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  1. Malcolm R. Forster & Alexey Kryukov (2003). The Emergence of the Macroworld: A Study of Intertheory Relations in Classical and Quantum Mechanics. Philosophy of Science 70 (5):1039-1051.
    Classical mechanics is empirically successful because the probabilistic mean values of quantum mechanical observables follow the classical equations of motion to a good approximation (Messiah 1970, 215). We examine this claim for the one‐dimensional motion of a particle in a box, and extend the idea by deriving a special case of the ideal gas law in terms of the mean value of a generalized force used to define “pressure.” The examples illustrate the importance of probabilistic averaging as a method of (...)
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  2. Kent Staley, Probability in Fine-Tuning Design Arguments.
    This paper examines probabilistic versions of the fine-tuning argument for design (FTA), with an emphasis on the interpretation of the probability statements involved in such arguments. Three categories of probability are considered: physical, epistemic, and logical. Of the three possibilities, I argue that only logical probability could possibly support a cogent probabilistic FTA. However, within that framework, the premises of the argument require a level of justification that has not been met, and, it is reasonable to believe, will not be (...)
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  3. Michael J. Wade, Rasmus Grønfeldt Winther, Aneil F. Agrawal & Charles J. Goodnight (2001). Alternative Definitions of Epistasis: Dependence and Interaction. Trends in Ecology and Evolution 16 (9):498-504.
    Although epistasis is at the center of the Fisher-Wright debate, biologists not involved in the controversy are often unaware that there are actually two different formal definitions of epistasis. We compare concepts of genetic independence in the two theoretical traditions of evolutionary genetics, population genetics and quantitative genetics, and show how independence of gene action (represented by the multiplicative model of population genetics) can be different from the absence of gene interaction (represented by the linear additive model of quantitative genetics). (...)
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Probability in the Philosophy of Religion
  1. Isaac Choi (forthcoming). Is Petitionary Prayer Superfluous? Oxford Studies in Philosophy of Religion.
  2. Josef Schurz (2007). Probability and Evolution. Why the Probability Argument of Creationists is Wrong. Journal for General Philosophy of Science 38 (1):163 - 165.
    Evolution is a time process. It proceeds in steps of definite length. The probability of each step is relatively high, so self organization of complex systems will be possible in finite time. Prerequisite for such a process is a selection rule, which certainly exists in evolution. Therefore, it would be wrong to calculate the probability of the formation of a complex system solely on the basis of the number of its components and as a momentary event.
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Probability in the Philosophy of Religion, Misc
  1. István Aranyosi (2013). God, Mind, and Logical Space. Palgrave Macmillan.
    In God, Mind and Logical Space István Aranyosi takes the reader on a journey for the mind by revisiting the fundamental questions and the everlasting debates in philosophy of religion, ontology, and the philosophy of mind. The first part deals with issues in ontology, and the author puts forward a radical view according to which all thinkable objects and states of affairs have an equal claim to existence in a way that renders existence a relative notion. In the second part (...)
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  2. Lara Buchak (forthcoming). Rational Faith and Justified Belief. In Tim O'Connor & Laura Goins (eds.), Religious Faith and Intellectual Virtue.
    In “Can it be rational to have faith?”, it was argued that to have faith in some proposition consists, roughly speaking, in stopping one’s search for evidence and committing to act on that proposition without further evidence. That paper also outlined when and why stopping the search for evidence and acting is rationally required. Because the framework of that paper was that of formal decision theory, it primarily considered the relationship between faith and degrees of belief, rather than between faith (...)
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  3. Lara Buchak (2014). Learning Not to Be Naïve: A Comment on the Exchange Between Perrine/Wykstra and Draper. In Trent Dougherty & Justin McBrayer (eds.), Skeptical Theism: New Essays. Oxford University Press.
    Does postulating skeptical theism undermine the claim that evil strongly confirms atheism over theism? According to Perrine and Wykstra, it does undermine the claim, because evil is no more likely on atheism than on skeptical theism. According to Draper, it does not undermine the claim, because evil is much more likely on atheism than on theism in general. I show that the probability facts alone do not resolve their disagreement, which ultimately rests on which updating procedure – conditionalizing or updating (...)
