Economic Experiments and Inference

Total Page:16

File Type:pdf, Size:1020Kb

Economic Experiments and Inference Economic experiments and inference Norbert Hirschauer (a), Sven Grüner (b), Oliver Mußhoff (c), and Claudia Becker (d) Abstract: Replication crisis and debates about p-values have raised doubts about what we can statisti- cally infer from research findings, both in experimental and observational studies. The goal of this paper is to provide an adequate differentiation of experimental studies that enables researchers to bet- ter understand which inferences can and – perhaps more important – cannot be made from particular designs. Keywords: Economic experiments, ceteris paribus, confounders, control, inference, randomization, random sampling, superpopulation JEL: B41, C18, C90 (a) Martin Luther University Halle-Wittenberg, Institute of Agricultural and Nutritional Sciences, Chair of Agribusiness Management, Karl-Freiherr-von-Fritsch-Str. 4, 06120 Halle (Saale), Germany. Corresponding author and presenter ([email protected]) (b) Martin Luther University Halle-Wittenberg, Institute of Agricultural and Nutritional Sciences, Chair of Agribusiness Management, Karl-Freiherr-von-Fritsch-Str. 4, 06120 Halle (Saale), Germany ([email protected]) (c) Georg August University Göttingen, Department for Agricultural Economics and Rural Develop- ment, Farm Management, Platz der Göttinger Sieben 5, 37073 Göttingen, Germany ([email protected]) (d) Martin Luther University Halle-Wittenberg, Institute of Business Studies, Chair of Statistics, Große Steinstraße 73, 06099 Halle (Saale), Germany. ([email protected]) 1 Economic experiments and inference Abstract: Replication crisis and debates about p-values have raised doubts about what we can statisti- cally infer from research findings, both in experimental and observational studies. The goal of this paper is to provide an adequate differentiation of experimental designs that enables researchers to bet- ter understand which inferences can and – perhaps more important –cannot be made from particular designs. Keywords: Economic experiments, ceteris paribus, confounders, control, inference, randomization, random sampling, superpopulation JEL: B41, C18, C90 1 Introduction Starting with CHAMBERLIN (1948), SAUERMANN and SELTEN (1959), HOGGATT (1959), SIEGEL and FOURAKER (1960), and SMITH (1962), economists have increasingly adopted experimental designs in empirical research over the last decades. Their motivation to do so was to obtain – compared to obser- vational studies – more reliable information about the causalities that govern the behavior of economic agents. Unfortunately, it seems that in the process of adopting the experimental method, no clear-cut and harmonized definition has emerged of what constitutes an economic experiment. Some scholars seem to use randomization as the defining quality of an experiment and equate “experiments” with “randomized controlled trials” (ATHEY and IMBEN 2017). Others include non-randomized designs into the definition as long as behavioral data are generated through a treatment manipulation (HARRISON and LIST (2004). One might speculate that economists tend to conceptually stretch the term “experi- ment” because the seemingly attractive label suggests that they have finally adopted “trustworthy” research methods that are comparable to those in the natural sciences. Whatever the reason, confusion regarding the often fundamentally different types of research designs that are labeled as experiments entails the risk of inferential errors. In general, the inferences that can be made from controlled experiments based on the ceteris paribus approach where “everything else but the item under investigation is held constant” (SAMUELSON and NORDHAUS 1985: 8) are different from those that can be made from observational studies. The former rely on the research design to ex ante ensure ceteris paribus conditions that facilitate the identification of the causal effects of a treatment. Observational studies, in contrast, rely on an ex post control of confounders through statistical modeling that, despite attempts to move from correlation to causation, does not provide a way of ascertaining causal relationships which is as reliable as a strong ex ante research design (ATHEY and IMBEN 2017). But even within experimental approaches, different designs facilitate different inferences. In this paper, we address the question of scientific and statistical induction and, more particularly, the role of the p-value for making inferences beyond the confines of a particular experimental study. What we aim at is an adequate differentiation of experimental designs that enables researchers to better un- derstand which inferences can and – perhaps more important –cannot be made from particular designs. 