{"title":"Causal Strength","authors":"J. Sprenger, S. Hartmann","doi":"10.1093/oso/9780199672110.003.0006","DOIUrl":"https://doi.org/10.1093/oso/9780199672110.003.0006","url":null,"abstract":"The question “When is C a cause of E?” is well-studied in philosophy—much more than the equally important issue of quantifying the causal strength between C and E. In this chapter, we transfer methods from Bayesian Confirmation Theory to the problem of explicating causal strength. We develop axiomatic foundations for a probabilistic theory of causal strength as difference-making and proceed in three steps: First, we motivate causal Bayesian networks as an adequate framework for defining and comparing measures of causal strength. Second, we demonstrate how specific causal strength measures can be derived from a set of plausible adequacy conditions (method of representation theorems). Third, we use these results to argue for a specific measure of causal strength: the difference that interventions on the cause make for the probability of the effect. An application to outcome measures in medicine and discussion of possible objections concludes the chapter.","PeriodicalId":140328,"journal":{"name":"Bayesian Philosophy of Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130974874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Scientific Objectivity","authors":"J. Sprenger, S. Hartmann","doi":"10.1093/oso/9780199672110.003.0011","DOIUrl":"https://doi.org/10.1093/oso/9780199672110.003.0011","url":null,"abstract":"Subjective Bayesianism is often criticized for a lack of objectivity: (i) it opens the door to the influence of values and biases, (ii) evidence judgments can vary substantially between scientists, (iii) it is not suited for informing policy decisions. We rebut these concerns by bridging the debates on scientific objectivity and Bayesian inference in statistics. First, we show that the above concerns arise equally for frequentist statistical inference. Second, we argue that the involved senses of objectivity are epistemically inert. Third, we show that Subjective Bayesianism promotes other, epistemically relevant senses of scientific objectivity—most notably by increasing the transparency of scientific reasoning.","PeriodicalId":140328,"journal":{"name":"Bayesian Philosophy of Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121147360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Explanatory Power","authors":"J. Sprenger, S. Hartmann","doi":"10.1093/oso/9780199672110.003.0007","DOIUrl":"https://doi.org/10.1093/oso/9780199672110.003.0007","url":null,"abstract":"This chapter motivates why, and under which circumstances, the explanatory power of a scientific hypothesis with respect to a body of evidence can be explicated by means of statistical relevance. This account is traced back to its historic roots in Peirce and Hempel and defended against its critics (e.g., contrasting statistical relevance to purely causal accounts of explanation). Then we derive various Bayesian explications of explanatory power using the method of representation theorems and we compare their properties from a normative point of view. Finally we evaluate how such measures of explanatory power can ground a theory of Inference to the Best Explanation (IBE).","PeriodicalId":140328,"journal":{"name":"Bayesian Philosophy of Science","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116603529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Problem of Old Evidence","authors":"J. Sprenger, S. Hartmann","doi":"10.1093/oso/9780199672110.003.0005","DOIUrl":"https://doi.org/10.1093/oso/9780199672110.003.0005","url":null,"abstract":"In science, phenomena are often unexplained by the available scientific theories. At some point, it may be discovered that a novel theory accounts for this phenomenon—and this seems to confirm the theory because a persistent anomaly is resolved. However, Bayesian confirmation theory—primarily a theory for updating beliefs in the light of learning new information—struggles to describe confirmation by such cases of “old evidence”. We discuss the two main varieties of the Problem of Old Evidence (POE)—the static and the dynamic POE—, criticize existing solutions and develop two novel Bayesian models. They show how the discovery of explanatory and deductive relationships, or the absence of alternative explanations for the phenomenon in question, can confirm a theory. Finally, we assess the overall prospects of Bayesian Confirmation Theory in the light of the POE.","PeriodicalId":140328,"journal":{"name":"Bayesian Philosophy of Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129740811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Conclusion: The Theme Revisited","authors":"J. Sprenger, S. Hartmann","doi":"10.1093/oso/9780199672110.003.0013","DOIUrl":"https://doi.org/10.1093/oso/9780199672110.003.0013","url":null,"abstract":"In this final chapter, we look back on the results of the book and the methods we used. In particular, we enter a discussion whether Bayesian philosophy of science can and should be labeled a proper scientific philosophy due to its combination of formal, conceptual, and empirical methods. Finally, we explore the limitations of the book and we sketch projects for future research (e.g., integrating our results with social epistemology of science and the philosophy of statistical inference).","PeriodicalId":140328,"journal":{"name":"Bayesian Philosophy of Science","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123278045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Theme: Bayesian Philosophy of Science","authors":"J. Sprenger, S. Hartmann","doi":"10.1093/oso/9780199672110.003.0014","DOIUrl":"https://doi.org/10.1093/oso/9780199672110.003.0014","url":null,"abstract":"This chapter sets the stage for what follows, introducing the reader to the philosophical principles and the mathematical formalism behind Bayesian