62,659 research outputs found
A statistical inference method for the stochastic reachability analysis.
The main contribution of this paper is the characterization of reachability problem associated to stochastic hybrid systems in terms of imprecise probabilities. This provides the connection between reachability problem and Bayesian statistics. Using generalised Bayesian statistical inference, a new concept of conditional reach set probabilities is defined. Then possible algorithms to compute the reach set probabilities are derived
Quantum Structures: An Attempt to Explain the Origin of their Appearance in Nature
We explain the quantum structure as due to the presence of two effects, (a) a
real change of state of the entity under influence of the measurement and, (b)
a lack of knowledge about a deeper deterministic reality of the measurement
process. We present a quantum machine, where we can illustrate in a simple way
how the quantum structure arises as a consequence of the two mentioned effects.
We introduce a parameter epsilon that measures the size of the lack of
knowledge on the measurement process, and by varying this parameter, we
describe a continuous evolution from a quantum structure (maximal lack of
knowledge) to a classical structure (zero lack of knowledge). We show that for
intermediate values of epsilon we find a new type of structure, that is neither
quantum nor classical. We apply the model that we have introduced to situations
of lack of knowledge about the measurement process appearing in other regions
of reality. More specifically we investigate the quantum-like structures that
appear in the situation of psychological decision processes, where the subject
is influenced during the testing, and forms some of his opinions during the
testing process. Our conclusion is that in the light of this explanation, the
quantum probabilities are epistemic and not ontological, which means that
quantum mechanics is compatible with a determinism of the whole.Comment: 22 pages, 8 figure
Negatively Biased Relevant Subsets Induced by the Most-Powerful One-Sided Upper Confidence Limits for a Bounded Physical Parameter
Suppose an observable x is the measured value (negative or non-negative) of a
true mean mu (physically non-negative) in an experiment with a Gaussian
resolution function with known fixed rms deviation s. The most powerful
one-sided upper confidence limit at 95% C.L. is UL = x+1.64s, which I refer to
as the "original diagonal line". Perceived problems in HEP with small or
non-physical upper limits for x<0 historically led, for example, to
substitution of max(0,x) for x, and eventually to abandonment in the Particle
Data Group's Review of Particle Physics of this diagonal line relationship
between UL and x. Recently Cowan, Cranmer, Gross, and Vitells (CCGV) have
advocated a concept of "power constraint" that when applied to this problem
yields variants of diagonal line, including UL = max(-1,x)+1.64s. Thus it is
timely to consider again what is problematic about the original diagonal line,
and whether or not modifications cure these defects. In a 2002 Comment,
statistician Leon Jay Gleser pointed to the literature on recognizable and
relevant subsets. For upper limits given by the original diagonal line, the
sample space for x has recognizable relevant subsets in which the quoted 95%
C.L. is known to be negatively biased (anti-conservative) by a finite amount
for all values of mu. This issue is at the heart of a dispute between Jerzy
Neyman and Sir Ronald Fisher over fifty years ago, the crux of which is the
relevance of pre-data coverage probabilities when making post-data inferences.
The literature describes illuminating connections to Bayesian statistics as
well. Methods such as that advocated by CCGV have 100% unconditional coverage
for certain values of mu and hence formally evade the traditional criteria for
negatively biased relevant subsets; I argue that concerns remain. Comparison
with frequentist intervals advocated by Feldman and Cousins also sheds light on
the issues.Comment: 22 pages, 7 figure
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