2 Experiments aimed at identifying causal treatment effects A study is generally considered to be experimental when a researcher deliberately introduces a well- defined treatment (also known as intervention) into a controlled environment. Identifying the effects of 2 the treatment on the units (subjects) under study requires a comparison; often a no-treatment group of subjects is compared to a with-treatment group. Two different designs are used to ensure control and thus ceteris paribus conditions: (i) Randomized controlled trials rely on a between-subject design and randomization to generate equivalence between compared groups; i.e. we randomly assign subjects to treatments to ensure that known and unknown confounders are balanced across treatment groups (sta- tistical independence). (ii) Non-randomized controlled trials, in contrast, rely on a within-subject de- sign and before-and-after comparisons; i.e. we try to hold everything but the treatment constant over time1 and compare the before-and-after-treatment outcomes for each subject of the experimental popu- lation.2 Table 1 sketches out experimental designs based on treatment comparisons. The label “experiment” is first of all used for studies that, instead of using survey data or pre-existing observational data, are based on a deliberate intervention and a design-based control over confounders. The persuasiveness of causal claims depends on the credibility of the alleged control. Comparing randomized treatment groups is generally held to be a more convincing device to identify causal relationships than before- and-after treatment comparisons (CHARNESS et al. 2012).3 This is due to the fact that randomization balances known and unknown confounders across treatment groups and thus ensures statistical inde- pendence.4 In contrast, efforts to hold everything else but the treatment constant over time in before- and-after comparisons are limited by the researcher’s capacity to identify and fix confounders. Table 1: Design-based control for confounding influences in experimental treatment comparisons Randomized-treatment-group com- Before-and-after-treatment compari- parison (between-subject design) son (within-subject design) Intervention by researcher Randomized controlled experi- Non-randomized controlled experi- (experimental study) ments/trials ments/trials No intervention by researcher “Natural experiments” - (observational study) Due to the particular credibility of randomization as a means to establish control over confounders, the use of the term “experiment” – accompanied by the label “natural” – has even been extended to obser- vational settings (see gray print in Table 1) where, instead of a treatment manipulation by a researcher, the socio-economic or natural environment has randomly assigned “treatments” among some set of units. Regarding this terminology, DUNNING (2013: 16) notes “that the label ‘natural experiment’ is perhaps unfortunate. […], the social and political forces that give rise to as-if random assignment of interventions are not generally ‘natural’ in any ordinary sense of that term. […], natural experiments 1 Trying to hold “everything” but the treatment constant over time can be difficult. A particular threat to causal inference arises when subjects’ properties change through treatment exposure. In other words, sequentially ex- posing subjects to multiple treatments may cause order effects that violate the ceteris paribus condition (CHARNESS et al. 2012). 2 The term “non-randomized controlled trial” is also used for between-subject designs when the technique of assigning subjects to treatments, e.g. alternate assignment, is not truly random but claimed to be as good as a random. 3 CZIBOR et al. (2019) emphasize that within-subject designs also have advantages. Besides the fact that they can more effectively make use of small experimental populations, they facilitate the identification of higher moments of the distribution. Whereas between-subject designs are limited to estimating average treatment effects, within- subject designs enable researchers to look at quantiles and assess heterogeneous treatment effects among sub- jects. 4 DUFLO et al. (2007) note that randomization only achieves that confounders are balanced across treatments “in expectation;” i.e. balance is only ensured if we have a “sufficiently” large experimental population to start with (law of large numbers). In the case of a very small experimental population, an observed difference between two randomized treatment groups could easily be contaminated by unbalanced confounders. 3 are observational studies, not true experiments, again, because they lack an experimental manipula- tion. In sum, natural experiments are neither natural nor experiments.”5 3 Inferences in experimental
Recommended publications
  • Introduction to Biostatistics
