Accounting Theory as a Bayesian Discipline introduces Bayesian theory and its role in statistical accounting information theory. The Bayesian statistical logic of probability, evidence and decision lies at the historical and modern center of accounting thought and research. It is not only the presumed rule of reasoning in analytical models of accounting disclosure, it is the default position for empiricists when hypothesizing about how the users of financial statements think. Bayesian logic comes to light throughout accounting research and is the soul of most strategic disclosure models. In addition, Bayesianism is similarly a large part of the stated & unstated motivation of empirical studies of how market prices & their implied costs of capital react to better financial disclosure.

The approach taken in this monograph is a Demski1973-like treatment of “accounting numbers” as “signals” rather than as “measurements”. It should be of course that “good” measurements like “quality earnings” reports make generally better signals. However, to be useful for decision making under uncertainty, accounting measurements need to have more than established accounting measurement virtues. This monograph explains what those Bayesian information attributes are, where they come from in Bayesian theory, and how they apply in statistical accounting information theory.

The Bayesian logic of probability, evidence and decision is the presumed rule of reasoning in analytical models of accounting disclosure. Any rational explication of the decades-old accounting notions of “information content”, “value relevance”, “decision useful”, and possibly conservatism, is inevitably Bayesian. By raising some of the probability principles, paradoxes and surprises in Bayesian theory, intuition in accounting theory about information, and its value, can be tested and enhanced. Of all the branches of the social sciences, accounting information theory begs Bayesian insights.

This monograph lays out the main logical constructs and principles of Bayesianism, and relates them to important contributions in the theoretical accounting literature. The approach taken is essentially “old-fashioned” normative statistics, building on the expositions of Demski, Ijiri, Feltham and other early accounting theorists who brought Bayesian theory to accounting theory. Some history of this nexus, and the role of business schools in the development of Bayesian statistics in the 1950^–₂₀1970_54yas, is described. Later developments in accounting, especially noisy rational expectations models under which the information reported by firms is endogenous, rather than unaffected or “drawn from nature”, make the task of Bayesian inference more difficult yet no different in principle.

The information user must still revise beliefs based on what is reported. The extra complexity is that users must allow for the firm’s perceived disclosure motives and other relevant background knowledge in their Bayesian models. A known strength of Bayesian modeling is that subjective considerations are admitted and formally incorporated. Allowances for perceived self-interest or biased reporting, along with any other apparent signal defects or “information uncertainty”, are part and parcel of Bayesian information theory.

Introduction
Bayesianism Early in Accounting Theory
1. Rise of Bayesian statistics
2. Bayes in US business schools
3. Early Bayesian accounting theorists
4. Postscript
Survey of Bayesian Fundamentals
1. All probability is subjective
2. Inference comes first
3. Bayesian learning
4. No objective priors
5. Independence is subjective
6. No distinction between risk and uncertainty
7. The likelihood function (ie. model)
8. Sufficiency and the likelihood principle
9. Coherence
10. Coherent means no “Dutch book”
11. Coherent is not necessarily accurate
12. Accuracy is relative
13. Odds form of Bayes theorem
14. Data can’t speak for itself
15. Ancillary information
16. Nuisance parameters “integrate out”
17. “Randomness” is subjective
18. “Exchangeable” samples
19. The Bayes factor
20. Conditioning on all evidence
21. Bayesian versus conventional inference
22. Simpson’s paradox
23. Data swamps prior
24. Stable estimation
25. Cromwell’s rule
26. Decisions follow inference
27. Inference, not estimation
28. Calibration
29. Economic scoring rules
30. Market scoring rules
31. Measures of information
32. Ex ante versus ex post accuracy
33. Sampling to forgone conclusion
34. Predictive distributions
35. Model averaging
36. Definition of a subjectivist Bayesian
37. What makes a Bayesian?
38. Rise of Bayesianism in data science
Case Study: Using All the Evidence
1. Interpreting “p-level ≤ α”
2. Bayesian interpretation of frequentist reports
3. A generic inference problem
Is Accounting Bayesian or Frequentist?
1. 2 Bayesian schools in accounting
2. Markowitz, subjectivist Bayesian
3. Characterization of information in accounting
4. Why accounting literature emphasizes “precision”
5. Bayesian description of information quality
6. Likelihood function of earnings
7. Capturing conditional conservatism
Decision Support Role of Accounting Information
1. A formal Bayesian model
2. Parallels with meteorology
3. Bayesian fundamental analysis
Demski1973’s Impossibility Result
1. Example: binary accounting signals
2. Conservatism and the user’s risk aversion
Does Information Reduce Uncertainty
1. Beaver1968’s prescription
2. Bayesian basics
3. Contrary views in accounting
4. Bayesian roots in finance
5. The general Bayesian law
6. Rogers et al 2009
7. Dye & Hughes2018
8. Why a Predictive Distribution?
9. Limits to certainty
10. Lewellen & Shanken2002
11. Neururer et al 2016
12. Veronesi1999
How Information Combines
1. Combining 2 risky signals
Ex Ante Effect of Greater Risk/Uncertainty
1. Risk adds to ex ante expected utility
2. Implications for Bayesian decision analysis
3. Volatility pumping
Ex Post Decision Outcomes
1. Practical investment
2. Economic Darwinism
3. Bayesian Darwinian selection
4. Good probability assessments
5. Implications for accounting information
Information Uncertainty
1. Bayesian definition of information uncertainty
2. Bayesian treatment of information uncertainty
3. Model risk as information risk
Conditioning Beliefs and the Cost of Capital
1. Numerical example
2. Interpretation
Reliance on the Normal-Normal Model
1. Intuitive counter-example
2. Appeal to the normal-normal model in accounting
3. Unknown variance, increasing after observation
4. Beyer2009
5. Armstrong et al 2016
Bayesian Subjective Beta
1. Core et al 2015
2. Verrecchia2001: Understated influence of the mean
3. Decision analysis effect of the mean
Other Bayesian Points of Interest
1. Accounting input in prediction models
2. Earnings quality and accurate probability assessments
3. Expected variance as a measure of information
4. Information stays relevant
5. Bayesian view of earnings management
6. Numerator versus denominator news
7. Mixtures of normals
8. Information content
9. Fundamental versus information risk
10. When information adds to information asymmetry
11. Value of independent information sources
12. How might market probabilities behave?
13. “Idiosyncratic” versus “undiversifiable” information
Conclusion
References