2,400 research outputs found
Simplicity, scientific inference and econometric modelling
Economic Schools;Econometric Models;Economic Methodology
A Natural Law of Succession
Consider the problem of multinomial estimation. You are given an alphabet of
k distinct symbols and are told that the i-th symbol occurred exactly n_i times
in the past. On the basis of this information alone, you must now estimate the
conditional probability that the next symbol will be i. In this report, we
present a new solution to this fundamental problem in statistics and
demonstrate that our solution outperforms standard approaches, both in theory
and in practice.Comment: 23 page
Algorithmic complexity for psychology: A user-friendly implementation of the coding theorem method
Kolmogorov-Chaitin complexity has long been believed to be impossible to
approximate when it comes to short sequences (e.g. of length 5-50). However,
with the newly developed \emph{coding theorem method} the complexity of strings
of length 2-11 can now be numerically estimated. We present the theoretical
basis of algorithmic complexity for short strings (ACSS) and describe an
R-package providing functions based on ACSS that will cover psychologists'
needs and improve upon previous methods in three ways: (1) ACSS is now
available not only for binary strings, but for strings based on up to 9
different symbols, (2) ACSS no longer requires time-consuming computing, and
(3) a new approach based on ACSS gives access to an estimation of the
complexity of strings of any length. Finally, three illustrative examples show
how these tools can be applied to psychology.Comment: to appear in "Behavioral Research Methods", 14 pages in journal
format, R package at http://cran.r-project.org/web/packages/acss/index.htm
Universal generalization and universal inter-item confusability
We argue that confusability between items should be distinguished from generalization between items. Shepard's data concern confusability, but the theories proposed by Shepard and by Tenenbaum & Griffiths concern generalization, indicating a gap between theory and data. We consider the empirical and theoretical work involved in bridging this gap
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