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  4. Lara Buchak (2012). Can It Be Rational to Have Faith? In Jacob Chandler & Victoria Harrison (eds.), Probability in the Philosophy of Religion. Oxford University Press. 225.
    This paper provides an account of what it is to have faith in a proposition p, in both religious and mundane contexts. It is argued that faith in p doesn’t require adopting a degree of belief that isn’t supported by one’s evidence but rather it requires terminating one’s search for further evidence and acting on the supposition that p. It is then shown, by responding to a formal result due to I.J. Good, that doing so can be rational in a (...)
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  5. Lara Buchak (2012). Can It Be Rational to Have Faith? In Jake Chandler & Victoria Harrison (eds.), Probability in the Philosophy of Religion. Oup Oxford. 225.
  6. Jake Chandler & Victoria Harrison (eds.) (2012). Probability in the Philosophy of Religion. OUP Oxford.
    At a time in which probability theory is exerting an unprecedented influence on epistemology and philosophy of science, promising to deliver an exact and unified foundation for the philosophy of rational inference and decision-making, it is worth remembering that the philosophy of religion has long proven to be an extremely fertile ground for the application of probabilistic thinking to traditional epistemological debates. This volume brings together original contributions from twelve contemporary researchers, both established and emerging, to offer a representative sample (...)
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  7. Georg J. W. Dorn (1987). Zu Bolzanos Wahrscheinlichkeitslehre. Philosophia Naturalis 24:423–441.
    Bolzano hat seine Wahrscheinlichkeitslehre in 15 Punkten im § 14 des zweiten Teils seiner Religionswissenschaft sowie in 20 Punkten im § 161 des zweiten Bandes seiner Wissenschaftslehre niedergelegt. (Ich verweise auf die Religionswissenschaft mit 'RW II', auf die Wissenschaftslehre mit 'WL II'.) In der RW II (vgl. p. 37) ist seine Wahrscheinlichkeitslehre eingebettet in seine Ausführungen "Über die Natur der historischen Erkenntniß, besonders in Hinsicht auf Wunder", und die Lehrsätze, die er dort zusammenstellt, dienen dem ausdrücklichen Zweck, mit mathematischem Rüstzeug (...)
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  8. Steven M. Duncan, Theism and Christianity.
    In this essay, I investigate the implications for the discussion of theism in philosophy of religion for the beliefs of ordinary Christians and conclude that, in light of its historical development, those implications are minimal.
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  9. William Hasker (2002). Is Christianity Probable? Swinburne's Apologetic Programme. Religious Studies 38 (3):253-264.
    Richard Swinburne's tetralogy on Christian doctrine, together with his earlier trilogy on the philosophy of theism, is one of the most important apologetic projects of recent times. This paper focuses on some difficulties with this project that stem from Swinburne's use of confirmation theory. Arguably, the problem of dwindling probabilities, pointed out by Plantinga, has not been solved. The paper is principally focused, however, on the ways in which Swinburne's confirmation theory contributes to his comparative neglect of the personal, existential (...)
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  10. Richard Swinburne (forthcoming). Bayes, God, and the Multiverse. Philosophical Explorations.
  1. Masanari Asano, Irina Basieva, Andrei Khrennikov, Masanori Ohya & Ichiro Yamato (2013). Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law. Foundations of Physics 43 (7):895-911.
    There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological (...)
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  2. Yemima Ben-Menahem & Meir Hemmo (eds.) (2012). Probability in Physics. Springer.
    Emch, G.G., Liu, C.: The Logic of Thermostatistical Physics. Springer, Berlin/ Heidelberg (2002) 11. Frigg, R., Werndl, C.: Entropy – a guide for the perplexed. Forthcoming in: Beisbart, C., Hartmann, S. (eds.) Probabilities in Physics. Oxford  ...
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  3. Dennis Dieks (2010). Physical and Philosophical Perspectives on Probability, Explanation and Time (Workshop of the ESF Programme "The Philosophy of Science in a European Perspective", Utrecht University, 19–20 October 2009). [REVIEW] Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 41 (2):383 - 388.
