ABSTRACT
CONTENTS 24.1 Introduction 524
24.1.1 Notation for Observations 524 24.1.2 Probability Models 525 24.1.3 Statistical Models 525 24.1.4 Maximum Likelihood Estimation 526
24.2 Chunks and Conditional Models 527 24.2.1 Bessel’s Personal Equations 527 24.2.2 Nuisance Effects and Attenuation 527 24.2.3 Chunking and Conditional Likelihood 528
24.2.3.1 Kinds of Chunking 528 24.2.3.2 Conditioning on the Within-Chunk Response 529 24.2.3.3 Chunks of Size 2 530
24.3 The Spherical Approximation 530 24.3.1 Chunks of Size 3 530 24.3.2 The von Mises-Fisher Distribution 531 24.3.3 The Spherical Likelihood Gradient 532 24.3.4 The Spherical Throttling Ratio 532 24.3.5 Some Normal Equations 534 24.3.6 The Chunk-Specific Correlation Coefficient 534 24.3.7 Assessing the Spherical Approximation 535
24.4 Related Methods 537 24.4.1 Iteratively Reweighted Least Squares 537 24.4.2 Marginal Regression 537
24.4.3 A Generalization to Many Features 538 24.4.4 Multiple-Stage Models 538
24.5 Conclusions 540 References 540
24.1 INTRODUCTION The foregoing chapters illustrate how data processing and statistical technologies can be applied to issues of scientific interest to astronomers. Here I focus on an inverse mapping: applying the physical intuition that astronomers possess to advance the science of statistical modeling. I found this remarkably easy to do, and I hope you enjoy the perspective.
