11,301 research outputs found
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
Symbol Emergence in Robotics: A Survey
Humans can learn the use of language through physical interaction with their
environment and semiotic communication with other people. It is very important
to obtain a computational understanding of how humans can form a symbol system
and obtain semiotic skills through their autonomous mental development.
Recently, many studies have been conducted on the construction of robotic
systems and machine-learning methods that can learn the use of language through
embodied multimodal interaction with their environment and other systems.
Understanding human social interactions and developing a robot that can
smoothly communicate with human users in the long term, requires an
understanding of the dynamics of symbol systems and is crucially important. The
embodied cognition and social interaction of participants gradually change a
symbol system in a constructive manner. In this paper, we introduce a field of
research called symbol emergence in robotics (SER). SER is a constructive
approach towards an emergent symbol system. The emergent symbol system is
socially self-organized through both semiotic communications and physical
interactions with autonomous cognitive developmental agents, i.e., humans and
developmental robots. Specifically, we describe some state-of-art research
topics concerning SER, e.g., multimodal categorization, word discovery, and a
double articulation analysis, that enable a robot to obtain words and their
embodied meanings from raw sensory--motor information, including visual
information, haptic information, auditory information, and acoustic speech
signals, in a totally unsupervised manner. Finally, we suggest future
directions of research in SER.Comment: submitted to Advanced Robotic
Fuzzy sets in nonparametric Bayes regression
A simple Bayesian approach to nonparametric regression is described using
fuzzy sets and membership functions. Membership functions are interpreted as
likelihood functions for the unknown regression function, so that with the help
of a reference prior they can be transformed to prior density functions. The
unknown regression function is decomposed into wavelets and a hierarchical
Bayesian approach is employed for making inferences on the resulting wavelet
coefficients.Comment: Published in at http://dx.doi.org/10.1214/074921708000000084 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
A Noninformative Prior on a Space of Distribution Functions
In a given problem, the Bayesian statistical paradigm requires the
specification of a prior distribution that quantifies relevant information
about the unknowns of main interest external to the data. In cases where little
such information is available, the problem under study may possess an
invariance under a transformation group that encodes a lack of information,
leading to a unique prior---this idea was explored at length by E.T. Jaynes.
Previous successful examples have included location-scale invariance under
linear transformation, multiplicative invariance of the rate at which events in
a counting process are observed, and the derivation of the Haldane prior for a
Bernoulli success probability. In this paper we show that this method can be
extended, by generalizing Jaynes, in two ways: (1) to yield families of
approximately invariant priors, and (2) to the infinite-dimensional setting,
yielding families of priors on spaces of distribution functions. Our results
can be used to describe conditions under which a particular Dirichlet Process
posterior arises from an optimal Bayesian analysis, in the sense that
invariances in the prior and likelihood lead to one and only one posterior
distribution
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