13,201 research outputs found
Predictive Reasoning in Subjective Bayesian Networks
Subjective Bayesian networks extend Bayesian networks by substituting the conditional probability distributions with subjective opinions. In that way they enable explicit representation of the uncertainty in the probabilistic information encoded in the network. In this paper we focus on predictive reasoning in subjective Bayesian networks and propose an inference method that is based on the operations of deduction and multiplication of subjective opinions. We demonstrate modelling and inference with subjective Bayesian networks through an example.
Literal Perceptual Inference
In this paper, I argue that theories of perception that appeal to Helmholtz’s idea of unconscious inference (“Helmholtzian” theories) should be taken literally, i.e. that the inferences appealed to in such theories are inferences in the full sense of the term, as employed elsewhere in philosophy and in ordinary discourse.
In the course of the argument, I consider constraints on inference based on the idea that inference is a deliberate acton, and on the idea that inferences depend on the syntactic structure of representations. I argue that inference is a personal-level but sometimes unconscious process that cannot in general be distinguished from association on the basis of the structures of the representations over which it’s defined. I also critique arguments against representationalist interpretations of Helmholtzian theories, and argue against the view that perceptual inference is encapsulated in a module
Bayesian Inference in Processing Experimental Data: Principles and Basic Applications
This report introduces general ideas and some basic methods of the Bayesian
probability theory applied to physics measurements. Our aim is to make the
reader familiar, through examples rather than rigorous formalism, with concepts
such as: model comparison (including the automatic Ockham's Razor filter
provided by the Bayesian approach); parametric inference; quantification of the
uncertainty about the value of physical quantities, also taking into account
systematic effects; role of marginalization; posterior characterization;
predictive distributions; hierarchical modelling and hyperparameters; Gaussian
approximation of the posterior and recovery of conventional methods, especially
maximum likelihood and chi-square fits under well defined conditions; conjugate
priors, transformation invariance and maximum entropy motivated priors; Monte
Carlo estimates of expectation, including a short introduction to Markov Chain
Monte Carlo methods.Comment: 40 pages, 2 figures, invited paper for Reports on Progress in Physic
Philosophy and the practice of Bayesian statistics
A substantial school in the philosophy of science identifies Bayesian
inference with inductive inference and even rationality as such, and seems to
be strengthened by the rise and practical success of Bayesian statistics. We
argue that the most successful forms of Bayesian statistics do not actually
support that particular philosophy but rather accord much better with
sophisticated forms of hypothetico-deductivism. We examine the actual role
played by prior distributions in Bayesian models, and the crucial aspects of
model checking and model revision, which fall outside the scope of Bayesian
confirmation theory. We draw on the literature on the consistency of Bayesian
updating and also on our experience of applied work in social science.
Clarity about these matters should benefit not just philosophy of science,
but also statistical practice. At best, the inductivist view has encouraged
researchers to fit and compare models without checking them; at worst,
theorists have actively discouraged practitioners from performing model
checking because it does not fit into their framework.Comment: 36 pages, 5 figures. v2: Fixed typo in caption of figure 1. v3:
Further typo fixes. v4: Revised in response to referee
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