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  4. Ellery Eells & James H. Fetzer (eds.) (2010). The Place of Probability in Science. Springer.
    To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...
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  5. Artur Ekert, Complex and Unpredictable Cardano.
    At a purely instrumental level, quantum theory is all about multiplication, addition and taking mod squares of complex numbers called probability amplitudes. The rules for combining amplitudes are deceptively simple. When two or more events are independent you multiply their respective probability amplitudes and when they are mutually exclusive you add them. Whenever you want to calculate probabilities you take mod squares of respective amplitudes. That’s it. If you are prepared to ignore the explanatory power of the theory (which you (...)
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  6. Ian G. Fuss & Daniel J. Navarro (2013). Open Parallel Cooperative and Competitive Decision Processes: A Potential Provenance for Quantum Probability Decision Models. Topics in Cognitive Science 5 (4):818-843.
    In recent years quantum probability models have been used to explain many aspects of human decision making, and as such quantum models have been considered a viable alternative to Bayesian models based on classical probability. One criticism that is often leveled at both kinds of models is that they lack a clear interpretation in terms of psychological mechanisms. In this paper we discuss the mechanistic underpinnings of a quantum walk model of human decision making and response time. The quantum walk (...)
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  7. Shan Gao, The Basis of Indeterminism.
    We show that the motion of particles may be essentially discontinuous and random.
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  8. Amihud Gilead (2014). Pure Possibilities and Some Striking Scientific Discoveries. Foundations of Chemistry 16 (2):149-163.
    Regardless or independent of any actuality or actualization and exempt from spatiotemporal and causal conditions, each individual possibility is pure. Actualism excludes the existence of individual pure possibilities, altogether or at least as existing independently of actual reality. In this paper, I demonstrate, on the grounds of my possibilist metaphysics—panenmentalism—how some of the most fascinating scientific discoveries in chemistry could not have been accomplished without relying on pure possibilities and the ways in which they relate to each other (for instance, (...)
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  9. Amihud Gilead (2013). Shechtman's Three Question Marks: Possibility, Impossibility, and Quasicrystals. [REVIEW] Foundations of Chemistry 15 (2):209-224.
    The revolutionary discovery of actual quasicrystals, thanks to Dan Shechtman’s stamina, is a golden opportunity to analyze once again the role that pure (“theoretical”) possibilities and saving them plays in scientific progress. Some theoreticians, primarily Alan Mackay, contributed to saving pure possibilities of quasicrystalline structures and to opening materials science for them. My analysis rests upon an original modal metaphysics—panenmentalism—which I introduced and have been developing since 1999, quite independently of any familiarity with modern crystallography, and which deals with saving (...)
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  10. Sheldon Goldstein (2012). Typicality and Notions of Probability in Physics. In. In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. 59--71.
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  11. Lucien Hardy & William K. Wootters (2012). Limited Holism and Real-Vector-Space Quantum Theory. Foundations of Physics 42 (3):454-473.
    Quantum theory has the property of “local tomography”: the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this paper a class of theories more holistic than quantum theory in that they are constrained only by “bilocal tomography”: the state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, (...)
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  12. James Hawthorne & Michael Silberstein (1995). For Whom the Bell Arguments Toll. Synthese 102 (1):99-138.
    We will formulate two Bell arguments. Together they show that if the probabilities given by quantum mechanics are approximately correct, then the properties exhibited by certain physical systems must be nontrivially dependent on thetypes of measurements performedand eithernonlocally connected orholistically related to distant events. Although a number of related arguments have appeared since John Bell's original paper (1964), they tend to be either highly technical or to lack full generality. The following arguments depend on the weakest of premises, and the (...)
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  13. Michael Heller, Leszek Pysiak & Wiesław Sasin (2011). Fundamental Problems in the Unification of Physics. Foundations of Physics 41 (5):905-918.
    We discuss the following problems, plaguing the present search for the “final theory”: (1) How to find a mathematical structure rich enough to be suitably approximated by the mathematical structures of general relativity and quantum mechanics? (2) How to reconcile nonlocal phenomena of quantum mechanics with time honored causality and reality postulates? (3) Does the collapse of the wave function contain some hints concerning the future quantum gravity theory? (4) It seems that the final theory cannot avoid the problem of (...)
