80,520 research outputs found
Robust estimation of risks from small samples
Data-driven risk analysis involves the inference of probability distributions
from measured or simulated data. In the case of a highly reliable system, such
as the electricity grid, the amount of relevant data is often exceedingly
limited, but the impact of estimation errors may be very large. This paper
presents a robust nonparametric Bayesian method to infer possible underlying
distributions. The method obtains rigorous error bounds even for small samples
taken from ill-behaved distributions. The approach taken has a natural
interpretation in terms of the intervals between ordered observations, where
allocation of probability mass across intervals is well-specified, but the
location of that mass within each interval is unconstrained. This formulation
gives rise to a straightforward computational resampling method: Bayesian
Interval Sampling. In a comparison with common alternative approaches, it is
shown to satisfy strict error bounds even for ill-behaved distributions.Comment: 13 pages, 3 figures; supplementary information provided. A revised
version of this manuscript has been accepted for publication in Philosophical
Transactions of the Royal Society A: Mathematical, Physical and Engineering
Science
Comparing stochastic design decision belief models : pointwise versus interval probabilities.
Decision support systems can either directly support a product designer or support an agent operating within a multi-agent system (MAS). Stochastic based decision support systems require an underlying belief model that encodes domain knowledge. The underlying supporting belief model has traditionally been a probability distribution function (PDF) which uses pointwise probabilities for all possible outcomes. This can present a challenge during the knowledge elicitation process. To overcome this, it is proposed to test the performance of a credal set belief model. Credal sets (sometimes also referred to as p-boxes) use interval probabilities rather than pointwise probabilities and therefore are more easier to elicit from domain experts. The PDF and credal set belief models are compared using a design domain MAS which is able to learn, and thereby refine, the belief model based on its experience. The outcome of the experiment illustrates that there is no significant difference between the PDF based and credal set based belief models in the performance of the MAS
Reconstructing the primordial power spectrum from the CMB
We propose a straightforward and model independent methodology for
characterizing the sensitivity of CMB and other experiments to wiggles,
irregularities, and features in the primordial power spectrum. Assuming that
the primordial cosmological perturbations are adiabatic, we present a function
space generalization of the usual Fisher matrix formalism, applied to a CMB
experiment resembling Planck with and without ancillary data. This work is
closely related to other work on recovering the inflationary potential and
exploring specific models of non-minimal, or perhaps baroque, primordial power
spectra. The approach adopted here, however, most directly expresses what the
data is really telling us. We explore in detail the structure of the available
information and quantify exactly what features can be reconstructed and at what
statistical significance.Comment: 43 pages Revtex, 23 figure
Finite size corrections to random Boolean networks
Since their introduction, Boolean networks have been traditionally studied in
view of their rich dynamical behavior under different update protocols and for
their qualitative analogy with cell regulatory networks. More recently, tools
borrowed from statistical physics of disordered systems and from computer
science have provided a more complete characterization of their equilibrium
behavior. However, the largest part of the results have been obtained in the
thermodynamic limit, which is often far from being reached when dealing with
realistic instances of the problem. The numerical analysis presented here aims
at comparing - for a specific family of models - the outcomes given by the
heuristic belief propagation algorithm with those given by exhaustive
enumeration. In the second part of the paper some analytical considerations on
the validity of the annealed approximation are discussed.Comment: Minor correction
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