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”. (shrink)

Bayesian model selection has frequently been the focus of philosophical inquiry (e.g., Forster, Br J Philos Sci 46:399–424, 1995; Bandyopadhyay and Boik, Philos Sci 66:S390–S402, 1999; Dowe et al., Br J Philos Sci 58:709–754, 2007). This paper argues that Bayesian model selection procedures are very diverse in their inferential target and their justification, and substantiates this claim by means of case studies on three selected procedures: MML, BIC and DIC. Hence, there is no tight link between Bayesian model selection and (...) Bayesian philosophy. Consequently, arguments for or against Bayesian reasoning based on properties of Bayesian model selection procedures should be treated with great caution. (shrink)

We consider the use of interventions for resolving a problem of unidentified statistical models. The leading examples are from latent variable modelling, an influential statistical tool in the social sciences. We first explain the problem of statistical identifiability and contrast it with the identifiability of causal models. We then draw a parallel between the latent variable models and Bayesian networks with hidden nodes. This allows us to clarify the use of interventions for dealing with unidentified statistical models. We end by (...) discussing the philosophical and methodological import of our result. (shrink)

Classic conceptions of model simplicity for machine learning are mainly based on the analysis of the structure of the model. Bayesian, Frequentist, information theoretic and expressive power concepts are the best known of them, which are reviewed in this work, along with their underlying assumptions and weaknesses. These approaches were developed before the advent of the Big Data deluge, which has overturned the importance of structural simplicity. The computational simplicity concept is presented, and it is argued that it is more (...) encompassing and closer to actual machine learning practices than the classic ones. In order to process the huge datasets which are commonplace nowadays, the computational complexity of the learning algorithm is the decisive factor to assess the viability of a machine learning strategy, while the classic accounts of simplicity play a surrogate role. Some of the desirable features of computational simplicity derive from its reliance on the learning system concept, which integrates key aspects of machine learning that are ignored by the classic concepts. Moreover, computational simplicity is directly associated with energy efficiency. In particular, the question of whether the maximum possibly achievable predictive accuracy should be attained, no matter the economic cost of the associated energy consumption pattern, is considered. (shrink)

Our scientific theories, like our cognitive structures in general, consist of propositions linked by evidential, explanatory, probabilistic, and logical connections. Those theoretical webs ‘impinge on the world at their edges,’ subject to a continuing barrage of incoming evidence. Our credences in the various elements of those structures change in response to that continuing barrage of evidence, as do the perceived connections between them. Here we model scientific theories as Bayesian nets, with credences at nodes and conditional links between them modelled (...) as conditional probabilities. We update those networks, in terms of both credences at nodes and conditional probabilities at links, through a temporal barrage of random incoming evidence. Robust patterns of punctuated equilibrium, suggestive of ‘normal science’ alternating with ‘paradigm shifts,’ emerge prominently in that change dynamics. The suggestion is that at least some of the phenomena at the core of the Kuhnian tradition are predictable in the typical dynamics of scientific theory change captured as Bayesian nets under even a random evidence barrage. (shrink)

We model scientific theories as Bayesian networks. Nodes carry credences and function as abstract representations of propositions within the structure. Directed links carry conditional probabilities and represent connections between those propositions. Updating is Bayesian across the network as a whole. The impact of evidence at one point within a scientific theory can have a very different impact on the network than does evidence of the same strength at a different point. A Bayesian model allows us to envisage and analyze the (...) differential impact of evidence and credence change at different points within a single network and across different theoretical structures. (shrink)

Eliminative reasoning seems to play an important role in the sciences, but should it be part of our best theory of science? Statistical evidence, prevalent across the sciences, causes problems for eliminative inference, supporting the view that probabilistic theories of confirmation provide a better framework for reasoning about evidence. Here I argue that deductive elimination has an important inferential role to play in science, one that is compatible with probabilistic approaches to evidence. Eliminative inferences help frame testing problems, an essential (...) step that determines the context for evaluating statistical evidence. I illustrate this process with examples from molecular evolutionary biology. (shrink)

Occam's razor—the idea that all else being equal, we should pick the simpler hypothesis—plays a prominent role in ordinary and scientific inference. But why are simpler hypotheses better? One attractive hypothesis known as Bayesian Occam's razor is that more complex hypotheses tend to be more flexible—they can accommodate a wider range of possible data—and that flexibility is automatically penalized by Bayesian inference. In two experiments, we provide evidence that people's intuitive probabilistic and explanatory judgments follow the prescriptions of BOR. In (...) particular, people's judgments are consistent with the two most distinctive characteristics of BOR: They penalize hypotheses as a function not only of their numbers of free parameters but also as a function of the size of the parameter space, and they penalize those hypotheses even when their parameters can be “tuned” to fit the data better than comparatively simpler hypotheses. (shrink)

Bayesians often assume, suppose, or conjecture that for any reasonable explication of the notion of simplicity a prior can be designed that will enforce a preference for hypotheses simpler in just that sense. But it is shown here that there are simplicity-driven approaches to curve-fitting problems that cannot be captured within the orthodox Bayesian framework.

:While Bayesian methods are widely used in economics and finance, the foundations of this approach remain controversial. In the contemporary statistical literature Bayesian Ockham’s razor refers to the observation that the Bayesian approach to scientific inference will automatically assign greater likelihood to a simpler hypothesis if the data are compatible with both a simpler and a more complex hypothesis. In this paper I will discuss a problem that results when Bayesian Ockham’s razor is applied to nested economic models. I will (...) argue that previous responses to the problem found in the philosophical literature are unsatisfactory and develop a novel reply to the problem. (shrink)

Sewall Wright ’s FST is a mathematical test widely used in empirical applications to characterize genetic and other differences between subpopulations, and to identify causes of those differences. Cockerham and Weir’s popular approach to statistical estimation of FST is based on an assumption sometimes formulated as a claim that actual populations tested are sampled from.