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📚 Statistical Inference for Everyone
Chapters ▾
1 Introduction to Probability2 Applications of Probability3 Random Sequences and Visualization4 Introduction to Model Comparison5 Applications of Model Comparison6 Introduction to Parameter Estimation7 Priors, Likelihoods, and Posteriors8 Common Statistical Significance Tests9 Applications of Parameter Estimation and Inference10 Multi-parameter Models11 Introduction to MCMC12 Concluding Thoughts13 Appendix A: Computational Analysis14 Appendix B: Notation and Standards15 Appendix C: Common Distributions and Their Properties16 Appendix D: Tables

Chapter 4: Introduction to Model Comparison

A model as we use the term in this book is a specific description of a possible state of nature. This is in contrast to an actual state of nature, which we practically never have access to. We can never know anything with 100% certainty, and must therefore be open to alternate possible explanations, or models, describing our observations. For example, in medicine such models could include “I have lung cancer,” “I have pneumonia,” and “I have a cold.” In physics, models could include “the Earth moves around the Sun” and “the Sun moves around the Earth.” We can imagine many possible models that are consistent with the observed data, and our job in doing statistical inference is to determine the probabilities of our models given the data we observe. In our notation, what we are always looking for is

Adapted from Statistical Inference for Everyone, by Brian Blais (Bryant University), licensed under CC BY-SA 4.0 (dual-licensed under the GNU FDL 1.2 or later; this adaptation uses the CC BY-SA grant). Changes were made; this adaptation is distributed under the same license. License: CC-BY-SA-4.0.