## Networking, Bayesian Style

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Roland Poellinger, Postdoctoral Researcher at the *Munich Center for Mathematical Philosophy* (MCMP) visited Professor Jan-Willem Romeijn, Head of the Department of Theoretical Philosophy at the University of Groningen, The Netherlands, from April to May, 2017.

When I was making plans to spend an intense research visit abroad in Spring 2017, there would not have been a better place for me than Groningen: What unites philosophers in Munich and Groningen is a strong focus on formal methods and Bayesian reasoning. In much of my work, Bayesian networks are the means of choice. Using such nets, I have looked at causal decision theory and paradox in causal reasoning. I developed ideas for integrating causal and non-causal knowledge in an extension of the Bayes net framework, and more recently I have become highly interested in using Bayes nets for reconstructing analogical arguments in science and for making explicit how analogies can help confirming scientific hypotheses. I guess, my interest in paradox also fueled my interest in analogy: In a recent book, Paul Bartha states that “[f]or Bayesians, it may seem quite clear that an analogical argument cannot provide confirmation” (Bartha, 2010). Well, that did not seem so clear to me. Bartha argues that any analogical argument E expressing the analogy relation between source and target domain is – if it is meant to support hypothesis H – necessarily already contained in one’s background knowledge K (as old evidence), such that Pr( H | E & K ) = Pr( H | K). The equality sign shouts at the Bayesian: no confirmation here! I do agree with the argument. But: Shouldn’t the powerful Bayesian framework be able to capture scientific strategies based on analogical reasoning? (See also Beebe & Poellinger, forthcoming) Many, many analogical arguments have proven fruitful for discovery and hypothesis testing in many, many research contexts: Physics, econometrics, medicine, etc. And in pharmacology – the current focus of my work – analogical arguments surface in deep and difficult questions about extrapolation. In his famous and influential paper “The Environment and Disease: Association or Causation?” (1965), *Sir Austin Bradford Hill* lists analogy as one of his famous guidelines towards an informed assessment of potential causes in epidemiology:

In some circumstances it would be fair to judge by analogy. With the effects of thalidomide and rubella before us we would surely be ready to accept slighter but similar evidence with another drug or another viral disease in pregnancy.

A recent paper by *Landes, Osimani, and Poellinger* (2017) explores the possibility of amalgamating all available, potentially heterogeneous evidence in a Bayesian reconstruction of scientific inference for the integrated probabilistic assessment of a drug’s causal side-effects: In this framework, a scientific hypothesis (i.e., a causal claim) is supported by some evidential report, if this evidence is deemed relevant to the hypothesis – most importantly, if study and target can be called *analogous*.

With many ideas (and many questions) about how to relate formal explications of similarity, analogy, extrapolation, and confirmation, I was more than happy to visit Prof. Jan-Willem Romeijn and his group at the *Department of Theoretical Philosophy* at the *University of Groningen* in April and May, 2017. Not only did my project benefit greatly from Jan-Willem Romeijn’s expertise in Bayesian reasoning and statistical methodology, I was also invited to present my project and speak about analogical inference patterns (see Poellinger, forthcoming) at the workshop on “Causality in Psychological Modeling” (15 May, 2017). This event was co-organized by Jan-Willem Romeijn and Markus Eronen (Groningen/Leuven) and featured Laura Bringmann (UG) Denny Borsboom (UvA), as well as Naftali Weinberger (Tilburg). Highly interesting discussions at the overlap of Bayesian reasoning, causal modeling, statistical methodology, and psychometrics are to be continued – which I am very much looking forward to.

I am thankful to Richard Pettigrew, the *Leverhulme Trust*, and the ERC research project “Philosophy of Pharmacology” (grant 639276; principal investigator: Barbara Osimani) for making this exchange happen, and for sparking many ideas I brought back home.

**References**

Bartha, P. F. A. (2010): By Parallel Reasoning: The Construction and Evaluation of Analogical Arguments, Oxford University Press.

Beebe, C. & Poellinger, R. (201X): Confirmation from Analog Models. (submitted)

Hill, A. B. (1965): The Environment and Disease: Association or Causation? Proceedings of the Royal Society of Medicine, 58(5), 295–300.

Landes, J., Osimani B., Poellinger R. (2017): Epistemology of Causal Inference in Pharmacology. Towards a Framework for the Assessment of Harms. European Journal for the Philosophy of Science. DOI: http://dx.doi.org/10.1007/s13194-017-0169-1

Poellinger, R. (201X) Analogy-Based Inference Patterns in Pharmacological Research. In: La Caze, A. & Osimani, B (eds.): Uncertainty in Pharmacology: Epistemology, Methods, and Decisions. Boston Studies in Philosophy of Science. Springer (forthcoming).

## Published in EJPS: "Epistemology of Causal Inference in Pharmacology"

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The paper *Epistemology of Causal Inference in Pharmacology: Towards a Framework for the Assessment of Harms* (47 pages; joint work by Jürgen Landes, Barbara Osimani, and Roland Poellinger) was just published in the *European Journal for Philosophy of Science*. From the abstract:

Philosophical discussions on causal inference in medicine are stuck in dyadic camps, each defending one kind of evidence or method rather than another as best support for causal hypotheses. Whereas Evidence Based Medicine advocates the use of Randomised Controlled Trials and systematic reviews of RCTs as gold standard, philosophers of science emphasise the importance of mechanisms and their distinctive informational contribution to causal inference and assessment. Some have suggested the adoption of a pluralistic approach to causal inference, and an inductive rather than hypothetico-deductive inferential paradigm. However, these proposals deliver no clear guidelines about how such plurality of evidence sources should jointly justify hypotheses of causal associations. We here develop such guidelines by first giving a philosophical analysis of the underpinnings of Hill’s (1965) viewpoints on causality. We then put forward an evidence-amalgamation framework adopting a Bayesian net approach to model causal inference in pharmacology for the assessment of harms. Our framework accommodates a number of intuitions already expressed in the literature concerning the EBM vs. pluralist debate on causal inference, evidence hierarchies, causal holism, relevance (external validity), and reliability.