    Introduction to Biostatistics Jie Yang, Ph.D. Associate Professor Department of Family, Population and Preventive Medicine Director Biostatistical Consulting Core Director Biostatistics and Bioinformatics Shared Resource, Stony Brook Cancer Center In collaboration with Clinical Translational Science Center (CTSC) and the Biostatistics and Bioinformatics Shared Resource (BB-SR), Stony Brook Cancer Center (SBCC). OUTLINE What is Biostatistics What does a biostatistician do • Experiment design, clinical trial design • Descriptive and Inferential analysis • Result interpretation What you should bring while consulting with a biostatistician WHAT IS BIOSTATISTICS • The science of (bio)statistics encompasses the design of biological/clinical experiments the collection, summarization, and analysis of data from those experiments the interpretation of, and inference from, the results How to Lie with Statistics (1954) by Darrell Huff. http://www.youtube.com/watch?v=PbODigCZqL8 GOAL OF STATISTICS Sampling POPULATION Probability SAMPLE Theory Descriptive Descriptive Statistics Statistics Inference Population Sample Parameters: Inferential Statistics Statistics: 흁, 흈, 흅… 푿ഥ , 풔, 풑ෝ,… PROPERTIES OF A “GOOD” SAMPLE • Adequate sample size (statistical power) • Random selection (representative) Sampling Techniques: 1.Simple random sampling 2.Stratified sampling 3.Systematic sampling 4.Cluster sampling 5.Convenience sampling STUDY DESIGN EXPERIEMENT DESIGN Completely Randomized Design (CRD) - Randomly assign the experiment units to the treatments
    [Show full text]
  • Experimentation Science: a Process Approach for the Complete Design of an Experiment
    Kansas State University Libraries New Prairie Press Conference on Applied Statistics in Agriculture 1996 - 8th Annual Conference Proceedings EXPERIMENTATION SCIENCE: A PROCESS APPROACH FOR THE COMPLETE DESIGN OF AN EXPERIMENT D. D. Kratzer K. A. Ash Follow this and additional works at: https://newprairiepress.org/agstatconference Part of the Agriculture Commons, and the Applied Statistics Commons This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License. Recommended Citation Kratzer, D. D. and Ash, K. A. (1996). "EXPERIMENTATION SCIENCE: A PROCESS APPROACH FOR THE COMPLETE DESIGN OF AN EXPERIMENT," Conference on Applied Statistics in Agriculture. https://doi.org/ 10.4148/2475-7772.1322 This is brought to you for free and open access by the Conferences at New Prairie Press. It has been accepted for inclusion in Conference on Applied Statistics in Agriculture by an authorized administrator of New Prairie Press. For more information, please contact [email protected]. Conference on Applied Statistics in Agriculture Kansas State University Applied Statistics in Agriculture 109 EXPERIMENTATION SCIENCE: A PROCESS APPROACH FOR THE COMPLETE DESIGN OF AN EXPERIMENT. D. D. Kratzer Ph.D., Pharmacia and Upjohn Inc., Kalamazoo MI, and K. A. Ash D.V.M., Ph.D., Town and Country Animal Hospital, Charlotte MI ABSTRACT Experimentation Science is introduced as a process through which the necessary steps of experimental design are all sufficiently addressed. Experimentation Science is defined as a nearly linear process of objective formulation, selection of experimentation unit and decision variable(s), deciding treatment, design and error structure, defining the randomization, statistical analyses and decision procedures, outlining quality control procedures for data collection, and finally analysis, presentation and interpretation of results.
    [Show full text]
  • Statistical Inferences Hypothesis Tests
    STATISTICAL INFERENCES HYPOTHESIS TESTS Maªgorzata Murat BASIC IDEAS Suppose we have collected a representative sample that gives some information concerning a mean or other statistical quantity. There are two main questions for which statistical inference may provide answers. 1. Are the sample quantity and a corresponding population quantity close enough together so that it is reasonable to say that the sample might have come from the population? Or are they far enough apart so that they likely represent dierent populations? 2. For what interval of values can we have a specic level of condence that the interval contains the true value of the parameter of interest? STATISTICAL INFERENCES FOR THE MEAN We can divide statistical inferences for the mean into two main categories. In one category, we already know the variance or standard deviation of the population, usually from previous measurements, and the normal distribution can be used for calculations. In the other category, we nd an estimate of the variance or standard deviation of the population from the sample itself. The normal distribution is assumed to apply to the underlying population, but another distribution related to it will usually be required for calculations. TEST OF HYPOTHESIS We are testing the hypothesis that a sample is similar enough to a particular population so that it might have come from that population. Hence we make the null hypothesis that the sample came from a population having the stated value of the population characteristic (the mean or the variation). Then we do calculations to see how reasonable such a hypothesis is. We have to keep in mind the alternative if the null hypothesis is not true, as the alternative will aect the calculations.
