论文标题
涵盖经典和动态案例的广义IFS贝叶斯方法和相关的变分原理
The generalized IFS Bayesian method and an associated variational principle covering the classical and dynamical cases
论文作者
论文摘要
我们介绍了一种普遍的IFS贝叶斯方法，以从先前的概率获得后验概率，以及一项广义贝叶斯的规则，该规则将考虑一个动态的和非动力的环境。给定损失函数$ {l} $，我们详细介绍了先前和后验项，它们的后果并展示了几个示例。将$θ$作为一组参数和$ y $作为一组数据（通常提供{随机示例}），一般IFS是可测量的地图$τ：θ\ times y \ y $，可以解释为映射$τ_θ：y \ y y \ y，y \ to y，\，θ\，θ\inθ$。我们将在这里获得结果的主要灵感来自Zellner（没有动态）的一篇论文，在该论文中，贝叶斯的规则与最小化{信息的原则有关。信息理论中信息的最小化。除其他结果外，我们介绍了先前的动力学元素，并通过热力学形式主义的ruelle操作员得出相应的后元。以这种动态贝叶斯规则的形式获得这种形式。
We introduce a general IFS Bayesian method for getting posterior probabilities from prior probabilities, and also a generalized Bayes' rule, which will contemplate a dynamical, as well as a non-dynamical setting. Given a loss function ${l}$, we detail the prior and posterior items, their consequences and exhibit several examples. Taking $Θ$ as the set of parameters and $Y$ as the set of data (which usually provides {random samples}), a general IFS is a measurable map $τ:Θ\times Y \to Y$, which can be interpreted as a family of maps $τ_θ:Y\to Y,\,θ\inΘ$. The main inspiration for the results we will get here comes from a paper by Zellner (with no dynamics), where Bayes' rule is related to a principle of minimization of {information.} We will show that our IFS Bayesian method which produces posterior probabilities (which are associated to holonomic probabilities) is related to the optimal solution of a variational principle, somehow corresponding to the pressure in Thermodynamic Formalism, and also to the principle of minimization of information in Information Theory. Among other results, we present the prior dynamical elements and we derive the corresponding posterior elements via the Ruelle operator of Thermodynamic Formalism; getting in this way a form of dynamical Bayes' rule.