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  14. Jenann Ismael, Probability in Classical Physics: The Fundamental Measure.
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  15. Edwin T. Jaynes (1973). The Well-Posed Problem. Foundations of Physics 3 (4):477-493.
    Many statistical problems, including some of the most important for physical applications, have long been regarded as underdetermined from the standpoint of a strict frequency definition of probability; yet they may appear wellposed or even overdetermined by the principles of maximum entropy and transformation groups. Furthermore, the distributions found by these methods turn out to have a definite frequency correspondence; the distribution obtained by invariance under a transformation group is by far the most likely to be observed experimentally, in the (...)
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  16. Adrian Kent (2010). One World Versus Many: The Inadequacy of Everettian Accounts of Evolution, Probability, and Scientific Confirmation. In Simon Saunders, Jonathan Barrett, Adrian Kent & David Wallace (eds.), Many Worlds?: Everett, Quantum Theory, & Reality. Oup Oxford.
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  17. Andrei Khrennikov (2005). The Principle of Supplementarity: A Contextual Probabilistic Viewpoint to Complementarity, the Interference of Probabilities and Incompatibility of Variables in Quantum Mechanics. Foundations of Physics 35 (10):1655-1693.
  18. Barry Loewer, Eric Winsberg & Brad Weslake (eds.) (forthcoming). Currently-Unnamed Volume Discussing David Albert's "Time and Chance&Quot;.
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  19. Ulrich Mohrhoff (2014). Manifesting the Quantum World. Foundations of Physics 44 (6):641-677.
    In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. Being part of the Scientific Image of the world, the theory concerns the process by which (the physical aspect of) what Sellars called the Manifest Image of the world comes into being. This process consists in the progressive differentiation of an intrinsically undifferentiated entity. By entering (...)
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  20. David Papineau (2010). A Scandal of Probability Theory. In Simon Saunders, Jonathan Barrett, Adrian Kent & David Wallace (eds.), Many Worlds?: Everett, Quantum Theory, & Reality. Oup Oxford.
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  21. Simon Saunders (2010). Chance in the Everett Interpretation. In Simon Saunders, Jonathan Barrett, Adrian Kent & David Wallace (eds.), Many Worlds?: Everett, Quantum Theory, & Reality. Oup Oxford.
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  22. Orly Shenker & Meir Hemmo (2011). Introduction to the Philosophy of Statistical Mechanics: Can Probability Explain the Arrow of Time in the Second Law of Thermodynamics? Philosophy Compass 6 (9):640-651.
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  23. Jennifer S. Trueblood & Jerome R. Busemeyer (2011). A Quantum Probability Account of Order Effects in Inference. Cognitive Science 35 (8):1518-1552.
    Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order effects by transforming a (...)
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  24. Sylvia Wenmackers & Danny E. P. Vanpoucke (2012). Models and Simulations in Material Science: Two Cases Without Error Bars. Statistica Neerlandica 66 (3):339–355.
    We discuss two research projects in material science in which the results cannot be stated with an estimation of the error: a spectroscopic ellipsometry study aimed at determining the orientation of DNA molecules on diamond and a scanning tunneling microscopy study of platinum-induced nanowires on germanium. To investigate the reliability of the results, we apply ideas from the philosophy of models in science. Even if the studies had reported an error value, the trustworthiness of the result would not depend on (...)
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Probability in the Physical Sciences, Misc
  1. Dennis Dieks (2010). Quantum Mechanics, Chance and Modality. Philosophica 83 (1):117-137.
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  2. Antony Eagle (forthcoming). Is the Past a Matter of Chance? In Alastair Wilson (ed.), Chance and Temporal Asymmetry. Oxford University Press.
  3. P. Hájíček (2009). Quantum Model of Classical Mechanics: Maximum Entropy Packets. [REVIEW] Foundations of Physics 39 (9):1072-1096.
    In a previous paper, a statistical method of constructing quantum models of classical properties has been described. The present paper concludes the description by turning to classical mechanics. The quantum states that maximize entropy for given averages and variances of coordinates and momenta are called ME packets. They generalize the Gaussian wave packets. A non-trivial extension of the partition-function method of probability calculus to quantum mechanics is given. Non-commutativity of quantum variables limits its usefulness. Still, the general form of the (...)