    [Show full text]
  • A Field Experiment with Job Seekers in Germany Search:Learning Job About IZA DP No
    IZA DP No. 9040 Learning about Job Search: A Field Experiment with Job Seekers in Germany Steffen Altmann Armin Falk Simon Jäger Florian Zimmermann May 2015 DISCUSSION PAPER SERIES Forschungsinstitut zur Zukunft der Arbeit Institute for the Study of Labor Learning about Job Search: A Field Experiment with Job Seekers in Germany Steffen Altmann University of Copenhagen and IZA Armin Falk University of Bonn, CEPR, CESifo, DIW, IZA and MPI Simon Jäger Harvard University and IZA Florian Zimmermann University of Zurich, CESifo and IZA Discussion Paper No. 9040 May 2015 IZA P.O. Box 7240 53072 Bonn Germany Phone: +49-228-3894-0 Fax: +49-228-3894-180 E-mail: [email protected] Any opinions expressed here are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but the institute itself takes no institutional policy positions. The IZA research network is committed to the IZA Guiding Principles of Research Integrity. The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. IZA is an independent nonprofit organization supported by Deutsche Post Foundation. The center is associated with the University of Bonn and offers a stimulating research environment through its international network, workshops and conferences, data service, project support, research visits and doctoral program. IZA engages in (i) original and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public.
    [Show full text]
  • The Focused Information Criterion in Logistic Regression to Predict Repair of Dental Restorations
    THE FOCUSED INFORMATION CRITERION IN LOGISTIC REGRESSION TO PREDICT REPAIR OF DENTAL RESTORATIONS Cecilia CANDOLO1 ABSTRACT: Statistical data analysis typically has several stages: exploration of the data set; deciding on a class or classes of models to be considered; selecting the best of them according to some criterion and making inferences based on the selected model. The cycle is usually iterative and will involve subject-matter considerations as well as statistical insights. The conclusion reached after such a process depends on the model(s) selected, but the consequent uncertainty is not usually incorporated into the inference. This may lead to underestimation of the uncertainty about quantities of interest and overoptimistic and biased inferences. This framework has been the aim of research under the terminology of model uncertainty and model averanging in both, frequentist and Bayesian approaches. The former usually uses the Akaike´s information criterion (AIC), the Bayesian information criterion (BIC) and the bootstrap method. The last weigths the models using the posterior model probabilities. This work consider model selection uncertainty in logistic regression under frequentist and Bayesian approaches, incorporating the use of the focused information criterion (FIC) (CLAESKENS and HJORT, 2003) to predict repair of dental restorations. The FIC takes the view that a best model should depend on the parameter under focus, such as the mean, or the variance, or the particular covariate values. In this study, the repair or not of dental restorations in a period of eighteen months depends on several covariates measured in teenagers. The data were kindly provided by Juliana Feltrin de Souza, a doctorate student at the Faculty of Dentistry of Araraquara - UNESP.
    [Show full text]
  • Field Experiments in Development Economics1 Esther Duflo Massachusetts Institute of Technology
    Field Experiments in Development Economics1 Esther Duflo Massachusetts Institute of Technology (Department of Economics and Abdul Latif Jameel Poverty Action Lab) BREAD, CEPR, NBER January 2006 Prepared for the World Congress of the Econometric Society Abstract There is a long tradition in development economics of collecting original data to test specific hypotheses. Over the last 10 years, this tradition has merged with an expertise in setting up randomized field experiments, resulting in an increasingly large number of studies where an original experiment has been set up to test economic theories and hypotheses. This paper extracts some substantive and methodological lessons from such studies in three domains: incentives, social learning, and time-inconsistent preferences. The paper argues that we need both to continue testing existing theories and to start thinking of how the theories may be adapted to make sense of the field experiment results, many of which are starting to challenge them. This new framework could then guide a new round of experiments. 1 I would like to thank Richard Blundell, Joshua Angrist, Orazio Attanasio, Abhijit Banerjee, Tim Besley, Michael Kremer, Sendhil Mullainathan and Rohini Pande for comments on this paper and/or having been instrumental in shaping my views on these issues. I thank Neel Mukherjee and Kudzai Takavarasha for carefully reading and editing a previous draft. 1 There is a long tradition in development economics of collecting original data in order to test a specific economic hypothesis or to study a particular setting or institution. This is perhaps due to a conjunction of the lack of readily available high-quality, large-scale data sets commonly available in industrialized countries and the low cost of data collection in developing countries, though development economists also like to think that it has something to do with the mindset of many of them.
