Page 74
3.4 Summary......Page 78
4.1 Introduction......Page 81
4.2 An Approach to Decoding......Page 82
4.3 Simplifying the Order Statistic Model......Page 92
4.4 Discussion......Page 94
5.1 Introduction......Page 102
5.2 Attention to Visual Motion......Page 103
5.3 The General Linear Model......Page 104
5.4 Parameter Estimation......Page 107
5.5 Posterior Probability Mapping......Page 110
5.6 Dynamic Causal Modeling......Page 113
5.7 Discussion......Page 118
III Making Sense of the World......Page 121
6.1 Introduction......Page 122
6.2 Coding and Decoding......Page 123
6.3 Representing Uncertainty with Population Codes......Page 127
6.4 Conclusion......Page 134
7.1 Computing, Invariance, and Throwing Away Information......Page 137
7.2 Computing Functions with Networks of Neurons: A General Algorithm......Page 138
7.3 Efficient Computing; Qualitative Analysis......Page 142
7.4 Efficient Computing; Quantitative Analysis......Page 143
7.5 Summary......Page 148
8.1 Introduction......Page 150
8.2 Computational Theories for Scene Segmentation......Page 153
8.3 A Computational Algorithm for the Weak-Membrane Model......Page 157
8.4 Generalizations of the Weak-Membrane Model......Page 161
8.5 Biological Evidence......Page 166
8.6 Summary and Discussion......Page 185
9.1 Introduction......Page 194
9.2 Psychophysical Tests of Bayesian Cue Integration......Page 196
9.3 Psychophysical Tests of Bayesian Priors......Page 200
9.4 Mixture models, Priors, and Cue Integration......Page 204
9.5 Conclusion......Page 209
IV Making Decisions and Movements......Page 212
10.1 Introduction......Page 213
10.2 The Diffusion-to-Bound Framework......Page 214
10.3 Derivation of Choice and Reaction Time Functions......Page 217
10.4 Implementation of Diffusion-to-Bound Framework in the Brain......Page 230
10.5 Conclusions......Page 237
11.1 Introduction......Page 242
11.2 Bayesian Inference through Belief Propagation......Page 243
11.3 Neural Implementations of Belief Propagation......Page 247
11.4 Results......Page 251
11.5 Discussion......Page 261
12 Optimal Control Theory......Page 271
12.1 Discrete Control: Bellman Equations......Page 272
12.2 Continuous Control: Hamilton-Jacobi-Bellman Equations......Page 275
12.3 Deterministic Control: Pontryagin's Maximum Principle......Page 279
12.4 Linear-Quadratic-Gaussian Control: Riccati Equations......Page 285
12.5 Optimal Estimation: Kalman Filter......Page 289
12.6 Duality of Optimal Control and Optimal Estimation......Page 292
12.7 Optimal Control as a Theory of Biological Movement......Page 296
13.1 Introduction......Page 301
13.2 Motor Decisions......Page 303
13.3 Utility: The Cost of Using our Muscles......Page 310
13.4 Neurobiology......Page 316
13.5 Discussion......Page 318
Contributors......Page 322
Index......Page 325
