nach oben

Journal of Quantitative Economics

Erschienen in:

30.12.2022 | Original Article

Abductive Inference and C. S. Peirce: 150 Years Later

verfasst von: Subhadeep Mukhopadhyay

Erschienen in: Journal of Quantitative Economics | Ausgabe 1/2023

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

This paper is about two things: (i) Charles Sanders Peirce (1837–1914)—an iconoclastic philosopher and polymath who is among the greatest of American minds. (ii) Abductive inference—a term coined by C. S. Peirce, which he defined as “the process of forming explanatory hypotheses. It is the only logical operation which introduces any new idea.”

1. Abductive inference and quantitative economics. Abductive inference plays a fundamental role in empirical scientific research as a tool for discovery and data analysis. Heckman and Singer (2017) strongly advocated “Economists should abduct.” Arnold Zellner (2007) stressed that “much greater emphasis on reductive [abductive] inference in teaching econometrics, statistics, and economics would be desirable.” But currently, there are no established theory or practical tools that can allow an empirical analyst to abduct. This paper attempts to fill this gap by introducing new principles and concrete procedures to the Economics and Statistics community. I termed the proposed approach as Abductive Inference Machine (AIM).

2. The historical Peirce’s experiment. In 1872, Peirce conducted a series of experiments to determine the distribution of response times to an auditory stimulus, which is widely regarded as one of the most significant statistical investigations in the history of nineteenth-century American mathematical research (Stigler in Ann Stat 239–265, 1978). On the 150th anniversary of this historical experiment, we look back at the Peircean-style abductive inference through a modern statistical lens. Using Peirce’s data, it is shown how empirical analysts can abduct in a systematic and automated manner using AIM.

Vorheriger Artikel Examining the Time Varying Spillover Dynamics of Indian Financial Indictors from Global and Local Economic Uncertainty

Nächster Artikel Heckscher-Ohlin Theory or the Modern Trade Theory: How the Overall Trade Characterizes at the Global Level?

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

U.S. Coast and Geodetic Survey was established on February 10, 1807, by President Thomas Jefferson. It was the nation’s first civilian scientific agency.

For further details on the experimental setup and the full dataset, consult the online Peirce Edition Project: vol 3, p. 133–160 of the chronological edition (Peirce 2009). It’s also available in the R-package quantreg

Peirce made a pioneering contribution to American statistics by developing the concepts that underpin nonparametric density estimation.

However, at that time no theory of GOF was available. It took 30 more years for an English mathematician, Karl Pearson, to make the breakthrough contribution in developing the formal language of the GOF.

The term “normal distribution” was coined by Peirce.

Even Wilson and Hilferty (1929) noted the same: ‘according to our previous experience such long series of observations generally reveal marked departures from the normal law.’

An average statistician uses data to confirm or reject a particular theory/model. A competent statistician uses data to sharpen their theory/model.

According to Peirce, every branch of scientific inquiry exhibits “the vital power of self-correction” that permits us to make progress and grow our knowledge; see, Burch and Parker (2022).

It would be pointless to waste computational resources on the redundant part of the data.

\(d_0(x)\) “fires” actions when the difference in information content between \(F_0\) and \(\widetilde{F}\) reaches a threshold.

The name was inspired from John Tukey (1977, p. 52).

This ‘Two Systems’ analogy was inspired by Daniel Kahneman’s work on ‘Thinking, Fast and Slow.’

Isaac Newton confronted a similar problem in the mid-1600s: He wanted to describe a falling object, which changes its speed every second. The challenge was: How to describe a “moving” object? His revolutionary idea was to focus on modeling the “change,” which led to the development of Calculus and Laws of Motion. Here we are concerned with a similar question: How to change probability distribution when confronted with new data? In our dyadic model (1), the sharpening function d provides the necessary “push to change.”

Under the null model, sample LP-statistic follows asymptotically \(\mathcal {N}(0,n^{-1/2})\).

See, for example, the work of Amos Golan (2018) and Esfandiar Maasoumi (1993) for an excellent review of the usefulness of ‘maxent information-theoretic thinking’ for econometrics and decision sciences. Additional recent works on the application of maximum-entropy techniques in empirical economics can be found in Buansing et al. (2020), Mao et al. (2020) and Lee et al. (2021).

