130,393 research outputs found
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
Exact 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, moments,
and other quantities. We prove asymptotic convergence and consistency results,
and illustrate the behavior of our model on some prototypical functions.Comment: 32 LaTeX pages, 9 figures, 5 theorems, 1 algorith
Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting
We present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations.
Certain strategy profiles are proved to be subgame perfect equilibria using a novel proof principle of predicate coinduction which is shown to be sound by reducing it to Kozen’s metric coinduction. We characterize all subgame perfect equilibria for the dollar auction game. The economically interesting feature is that in order to prove these results we do not need to rely on continuity assumptions on the payoffs which amount to discounting the future.
In particular, we prove a form of one-deviation principle without any such assumptions. This suggests that coalgebra supports a more adequate treatment of infinite-horizon models in game theory and economics
Two-weight dyadic Hardy's inequalities
We give a survey of results and proofs on two-weight Hardy's inequalities on
infinite trees. Most of the results are already known, but some appear here for
the first time. Among the new results that we prove there is the
characterization of the compactness of the Hardy operator, a reverse H\"older
inequality for trace measures and a simple proof of the characterization of
trace measures based on a monotonicity argument. Furthermore we give a
probabilistic proof of an inequality due to Wolff. We also provide a list of
open problems and suggest some possible lines of future research.Comment: 54 pages, 2 figure
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