Hostname: page-component-7bb8b95d7b-cx56b Total loading time: 0 Render date: 2024-09-12T14:21:39.306Z Has data issue: false hasContentIssue false
  • English
  • Français

New Semantics for Bayesian Inference: The Interpretive Problem and Its Solutions

Published online by Cambridge University Press:  01 January 2022

Olav Benjamin Vassend
Get access Rights & Permissions [Opens in a new window]

Abstract

Scientists often study hypotheses that they know to be false. This creates an interpretive problem for Bayesians because the probability assigned to a hypothesis is typically interpreted as the probability that the hypothesis is true. I argue that solving the interpretive problem requires coming up with a new semantics for Bayesian inference. I present and contrast two new semantic frameworks, and I argue that both of them support the claim that there is pervasive pragmatic encroachment on whether a given Bayesian probability assignment is rational.

Type
Research Article
Information
Philosophy of Science , Volume 86 , Issue 4 , October 2019 , pp. 696 - 718
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

I am grateful to audiences at the 2016 meeting of the Philosophy of Science Association, the University of Wisconsin–Madison, and Nanyang Technological University. I am indebted to conversations with Kenny Easwaran, Andrew Forcehimes, Andrea Guardo, and Reuben Stern, in particular, and I am especially thankful to Malcolm Forster, Elliott Sober, Jan Sprenger, and Mike Titelbaum for reading and giving comments on an earlier draft of the article. Research for this article was supported by Nanyang Technological University Start-Up Grant M4082134.