inference and its scientific applications. We explain and motivate the representation of graded epistemic attitudes (“degrees of belief”) by means of specific mathematical structures: probabilities. Then we show how these attitudes are supposed to change upon learning new evidence (“Bayesian Conditionalization”), and how all this relates to theory evaluation, action and decision-making. After sketching the different varieties of Bayesian inference, we present Causal Bayesian Networks as an intuitive graphical tool for making Bayesian inference and we give an overview over the contents of the book.","PeriodicalId":140328,"journal":{"name":"Bayesian Philosophy of Science","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121952644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Learning Conditional Evidence","authors":"J. Sprenger, S. Hartmann","doi":"10.1093/oso/9780199672110.003.0004","DOIUrl":"https://doi.org/10.1093/oso/9780199672110.003.0004","url":null,"abstract":"Learning indicative conditionals and learning relative frequencies have one thing in common: they are examples of conditional evidence, that is, evidence that includes a suppositional element. Standard Bayesian theory does not describe how such evidence affects rational degrees of belief, and natural solutions run into major problems. We propose that conditional evidence is best modeled by a combination of two strategies: First, by generalizing Bayesian Conditionalization to minimizing an appropriate divergence between prior and posterior probability distribution. Second, by representing the relevant causal relations and the implied conditional independence relations in a Bayesian network that constrains both prior and posterior. We show that this approach solves several well-known puzzles about learning conditional evidence (e.g., the notorious Judy Benjamin problem) and that learning an indicative conditional can often be described adequately by conditionalizing on the associated material conditional.","PeriodicalId":140328,"journal":{"name":"Bayesian Philosophy of Science","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114654350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Scientific Realism and the No Miracles Argument","authors":"J. Sprenger, S. Hartmann","doi":"10.1093/oso/9780199672110.003.0003","DOIUrl":"https://doi.org/10.1093/oso/9780199672110.003.0003","url":null,"abstract":"The No Miracles Argument (NMA) is perhaps the most prominent argument in the debate about scientific realism. It contends that the truth of our best scientific theories is the only hypothesis that does not make the astonishing predictive and explanatory success of science a mystery. However, the argument has been criticized from a Bayesian point of view as committing the base rate fallacy. We provide two Bayesian models (one related to the individual-theory-based NMA and one related to the frequency-based NMA) that respond to that objection. The first model takes into account the observed stability of mature scientific theories, the second the success frequency of theories within a scientific discipline. We conclude that the NMA can be used to defend the realist thesis and that its validity is a highly context-sensitive matter.","PeriodicalId":140328,"journal":{"name":"Bayesian Philosophy of Science","volume":"15 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130497508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Simplicity and Model Selection","authors":"J. Sprenger, S. Hartmann","doi":"10.1093/oso/9780199672110.003.0010","DOIUrl":"https://doi.org/10.1093/oso/9780199672110.003.0010","url":null,"abstract":"Is simplicity a virtue of a good scientific theory, and are simpler theories more likely to be true or predictively successful? If so, how much should simplicity count vis-à-vis predictive accuracy? We address this question using Bayesian inference, focusing on the context of statistical model selection and an interpretation of simplicity via the degree of freedoms of a model. We rebut claims to prove the epistemic value of simplicity by means of showing its particular role in Bayesian model selection strategies (e.g., the BIC or the MML). Instead, we show that Bayesian inference in the context of model selection is usually done in a philosophically eclectic, instrumental fashion that is more tuned to practical applications than to philosophical foundations. Thus, these techniques cannot justify a particular “appropriate weight of simplicity in model selection”.","PeriodicalId":140328,"journal":{"name":"Bayesian Philosophy of Science","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133603920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hypothesis Tests and Corroboration","authors":"J. Sprenger, S. Hartmann","doi":"10.1093/oso/9780199672110.003.0009","DOIUrl":"https://doi.org/10.1093/oso/9780199672110.003.0009","url":null,"abstract":"According to Popper and other influential philosophers and scientists, scientific knowledge grows by repeatedly testing our best hypotheses. However, the interpretation of non-significant results—those that do not lead to a “rejection” of the tested hypothesis—poses a major philosophical challenge. To what extent do they corroborate the tested hypothesis or provide a reason to accept it? In this chapter, we prove two impossibility results for measures of corroboration that follow Popper’s criterion of measuring both predictive success and the testability of a hypothesis. Then we provide an axiomatic characterization of a more promising and scientifically useful concept of corroboration and discuss implications for the practice of hypothesis testing and the concept of statistical significance.","PeriodicalId":140328,"journal":{"name":"Bayesian Philosophy of Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130487787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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