    [Show full text]
  • On Boundaries Between Field Experiment, Action Research and Design Research
    Pertti Järvinen On boundaries between field experiment, action research and design research UNIVERSITY OF TAMPERE SCHOOL OF INFORMATION SCIENCES REPORTS IN INFORMATION SCIENCES 14 TAMPERE 2012 UNIVERSITY OF TAMPERE SCHOOL OF INFORMATION SCIENCES REPORTS IN INFORMATION SCIENCES 14 JUNE 2012 Pertti Järvinen On boundaries between field experiment, action research and design research SCHOOL OF INFORMATION SCIENCES FIN‐33014 UNIVERSITY OF TAMPERE ISBN 978‐951‐44‐8883‐2 ISSN‐L 1799‐8158 ISSN 1799‐8158 On boundaries between field experiment, action research and design research Pertti Järvinen School of Information Sciences University of Tampere Abstract The practice-science gap is often emphasized during the last years. It has also had such a form as competition between relevance and rigor, although both must be taken care. The three research methods (field experiment, action research and design research) are sometimes recommended to be used interchangeable. But we shall show they are quite different. We try to analyze and describe their boundaries and division of labor between practitioners and researchers. We shall also correct some long-lasting misconceptions and propose some further research topic. Introduction Mathiassen and Nielsen (2008) studied the articles published in the Scandinavian Journal of Information Systems during 20 years and found that empirical articles have a great share of the all the published articles. Majority of the authors are from the Scandinavian countries. This seems to show that practice is much appreciated among the Scandinavian researchers and practical emphasis is characteristic in the Scandinavian research culture. We shall in this paper consider three empirical research methods (field experiment, action research and design research).
    [Show full text]
  • Field Experiments: a Bridge Between Lab and Naturally-Occurring Data
    NBER WORKING PAPER SERIES FIELD EXPERIMENTS: A BRIDGE BETWEEN LAB AND NATURALLY-OCCURRING DATA John A. List Working Paper 12992 http://www.nber.org/papers/w12992 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 March 2007 *This study is based on plenary talks at the 2005 International Meetings of the Economic Science Association, the 2006 Canadian Economic Association, and the 2006 Australian Econometric Association meetings. The paper is written as an introduction to the BE-JEAP special issue on Field Experiments that I have edited; thus my focus is on the areas to which these studies contribute. Some of the arguments parallel those contained in my previous work, most notably the working paper version of Levitt and List (2006) and Harrison and List (2004). Don Fullerton, Dean Karlan, Charles Manski, and an anonymous reporter provided remarks that improved the study. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research. © 2007 by John A. List. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Field Experiments: A Bridge Between Lab and Naturally-Occurring Data John A. List NBER Working Paper No. 12992 March 2007 JEL No. C9,C90,C91,C92,C93,D01,H41,Q5,Q51 ABSTRACT Laboratory experiments have been used extensively in economics in the past several decades to lend both positive and normative insights into a myriad of important economic issues.
    [Show full text]
  • Double Blind Trials Workshop
    Double Blind Trials Workshop Introduction These activities demonstrate how double blind trials are run, explaining what a placebo is and how the placebo effect works, how bias is removed as far as possible and how participants and trial medicines are randomised. Curriculum Links KS3: Science SQA Access, Intermediate and KS4: Biology Higher: Biology Keywords Double-blind trials randomisation observer bias clinical trials placebo effect designing a fair trial placebo Contents Activities Materials Activity 1 Placebo Effect Activity Activity 2 Observer Bias Activity 3 Double Blind Trial Role Cards for the Double Blind Trial Activity Testing Layout Background Information Medicines undergo a number of trials before they are declared fit for use (see classroom activity on Clinical Research for details). In the trial in the second activity, pupils compare two potential new sunscreens. This type of trial is done with healthy volunteers to see if the there are any side effects and to provide data to suggest the dosage needed. If there were no current best treatment then this sort of trial would also be done with patients to test for the effectiveness of the new medicine. How do scientists make sure that medicines are tested fairly? One thing they need to do is to find out if their tests are free of bias. Are the medicines really working, or do they just appear to be working? One difficulty in designing fair tests for medicines is the placebo effect. When patients are prescribed a treatment, especially by a doctor or expert they trust, the patient’s own belief in the treatment can cause the patient to produce a response.
