257 research outputs found
New Theory about Old Evidence:A framework for open-minded Bayesianism
We present a conservative extension of a Bayesian account of confirmation that can deal with the problem of old evidence and new theories. So-called open-minded Bayesianism challenges the assumption-implicit in standard Bayesianism-that the correct empirical hypothesis is among the ones currently under consideration. It requires the inclusion of a catch-all hypothesis, which is characterized by means of sets of probability assignments. Upon the introduction of a new theory, the former catch-all is decomposed into a new empirical hypothesis and a new catch-all. As will be seen, this motivates a second update rule, besides Bayes' rule, for updating probabilities in light of a new theory. This rule conserves probability ratios among the old hypotheses. This framework allows for old evidence to confirm a new hypothesis due to a shift in the theoretical context. The result is a version of Bayesianism that, in the words of Earman, "keep[s] an open mind, but not so open that your brain falls out"
Belief Revision for Growing Awareness
The Bayesian maxim for rational learning could be described as conservative
change from one probabilistic belief or credence function to another in response to
newinformation. Roughly: âHold fixed any credences that are not directly affected
by the learning experience.â This is precisely articulated for the case when we
learn that some proposition that we had previously entertained is indeed true (the
rule of conditionalisation). But can this conservative-change maxim be extended
to revising oneâs credences in response to entertaining propositions or concepts
of which one was previously unaware? The economists Karni and VierĂž (2013,
2015) make a proposal in this spirit. Philosophers have adopted effectively the
same rule: revision in response to growing awareness should not affect the relative
probabilities of propositions in oneâs âoldâ epistemic state. The rule is compelling,
but only under the assumptions that its advocates introduce. It is not a general
requirement of rationality, or so we argue. We provide informal counterexamples.
And we show that, when awareness grows, the boundary between oneâs âoldâ and
ânewâ epistemic commitments is blurred. Accordingly, there is no general notion
of conservative change in this setting
Induction and Deduction in Baysian Data Analysis
The classical or frequentist approach to statistics (in which inference is centered on significance testing), is associated with a philosophy in which science is deductive and follows Popperis doctrine of falsification. In contrast, Bayesian inference is commonly associated with inductive reasoning and the idea that a model can be dethroned by a competing model but can never be directly falsified by a significance test. The purpose of this article is to break these associations, which I think are incorrect and have been detrimental to statistical practice, in that they have steered falsificationists away from the very useful tools of Bayesian inference and have discouraged Bayesians from checking the fit of their models. From my experience using and developing Bayesian methods in social and environmental science, I have found model checking and falsification to be central in the modeling process.philosophy of statistics, decision theory, subjective probability, Bayesianism, falsification, induction, frequentism
On the truth-convergence of open-minded Bayesianism
Wenmackers and Romeijn [38] formalize ideas going back to Shimony [33] and Putnam [28] into an open-minded Bayesian inductive logic, that can dynamically incorporate statistical hypotheses proposed in the course of the learning process. In this paper, we show that Wenmackers and Romeijnâs proposal does not preserve the classical Bayesian consistency guarantee of merger with the true hypothesis. We diagnose the problem, and offer a forward-looking open-minded Bayesians that does preserve a version of this guarantee
On the Truth-Convergence of Open-Minded Bayesianism
Wenmackers and Romeijn (2016) formalize ideas going back to Shimony (1970) and Putnam (1963) into an open-minded Bayesian inductive logic, that can dynamically incorporate statistical hypotheses proposed in the course of the learning process. In this paper, we show that Wenmackers and Romeijn's proposal does not preserve the classical Bayesian consistency guarantee of merger with the true hypothesis. We diagnose the problem, and offer a forward-looking open-minded Bayesians that does preserve a version of this guarantee
"Not only defended but also applied": The perceived absurdity of Bayesian inference
The missionary zeal of many Bayesians of old has been matched, in the other
direction, by a view among some theoreticians that Bayesian methods are
absurd-not merely misguided but obviously wrong in principle. We consider
several examples, beginning with Feller's classic text on probability theory
and continuing with more recent cases such as the perceived Bayesian nature of
the so-called doomsday argument. We analyze in this note the intellectual
background behind various misconceptions about Bayesian statistics, without
aiming at a complete historical coverage of the reasons for this dismissal.Comment: 10 pages, to appear in The American Statistician (with discussion
Bayes, Hume, and Miracles
Recent attempts to cast Humeâs argument against miracles in a Bayesian form are examined. It is shown how the Bayesian apparatus does serve to clarify the structure and substance of Humeâs argument. But the apparatus does not underwrite Humeâs various claims, such as that no testimony serves to establish the credibility of a miracle; indeed, the Bayesian analysis reveals various conditions under which it would be reasonable to reject the more interesting of Humeâs claims
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