Find the published version online here or check out the pre-print version on the PhilSci archive server.

## Recording of "The Mind-Brain Entanglement" on iTunes

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The recording of Roland Poellinger's talk on "The Mind-Brain Entanglement" (at LMU Munich, 14 May 2014) is now online and freely available on iTunes U and LMUcast: Click here to download the file or watch the video online.

Abstract: Listing *The Nonreductivist’s Troubles with Mental Causation* (1993) Jaegwon Kim suggested that the only remaining alternatives are the eliminativist’s standpoint or plain denial of the mind’s causal powers if we want to uphold the closure of the physical and reject causal overdetermination at the same time. Nevertheless, explaining stock market trends by referring to investors’ fear of loss is a very familiar example of attributing reality to both domains and acknowledging the mind’s interaction with the world: "if you pick a physical event and trace its causal ancestry or posterity, you may run into mental events" (Kim 1993). In this talk I will use the formal framework of Bayes net causal models in an interventionist understanding (as devised, e.g., by Judea Pearl in *Causality*, 2000) to make the concept of causal influence precise. Investigating structurally similar cases of conflicting causal intuitions will motivate a natural extension of the interventionist Bayes net framework, *Causal Knowledge Patterns*, in which our intuition that the mind makes a difference finds an expression.

Update: More than 600 views and downloads of the recording in the first 10 days online! Thanks!

## "Formal Informal: Imprecise Probabilities" | MCMP joint event with Foundations of Statistics (4 Feb, 2013)

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On Monday, 4 February, 2013, the MCMP is meeting the LMU Stats Department once again: The third edition of our series "Formal Informal" will center about "Imprecise Probabilities" this time. Join us for the discussion in an open round at 6:00pm, Alte Bibliothek, room 245 (Ludwigstraße 33). Presenters will be Thomas Augustin (Statistics/LMU), Radin Dardashti (MCMP/LMU), Marco Cattaneo (Statistics/LMU), Seamus Bradley (MCMP/LMU), and Stephan Hartmann (MCMP/LMU).

From the manifesto: Probability plays a fundamental role in our attempt to grasp and quantify uncertainty. However, considering the common case of limited knowledge about an event, the assignment of precise probabilities can be regarded as a limitation of the approach. Generalising probability theory to imprecise or interval probabilities offers a broader framework within which to discuss uncertainty. This approach has recently become quite popular due to its successful applications in many areas, ranging from social epistemology to econometrics and artificial intelligence.

This edition of Formal Informal will discuss foundations, applications, and problems of Imprecise Probabilities within statistics, philosophy, and physics.

Download the invitation here as a PDF document.

## Imprecise prediction and reliability in intervals - talk at WPMSIIP'12 (13 September, 2012)

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On 13 September, 2012, Roland Poellinger gives a talk at the Fifth Workshop on Principles and Methods of Statistical Inference with Interval Probability (WPMSIIP'12) in Munich, the title: "Superimposing Imprecise Evidence onto Stable Causal Knowledge: Analyzing ‘Prediction’ in the Newcomb Case". The talk sketches a possible extension of the CKP framework and outlines an agenda for introducing interval probabilities into causal reasoning, where specific concepts need to be formalized in an imprecise way – (un)reliability as quality of prediction in the Newcomb case. From the abstract:

In this talk I will prepare the ground for a understanding of causality that enables the causal decision theorist to answer Nozick’s challenge with the solution of one-boxing by drawing on the framework of *causal knowledge patterns*, i.e., Bayes net causal models built upon stable causal relations (cf. Pearl 1995 and 2000/2009) augmented by non-causal knowledge (*epistemic contours*). This rendition allows the careful re-examination of all relevant notions in the original story and facilitates approaching the following questions:

- How may causality in general be understood to allow causal inference from hybrid patterns encoding subjective knowledge?
- How can the notion of
*prediction*be analyzed – philosophically and formally? - If all relations given in the model represent stable causal knowledge, how can imprecise evidence be embedded formally? Or in other words: How can the
*unreliable predictor*be modeled without discarding the core structure?

Finally, in what way could *unreliable prediction* be modeled with interval probability, as motivated by considerations in Nozick’s treatise? And what should be the interpretation of such a rendition?

## "Formal Informal: The Markov Assumption" | MCMP joint event with Foundations of Statistics (13 June, 2012)

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On 13 June, 2012, the MCMP is meeting the LMU Stats Department again: "Formal Informal" will center about "The Markov Assumption". Join us for the discussion in an open round at 6:30pm, Alte Bibliothek, room 245 (Ludwigstraße 33). Presenters will be Conor Mayo-Wilson (CMU Philosophy, currently visitor at the MCMP), Marco Cattaneo (LMU Statistics), and Roland Poellinger (MCMP/LMU).

From the manifesto: Bayesian nets are a powerful means of representing conditional independencies between variables in compact manner. Whatever the size of the domain, consistent inference is facilitated by one simple local requirement: The Markov assumption states that a variable is independent of all other non-successors given the values of its parents in the graph. In causal guise: Direct causes screen off their direct effects from other causal influences. What other ways of reading the Markov assumption are there? Why is it justified? Where does it hold? How can it be bent?

Download the invitation here as a PDF document.