    [Show full text]
  • Observational Studies and Bias in Epidemiology
    The Young Epidemiology Scholars Program (YES) is supported by The Robert Wood Johnson Foundation and administered by the College Board. Observational Studies and Bias in Epidemiology Manuel Bayona Department of Epidemiology School of Public Health University of North Texas Fort Worth, Texas and Chris Olsen Mathematics Department George Washington High School Cedar Rapids, Iowa Observational Studies and Bias in Epidemiology Contents Lesson Plan . 3 The Logic of Inference in Science . 8 The Logic of Observational Studies and the Problem of Bias . 15 Characteristics of the Relative Risk When Random Sampling . and Not . 19 Types of Bias . 20 Selection Bias . 21 Information Bias . 23 Conclusion . 24 Take-Home, Open-Book Quiz (Student Version) . 25 Take-Home, Open-Book Quiz (Teacher’s Answer Key) . 27 In-Class Exercise (Student Version) . 30 In-Class Exercise (Teacher’s Answer Key) . 32 Bias in Epidemiologic Research (Examination) (Student Version) . 33 Bias in Epidemiologic Research (Examination with Answers) (Teacher’s Answer Key) . 35 Copyright © 2004 by College Entrance Examination Board. All rights reserved. College Board, SAT and the acorn logo are registered trademarks of the College Entrance Examination Board. Other products and services may be trademarks of their respective owners. Visit College Board on the Web: www.collegeboard.com. Copyright © 2004. All rights reserved. 2 Observational Studies and Bias in Epidemiology Lesson Plan TITLE: Observational Studies and Bias in Epidemiology SUBJECT AREA: Biology, mathematics, statistics, environmental and health sciences GOAL: To identify and appreciate the effects of bias in epidemiologic research OBJECTIVES: 1. Introduce students to the principles and methods for interpreting the results of epidemio- logic research and bias 2.
    [Show full text]
  • What Is Statistic?
    What is Statistic? OPRE 6301 In today’s world. ...we are constantly being bombarded with statistics and statistical information. For example: Customer Surveys Medical News Demographics Political Polls Economic Predictions Marketing Information Sales Forecasts Stock Market Projections Consumer Price Index Sports Statistics How can we make sense out of all this data? How do we differentiate valid from flawed claims? 1 What is Statistics?! “Statistics is a way to get information from data.” Statistics Data Information Data: Facts, especially Information: Knowledge numerical facts, collected communicated concerning together for reference or some particular fact. information. Statistics is a tool for creating an understanding from a set of numbers. Humorous Definitions: The Science of drawing a precise line between an unwar- ranted assumption and a forgone conclusion. The Science of stating precisely what you don’t know. 2 An Example: Stats Anxiety. A business school student is anxious about their statistics course, since they’ve heard the course is difficult. The professor provides last term’s final exam marks to the student. What can be discerned from this list of numbers? Statistics Data Information List of last term’s marks. New information about the statistics class. 95 89 70 E.g. Class average, 65 Proportion of class receiving A’s 78 Most frequent mark, 57 Marks distribution, etc. : 3 Key Statistical Concepts. Population — a population is the group of all items of interest to a statistics practitioner. — frequently very large; sometimes infinite. E.g. All 5 million Florida voters (per Example 12.5). Sample — A sample is a set of data drawn from the population.
    [Show full text]
  • Structured Statistical Models of Inductive Reasoning
    CORRECTED FEBRUARY 25, 2009; SEE LAST PAGE Psychological Review © 2009 American Psychological Association 2009, Vol. 116, No. 1, 20–58 0033-295X/09/$12.00 DOI: 10.1037/a0014282 Structured Statistical Models of Inductive Reasoning Charles Kemp Joshua B. Tenenbaum Carnegie Mellon University Massachusetts Institute of Technology Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. This article presents a Bayesian framework that attempts to meet both goals and describe 4 applications of the framework: a taxonomic model, a spatial model, a threshold model, and a causal model. Each model makes probabi- listic inferences about the extensions of novel properties, but the priors for the 4 models are defined over different kinds of structures that capture different relationships between the categories in a domain. The framework therefore shows how statistical inference can operate over structured background knowledge, and the authors argue that this interaction between structure and statistics is critical for explaining the power and flexibility of human reasoning. Keywords: inductive reasoning, property induction, knowledge representation, Bayesian inference Humans are adept at making inferences that take them beyond This article describes a formal approach to inductive inference the limits of their direct experience.
    [Show full text]