These sets of specially-designed functions provide the simplest and most likely explanation of how the model \(f_0\) differs from reality.

Also see Peirce’s 1979 article on “Economy of Research,” which is widely regarded as the first real attempt to establish the fundamental principles of marginal utility theory Stephen Stigler brought this to my attention.

Also, some misspecifications may be harmless as far as the final decision-making is concerned. Knowing the nature of deficiency can help us avoid over-complicating the model-0.

Discovery is much harder than prediction because one can go away with good prediction without understanding. But for discovery, understanding ‘how and why’ is a must.

It tells empirical analysts where to AIM as they search for possible new discoveries.

In our context, the theory of Laplace’s law of error was confronted with Peirce’s experimental data.

As Herbert Simon said: “Anything that gives us new knowledge gives us an opportunity to be more rational.” From that perspective, AIM could be a powerful tool to guide economic agents in making rational decisions under uncertainty. More details can be found in Mukhopadhyay (2022b).

In other words, we don’t believe in the ‘one-fits-all’ model. Our goal is to provide economists with a systemic principle for iteratively revising their preliminary models by confronting them with real-world data.

It is fundamentally different from model selection or multiple hypothesis testing, which deals with a pre-determined set of alternative models. Model discovery and model selection are two very different things.

Arnold Zellner (2007): ‘a much heavier emphasis on sophisticated simplicity in econometrics is needed.’

In more simple terms, AIM = Learning from data by standing on the foundation of existing knowledge.

A miraculous year: In 1872, exactly the same year of Peirce’s experiment, Ludwig Boltzmann established the probabilistic (statistical) foundation of the entropy function—the birth of modern information theory. As we have seen in this article, Peircean abduction and information theory are intimately connected through the concept of density-sharpening. As a matter of fact, AIM stands on three pillars: Abductive inference + information theory + density-sharpening law.

Bailey, D.C. 2017. Not normal: the uncertainties of scientific measurements. Royal Society Open Science 4 (1): 160600.CrossRef

Box, G.E. 1976. Science and Statistics. The Journal of the American Statistical Association 71 (356): 791–799.CrossRef

Box, G. 2001. Statistics for discovery. Journal of Applied Statistics 28 (3–4): 285–299.CrossRef

Buansing, T.T., A. Golan, and A. Ullah. 2020. An information-theoretic approach for forecasting interval-valued sp500 daily returns. International Journal of Forecasting 36 (3): 800–813.CrossRef

Burch, R. and K. A. Parker (2022). Charles Sanders Peirce. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2022 ed.). Stanford University.

Crease, R.P. 2009. Charles Sanders Peirce and the first absolute measurement standard. Physics Today 62 (12): 39.CrossRef

Golan, A. 2018. Foundations of info-metrics: modeling, inference, and imperfect information. Oxford University Press.

Haavelmo, T. (1944). The probability approach in econometrics. Econometrica: Journal of the Econometric Society, iii–115.

Hanson, N. R. (1965). Patterns of discovery: an inquiry into the conceptual foundations of science. CUP Archive.

Heckman, J.J., and B. Singer. 2017. Abducting economics. American Economic Review 107 (5): 298–302.CrossRef

Jaynes, E.T. 1957. Information theory and statistical mechanics. Physical Reviews 106 (4): 620.CrossRef

Laplace, P. S. (1774). Mémoire sur la probabilité de causes par les évenements. Mémoire de l’académie royale des sciences.

Lee, T.-H., M.Y. Mao, and A. Ullah. 2021. Maximum entropy analysis of consumption-based capital asset pricing model and volatility. Journal of Econometric Methods 10 (1): 1–19.CrossRef

Maasoumi, E. 1993. A compendium to information theory in economics and econometrics. Econometric Reviews 12 (2): 137–181.CrossRef

Mao, Y., A. Ullah, et al. (2020). Information theoretic estimation of econometric functions. Forthcoming in Advances in Info-Metrics: Information and Information Processing across Disciplines.

McCarthy, J., M. L. Minsky, N. Rochester, and C. E. Shannon (1955). A proposal for the Dartmouth Summer Research Project on Artificial Intelligence. Online: http://www-formal.stanford.edu/jmc/history/dartmouth.pdf.

