3,718 research outputs found
The Principal Principle Implies the Principle of Indifference
We argue that David Lewisâs principal principle implies a version of the principle of indifference. The same is true for similar principles that need to appeal to the concept of admissibility. Such principles are thus in accord with objective Bayesianism, but in tension with subjective Bayesianism.
1 The Argument
2 Some Objections Me
Bayes and health care research.
Bayesâ rule shows how one might rationally change oneâs beliefs in the light of evidence. It is the foundation of a statistical method called Bayesianism. In health care research, Bayesianism has its advocates but the dominant statistical method is frequentism.
There are at least two important philosophical differences between these methods. First, Bayesianism takes a subjectivist view of probability (i.e. that probability scores are statements of subjective belief, not objective fact) whilst frequentism takes an objectivist view. Second, Bayesianism is explicitly inductive (i.e. it shows how we may induce views about the world based on partial data from it) whereas frequentism is at least compatible with non-inductive views of scientific method, particularly the critical realism of Popper.
Popper and others detail significant problems with induction. Frequentismâs apparent ability to avoid these, plus its ability to give a seemingly more scientific and objective take on probability, lies behind its philosophical appeal to health care researchers.
However, there are also significant problems with frequentism, particularly its inability to assign probability scores to single events. Popper thus proposed an alternative objectivist view of probability, called propensity theory, which he allies to a theory of corroboration; but this too has significant problems, in particular, it may not successfully avoid induction. If this is so then Bayesianism might be philosophically the strongest of the statistical approaches. The article sets out a number of its philosophical and methodological attractions. Finally, it outlines a way in which critical realism and Bayesianism might work together.
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Reverse Bayesianism and Act Independence
Karni and VierĂž (2013) propose a model of belief revision under growing awarenessâreverse Bayesianismâwhich posits that as a person becomes aware of new acts, consequences, or act-consequence links, she revises her beliefs over an expanded state space in a way that preserves the relative likelihoods of events in the original state space. A key feature of the model is that reverse Bayesianism does not fully determine the revised probability distribution. We provide an assumptionâact independenceâthat imposes additional restrictions on reverse Bayesian belief revision. We show that with act independence knowledge of the probabilities of the new act events in the expanded state space is sufficient to fully determine the revised probability distribution in each case of growing awareness. We also explore what additional knowledge is required for reverse Bayesianism to pin down the revised probabilities without act independence
Evidential Probabilities and Credences
Enjoying great popularity in decision theory, epistemology, and philosophy of science, Bayesianism as understood here is fundamentally concerned with epistemically ideal rationality. It assumes a tight connection between evidential probability and ideally rational credence, and usually interprets evidential probability in terms of such credence. Timothy Williamson challenges Bayesianism by arguing that evidential probabilities cannot be adequately interpreted as the credences of an ideal agent. From this and his assumption that evidential probabilities cannot be interpreted as the actual credences of human agents either, he concludes that no interpretation of evidential probabilities in terms of credence is adequate. I argue to the contrary. My overarching aim is to show on behalf of Bayesians how one can still interpret evidential probabilities in terms of ideally rational credence and how one can maintain a tight connection between evidential probabilities and ideally rational credence even if the former cannot be interpreted in terms of the latter. By achieving this aim I illuminate the limits and prospects of Bayesianism
The objective Bayesian conceptualisation of proof and reference class problems
The objective Bayesian view of proof (or logical probability, or
evidential support) is explained and defended: that the relation of
evidence to hypothesis (in legal trials, science etc) is a strictly
logical one, comparable to deductive logic. This view is
distinguished from the thesis, which had some popularity in law in
the 1980s, that legal evidence ought to be evaluated using
numerical probabilities and formulas. While numbers are not
always useful, a central role is played in uncertain reasoning by the
âproportional syllogismâ, or argument from frequencies, such as
ânearly all aeroplane flights arrive safely, so my flight is very
likely to arrive safelyâ. Such arguments raise the âproblem of the
reference classâ, arising from the fact that an individual case may
be a member of many different classes in which frequencies differ.
For example, if 15 per cent of swans are black and 60 per cent of
fauna in the zoo is black, what should I think about the likelihood
of a swan in the zoo being black? The nature of the problem is
explained, and legal cases where it arises are given. It is explained
how recent work in data mining on the relevance of features for
prediction provides a solution to the reference class problem
Troubles with Bayesianism: An introduction to the psychological immune system
A Bayesian mind is, at its core, a rational mind. Bayesianism is thus well-suited to predict and explain mental processes that best exemplify our ability to be rational. However, evidence from belief acquisition and change appears to show that we do not acquire and update information in a Bayesian way. Instead, the principles of belief acquisition and updating seem grounded in maintaining a psychological immune system rather than in approximating
a Bayesian processor
Tort Liability and Unawareness
Unawareness is a form of bounded rationality where a person fails to conceive all feasible acts or consequences or to perceive as feasible all conceivable act-consequence links. We study the implications of unawareness for tort law, where relevant examples include the discovery of a new product or technology (new act), of a new disease or injury (new consequence), or that a product can cause an injury (new link). We argue that negligence has an important advantage over strict liability in a world with unawarenessânegligence, through the stipulation of due care standards, spreads awareness about the updated probability of harm
Imprecise Bayesianism and Global Belief Inertia
Traditional Bayesianism requires that an agentâs degrees of belief be represented by a real-valued, probabilistic credence function. However, in many cases it seems that our evidence is not rich enough to warrant such precision. In light of this, some have proposed that we instead represent an agentâs degrees of belief as a set of credence functions. This way, we can respect the evidence by requiring that the set, often called the agentâs credal state, includes all credence functions that are in some sense compatible with the evidence. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In this article I argue that the problem is much more general than has been appreciated so far, and that itâs difficult to avoid it without compromising the initial evidentialist motivation. _1_ Introduction _2_ Precision and Its Problems _3_ Imprecise Bayesianism and Respecting Ambiguous Evidence _4_ Local Belief Inertia _5_ From Local to Global Belief Inertia _6_ Responding to Global Belief Inertia _7_ Conclusio
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