1,416,053 research outputs found
Maximizing the probability of attaining a target prior to extinction
We present a dynamic programming-based solution to the problem of maximizing
the probability of attaining a target set before hitting a cemetery set for a
discrete-time Markov control process. Under mild hypotheses we establish that
there exists a deterministic stationary policy that achieves the maximum value
of this probability. We demonstrate how the maximization of this probability
can be computed through the maximization of an expected total reward until the
first hitting time to either the target or the cemetery set. Martingale
characterizations of thrifty, equalizing, and optimal policies in the context
of our problem are also established.Comment: 22 pages, 1 figure. Revise
Optimal properties of some Bayesian inferences
Relative surprise regions are shown to minimize, among Bayesian credible
regions, the prior probability of covering a false value from the prior. Such
regions are also shown to be unbiased in the sense that the prior probability
of covering a false value is bounded above by the prior probability of covering
the true value. Relative surprise regions are shown to maximize both the Bayes
factor in favor of the region containing the true value and the relative belief
ratio, among all credible regions with the same posterior content. Relative
surprise regions emerge naturally when we consider equivalence classes of
credible regions generated via reparameterizations.Comment: Published in at http://dx.doi.org/10.1214/07-EJS126 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Envelopes of conditional probabilities extending a strategy and a prior probability
Any strategy and prior probability together are a coherent conditional
probability that can be extended, generally not in a unique way, to a full
conditional probability. The corresponding class of extensions is studied and a
closed form expression for its envelopes is provided. Then a topological
characterization of the subclasses of extensions satisfying the further
properties of full disintegrability and full strong conglomerability is given
and their envelopes are studied.Comment: 2
Fast non-parametric Bayesian inference on infinite trees
Given i.i.d. data from an unknown distribution,
we consider the problem of predicting future items.
An adaptive way to estimate the probability density
is to recursively subdivide the domain to an appropriate
data-dependent granularity. A Bayesian would assign a
data-independent prior probability to "subdivide", which leads
to a prior over infinite(ly many) trees. We derive an exact, fast,
and simple inference algorithm for such a prior, for the data
evidence, the predictive distribution, the effective model
dimension, and other quantities
Fast Non-Parametric Bayesian Inference on Infinite Trees
Given i.i.d. data from an unknown distribution, we consider the problem of
predicting future items. An adaptive way to estimate the probability density is
to recursively subdivide the domain to an appropriate data-dependent
granularity. A Bayesian would assign a data-independent prior probability to
"subdivide", which leads to a prior over infinite(ly many) trees. We derive an
exact, fast, and simple inference algorithm for such a prior, for the data
evidence, the predictive distribution, the effective model dimension, and other
quantities.Comment: 8 twocolumn pages, 3 figure
Appropriate Methodology of Statistical Tests According to Prior Probability and Required Objectivity
In contrast to its common definition and calculation, interpretation of
p-values diverges among statisticians. Since p-value is the basis of various
methodologies, this divergence has led to a variety of test methodologies and
evaluations of test results. This chaotic situation has complicated the
application of tests and decision processes. Here, the origin of the divergence
is found in the prior probability of the test. Effects of difference in Pr(H0 =
true) on the character of p-values are investigated by comparing real
microarray data and its artificial imitations as subjects of Student's t-tests.
Also, the importance of the prior probability is discussed in terms of the
applicability of Bayesian approaches. Suitable methodology is found in
accordance with the prior probability and purpose of the test.Comment: 16 pages, 3 figures, and 1 tabl
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