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  4. Iñaki San Pedro & Mauricio Suárez (2009). Reichenbach’s Common Cause Principle and Indeterminism: A Review. In José Luis González Recio (ed.), Philosophical Essays on Physics and Biology. Georg Olms Verlag. 223-250.
    We offer a review of some of the most influential views on the status of Reichenbach’s Principle of the Common Cause (RPCC) for genuinely indeterministic systems. We first argue that the RPCC is properly a conjunction of two distinct claims, one metaphysical and another methodological. Both claims can and have been contested in the literature, but here we simply assume that the metaphysical claim is correct, in order to focus our analysis on the status of the methodological claim. We briefly (...)
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Applications of Probability, Misc
  1. Nick Bostrom, A Doomsday Argument Primer.
    Rarely does philosophy produce empirical predictions. The Doomsday argument is an important exception. From seemingly trivial premises it seeks to show that the risk that humankind will go extinct soon has been systematically underestimated. Nearly everybody's first reaction is that there must be something wrong with such an argument. Yet despite being subjected to intense scrutiny by a growing number of philosophers, no simple flaw in the argument has been identified.
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  2. Ellery Eells & James H. Fetzer (eds.) (2010). The Place of Probability in Science. Springer.
    To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...
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  3. Peter Milne (2012). Probability as a Measure of Information Added. Journal of Logic, Language and Information 21 (2):163-188.
    Some propositions add more information to bodies of propositions than do others. We start with intuitive considerations on qualitative comparisons of information added . Central to these are considerations bearing on conjunctions and on negations. We find that we can discern two distinct, incompatible, notions of information added. From the comparative notions we pass to quantitative measurement of information added. In this we borrow heavily from the literature on quantitative representations of qualitative, comparative conditional probability. We look at two ways (...)
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  4. Piers Rawling (1999). Reasonable Doubt and the Presumption of Innocence: The Case of the Bayesian Juror. Topoi 18 (2):117-126.
    There is a substantial literature on the Bayesian approach, and the application of Bayes'' theorem, to legal matters. However, I have found no discussion that explores fully the issue of how a Bayesian juror might be led from an initial "presumption of innocence" to the judgment (required for conviction in criminal cases) that the suspect is "guilty beyond a reasonable doubt". I shall argue here that a Bayesian juror, if she acts in accord with what the law prescribes, will virtually (...)
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  5. Josef Schurz (2007). Probability and Evolution. Why the Probability Argument of Creationists is Wrong. Journal for General Philosophy of Science 38 (1):163 - 165.
    Evolution is a time process. It proceeds in steps of definite length. The probability of each step is relatively high, so self organization of complex systems will be possible in finite time. Prerequisite for such a process is a selection rule, which certainly exists in evolution. Therefore, it would be wrong to calculate the probability of the formation of a complex system solely on the basis of the number of its components and as a momentary event.
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  6. Neven Sesardic (2007). Sudden Infant Death or Murder? A Royal Confusion About Probabilities. British Journal for the Philosophy of Science 58 (2):299 - 329.
    In this article I criticize the recommendations of some prominent statisticians about how to estimate and compare probabilities of the repeated sudden infant death and repeated murder. The issue has drawn considerable public attention in connection with several recent court cases in the UK. I try to show that when the three components of the Bayesian inference are carefully analyzed in this context, the advice of the statisticians turns out to be problematic in each of the steps.
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  7. Joel D. Velasco (2008). The Prior Probabilities of Phylogenetic Trees. Biology and Philosophy 23 (4):455-473.
    Bayesian methods have become among the most popular methods in phylogenetics, but theoretical opposition to this methodology remains. After providing an introduction to Bayesian theory in this context, I attempt to tackle the problem mentioned most often in the literature: the “problem of the priors”—how to assign prior probabilities to tree hypotheses. I first argue that a recent objection—that an appropriate assignment of priors is impossible—is based on a misunderstanding of what ignorance and bias are. I then consider different methods (...)
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