References

Bernardo, José M., and Smith, Adrian F. M.. 1994. Bayesian Theory. New York: Wiley.CrossRefGoogle Scholar
Bissiri, Pier G., Holmes, Chris, and Walker, Stephen. 2016. “A General Framework for Updating Belief Distributions.” Journal of the Royal Statistical Society B 78 (5): 1103–30..Google ScholarPubMed
Box, George E. P. 1980. “Sampling and Bayes’ Inference in Scientific Modelling and Robustness.” Journal of the Royal Statistical Society A 143 (4): 383–430..CrossRefGoogle Scholar
Cevolani, Gustavo, Crupi, Vincenzo, and Festa, Roberto. 2010. “The Whole Truth about Linda: Probability, Verisimilitude, and a Paradox of Conjunction.” In New Essays in Logic and Philosophy of Science, ed. D’Agostino, Marcello, Laudisa, Federico, Giorello, Giulio, Pievani, Telmo, and Sinigaglia, Corrado, 603–15. London: College.Google Scholar
Choi, Jae Won, Cha, Yumi, Kim, Hae-Dong, and Lu, Riyu. 2016. “Relationship between the Maximum Wind Speed and the Minimum Sea Level Pressure for Tropical Cyclones in the Western North Pacific.” Journal of Climatology and Weather Forecasting 4 (3). doi:10.4172/2332-2594.1000180.CrossRefGoogle Scholar
De Heide, Rianne, and Grünwald, Peter D.. 2018. “Why Optional Stopping Is a Problem for Bayesians.” arXiv.org, Cornell University. https://arxiv.org/abs/1708.08278.Google Scholar
Fantl, Jeremy, and McGrath, Matthew. 2002. “Evidence, Pragmatics, and Justification.” Philosophical Review 111 (1): 67–94..CrossRefGoogle Scholar
Festa, Roberto. 1993. Optimum Inductive Methods: A Study in Inductive Probability, Bayesian Statistics, and Verisimilitude. Dordrecht: Springer.CrossRefGoogle Scholar
Forster, Malcolm R. 1995. “Bayes and Bust: Simplicity as a Problem for a Probabilist’s Approach to Confirmation.” British Journal for the Philosophy of Science 46 (3): 399–424..CrossRefGoogle Scholar
Forster, Malcolm R., and Sober, Elliott. 1994. “How to Tell When Simpler, More Unified, or Less AD Hoc Theories Will Provide More Accurate Predictions.” British Journal for the Philosophy of Science 45 (1): 1–35..CrossRefGoogle Scholar
Gelman, Andrew, and Shalizi, Cosma Rohilla. 2013. “Philosophy and the Practice of Bayesian Statistics.” British Journal of Mathematical and Statistical Psychology 66:8–38.CrossRefGoogle ScholarPubMed
Heggarty, Paul, Maguire, Warren, and McMahon, April. 2010. “Splits or Waves? Trees or Webs? How Divergence Measures and Network Analysis Can Unravel Language Histories.” Philosophical Transactions of the Royal Society B 365 (1559): 3829–43..Google ScholarPubMed
Hewitt, Edwin. and Savage, Leonard J.. 1955. “Symmetric Measures on Cartesian Products.” Transactions of the American Mathematical Society 80:470–501.CrossRefGoogle Scholar
Hilpinen, Risto. 1976. “Approximate Truth and Truthlikeness.” In Formal Methods in the Methodology of Empirical Sciences, 19–42. Dordrecht: Springer.CrossRefGoogle Scholar
Jaynes, E. T. 2003. Probability Theory: The Logic of Science. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Key, Jane T., Pericchi, Luis R., and Smith, Adrian F. M.. 1999. “Bayesian Model Choice: What and Why?” In Bayesian Statistics 6, ed. Bernardo, José M., Berger, James O., Dawid, A. Phillip, and M, Adrian F.. Smith, 343–70 Oxford: Oxford University Press.Google Scholar
Knaff, John A., and Zehr, Raymond M.. 2007. “Reexamination of Tropical Cyclone Wind-Pressure Relationship.” Weather and Forecasting 22 (1): 71–88..CrossRefGoogle Scholar
Lewis, David K. 1973. Counterfactuals. Oxford: Blackwell.Google Scholar
Lindley, Dennis V. 1972. Bayesian Statistics, A Review. Montpellier, VT: Capital City.CrossRefGoogle Scholar
Morey, Richard D., Romeijn, Jan-Willem, and Rouder, Jeffrey N.. 2013. “The Humble Bayesian: Model Checking from a Fully Bayesian Perspective.” British Journal of Mathematical and Statistical Psychology 66 (1): 68–75..CrossRefGoogle ScholarPubMed
Moss, Sarah. 2018. Probabilistic Knowledge. Oxford: Oxford University Press.CrossRefGoogle Scholar
Niiniluoto, Iikka. 1986. “Truthlikeness and Bayesian Estimation.” Synthese 67 (2): 321–46..CrossRefGoogle Scholar
Niiniluoto, Iikka. 1987. Truthlikeness. Dordrecht: Springer.CrossRefGoogle Scholar
Niiniluoto, Iikka. 1998. “Verisimilitude: The Third Period.” British Journal for the Philosophy of Science 49 (1): 1–29..CrossRefGoogle Scholar
Northcott, Robert. 2013. “Verisimilitude: A Causal Approach.” Synthese 190 (9): 1471–88..CrossRefGoogle Scholar
Oddie, Graham. 2019. “What Accuracy Could Not Be.” British Journal for the Philosophy of Science 70 (2): 551–80..CrossRefGoogle Scholar
O’Malley, Maureen A., Martin, William, and Dupre, John. 2010. “The Tree of Life: Introduction to an Evolutionary Debate.” Biology and Philosophy 25:441–53.CrossRefGoogle Scholar
Popper, Karl. 1963. Conjectures and Refutations: The Growth of Scientific Knowledge. London: Hutchinson.Google Scholar
Roeber, Blake. 2018. “The Pragmatic Encroachment Debate.” Noûs 52 (1): 171–95..CrossRefGoogle Scholar
Rosenkrantz, Roger. 1980. “Measuring Truthlikeness.” Synthese 45 (3): 463–87..CrossRefGoogle Scholar
Ross, Jacob, and Schroeder, Mark. 2014. “Belief, Credence, and Pragmatic Encroachment.” Philosophy and Phenomenological Research 88 (2): 259–88..CrossRefGoogle Scholar
Rubin, Katherine. 2015. “Total Pragmatic Encroachment and Epistemic Permissiveness.” Pacific Philosophical Quarterly 96 (1): 12–30..CrossRefGoogle Scholar
Schroeder, Mark. 2017. “Rational Stability under Pragmatic Encroachment.” Unpublished manuscript, University of Southern California. https://static1.squarespace.com/static/55505fc8e4b032b4451e4a90/t/59ab96e4cd39c3b55f92d05d/1504417508849/Schroeder+Rational+Stability.pdf.Google Scholar
Shaffer, Michael J. 2001. “Bayesian Confirmation of Theories That Incorporate Idealizations.” Philosophy of Science 68 (1): 36–52..CrossRefGoogle Scholar
Sprenger, Jan. 2009. “Statistics between Inductive Logic and Empirical Science.” Journal of Applied Logic 7 (2): 239–50..CrossRefGoogle Scholar
Sprenger, Jan. 2017. “Conditional Degree of Belief.” Unpublished manuscript, PhilSci archive. http://philsci-archive.pitt.edu/13515/.Google Scholar
Stanley, Jason. 2005. Knowledge and Practical Interests. Oxford: Oxford University Press.CrossRefGoogle Scholar
Velasco, Joel D. 2012. “The Future of Systematics: Tree Thinking without the Tree.” Philosophy of Science 79 (5): 624–36..CrossRefGoogle Scholar
Walker, Stephen G. 2013. “Bayesian Inference with Misspecified Models.” Journal of Statistical Planning and Inference 143:1621–33.Google Scholar