Minsky, M. 1966. Artificial intelligence. Scientific American 215 (3): 257.CrossRef

Mukhopadhyay, S. (2022) A Maximum Entropy Copula Model for Mixed Data: Representation, Estimation, and Applications. Journal of Nonparametric Statistics, 34 (4): 1036-1062.

Mukhopadhyay, S. (2022b). Modelplasticity and abductive decision making. Technical Report, arXiv:2203.03040, 1–27.

Mukhopadhyay, S. 2017. Large-scale mode identification and data-driven sciences. Electronic Journal of Statistics 11 (1): 215–240.CrossRef

Mukhopadhyay, S., and D. Fletcher. 2018. Generalized empirical Bayes modeling via frequentist goodness-of-fit. Nature Scientific Report 8 (9983): 1–15.

Mukhopadhyay, S., and E. Parzen. 2020. Nonparametric universal copula modeling. Applied Stochastic Models in Business and Industry, special issue on “Data Science’’ 36 (1): 77–94.

Parkes, D.C., and M.P. Wellman. 2015. Economic reasoning and artificial intelligence. Science 349 (6245): 267–272.CrossRef

Peirce, C. S. (1873). On the theory of errors of observation. Report of the Superintendent of the U.S. Coast Survey, 200–224.

Peirce, C. S. (1901). The proper treatment of hypotheses: a preliminary chapter, toward an examination of hume’s argument against miracles, in its logic and in its history. MS 692, 890–904.

Peirce, C. S. (1931–58). The collected papers of Charles Sanders Peirce, eds. C Hartshorne, P Weiss (vols. 1-6) and A Burks (vols. 7-8), Cambridge, MA: Harvard University Press, 1931-58 and 1960-66.

Peirce, C. 1902. Minute logic, Chapter I. Intended characters of this treatise. Digital Companion to CS Peirce.

Peirce, C.S. 2009. Writings of Charles S. Peirce: a chronological edition, vol. 3, 1872–1878. Indiana University Press.

Rao, C.R. 2001. Statistics: reflections on the past and visions for the future. Communications in Statistics-Theory and Methods 30 (11): 2235–2257.CrossRef

Russell, B. 1959. Wisdom of the west, a historical survey of western philosophy in its social and political setting. Garden City, NY: Doubleday.

Simon, H. A. (1988). The science of design: creating the artificial. Design Issues, 67–82.

Stigler, S. M. (1978). Mathematical statistics in the early states. The Annals of Statistics, 239–265.

Tukey, J. W. (1972). Exploratory data analysis: as part of a larger whole. In Proceedings of the 18th conference on design of experiments in Army research and development I. Washington, DC, Volume 1010.

Tukey, J.W. 1969. Analyzing data: Sanctification or detective work? American Psychologist 24 (2): 83.CrossRef

Tukey, J.W. 1977. Exploratory data analysis, vol. 2. Mass: Reading.

Wilson, E.B., and M.M. Hilferty. 1929. Note on C. S. Peirce’s experimental discussion of the law of errors. Proceedings of the National Academy of Sciences of USA 15 (2): 120.CrossRef

Zellner, A. 2007. Philosophy and objectives of econometrics. Journal of Econometrics 136 (2): 331–339.CrossRef

Titel: Abductive Inference and C. S. Peirce: 150 Years Later
verfasst von: Subhadeep Mukhopadhyay
Publikationsdatum: 30.12.2022
Verlag: Springer India
Erschienen in: Journal of Quantitative Economics / Ausgabe 1/2023
Print ISSN: 0971-1554
Elektronische ISSN: 2364-1045
DOI: https://doi.org/10.1007/s40953-022-00332-9

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 1/2023

Examining the Time Varying Spillover Dynamics of Indian Financial Indictors from Global and Local Economic Uncertainty

Can Income Inequality be Affected by the Interaction Between ICTs and Human Capital?: The Evidence from Developing Countries

Electricity Tariff Changes and Consumer Sentiment on Household Consumption Expenditure in Malaysia

Nowcasting India’s Quarterly GDP Growth: A Factor-Augmented Time-Varying Coefficient Regression Model (FA-TVCRM)

Multiscale Agricultural Commodities Forecasting Using Wavelet-SARIMA Process

The Determinants of Firm’s Growth in the Telecommunication Services Industry: Empirical Evidence from India