Bayesian Calibration of p‐Values from Fisher's Exact Test

p‐Values are commonly transformed to lower bounds on Bayes factors, so‐called minimum Bayes factors. For the linear model, a sample‐size adjusted minimum Bayes factor over the class of g‐priors on the regression coefficients has recently been proposed (Held & Ott, The American Statistician 70(4), 335–341, 2016). Here, we extend this methodology to a logistic regression to obtain a sample‐size adjusted minimum Bayes factor for 2 × 2 contingency tables. We then study the relationship between this minimum Bayes factor and two‐sided p‐values from Fisher's exact test, as well as less conservative alternatives, with a novel parametric regression approach. It turns out that for all p‐values considered, the maximal evidence against the point null hypothesis is inversely related to the sample size. The same qualitative relationship is observed for minimum Bayes factors over the more general class of symmetric prior distributions. For the p‐values from Fisher's exact test, the minimum Bayes factors do on average not tend to the large‐sample bound as the sample size becomes large, but for the less conservative alternatives, the large‐sample behaviour is as expected.     

论非物质文化遗产与区域经济建设——以吴桥杂技为例

非物质文化遗产在连结民族感情、传承中华民族文化等方面具有不可替代的作用。要充分发挥非物质文化遗产的作用,必须不断完善保护措施和开发新的思路。本文以吴桥杂技作为个案,以非物质文化遗产与经济之间的关系作为切入点,对两者之间的互动性进行了研究,探讨了开发与保护非物质文化遗产的新思路。     

Switching VARMA Term Structure Models

The purpose of this article is to propose a global discrete-timemodeling of the term structure of interest rates which is ableto capture simultaneously the following important features:(i) a historical dynamics of the factor driving term structureshapes involving several lagged values, and switching regimes;(ii) a specification of the stochastic discount factor (SDF)with time-varying and regime-dependent risk-premia; (iii) explicitor quasi explicit formulas for zero-coupon bond (ZCB) and interestrate derivative prices. We develop the switching autoregressivenormal (SARN) and the switching vector autoregressive normal(SVARN) Factor-Based Term Structure Models of order p. The factoris considered as a latent variable or an observable variable:in the second case the factor is a vector of several yields.Regime shifts are described by a Markov chain with (historical)nonhomogeneous transition probabilities. An empirical analysisof bivariate VAR(p) and SVARN(p) Factor-Based Term StructureModels, using monthly observations of the U.S. term structureof interest rates, and a goodness-of-fit and expectation hypothesispuzzle comparison with competing models in the literature, showsthe determinant role played by the observable nature of thefactor, lags, and switching regimes in the term structure modeling.     

Intra-Industry Trade in Intermediate Goods and Final Goods in a General Equilibrium Setting

This article develops a dual general equilibrium model to analyze the effects of intra-industry trade in both intermediate goods and final goods on the productivity in the final good production. Intra-industry trade in intermediate goods determines an increase in the number of intermediate good varieties available in the final good production, and intra-industry trade in final goods determines a reduction in the number of adaptations of an intermediate good to the final good production. Thereby, the productivity in the final good production increases. Different shares of intra-industry trade in intermediate goods and final goods in a general equilibrium setting implies that Jones' p713/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">magnification effectp713/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> and both the Rybczynski theorem and the Stolper-Samuelson theorem are not valid.     

“Buy Domestic” Campaigns and Optimal Tariffs

This paper attempts to analyze the strategic use of optimal tariffs and to examine the effects of national bias on the optimal trade policy and social welfare in a two-country, two-good, price competition model derived from Neven et al. (1991). The major findings are as follows. (1) If all consumers prefer the domestic good, then p5613q5u3c3wx/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">buy domesticp5613q5u3c3wx/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> campaigns will decrease the prohibitive tariff rate and increase local welfare. (2) If at least some consumers prefer the foreign good, but not to a great extent, then p5613q5u3c3wx/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">buy domesticp5613q5u3c3wx/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> campaigns will not change the optimal tariff rate, but may improve local welfare. (3) When all consumers greatly prefer the foreign good, then promotion of p5613q5u3c3wx/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">buy domesticp5613q5u3c3wx/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> decreases the optimal tariff rate, but it cannot improve social welfare. With this framework, we also prove that p5613q5u3c3wx/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">buy domesticp5613q5u3c3wx/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> campaigns serve as a substitute for tariffs with respect to a strategic trade policy.     

A Bayesian Formulation of Exploratory Data Analysis and Goodness‐of‐fit Testing*

Exploratory data analysis (EDA) and Bayesian inference (or, more generally, complex statistical modeling)—which are generally considered as unrelated statistical paradigms—can be particularly effective in combination. In this paper, we present a Bayesian framework for EDA based on posterior predictive checks. We explain how posterior predictive simulations can be used to create reference distributions for EDA graphs, and how this approach resolves some theoretical problems in Bayesian data analysis. We show how the generalization of Bayesian inference to include replicated data yp>repp> and replicated parameters θp>repp> follows a long tradition of generalizations in Bayesian theory. On the theoretical level, we present a predictive Bayesian formulation of goodness‐of‐fit testing, distinguishing between p‐values (posterior probabilities that specified antisymmetric discrepancy measures will exceed 0) and u‐values (data summaries with uniform sampling distributions). We explain that p‐values, unlike u‐values, are Bayesian probability statements in that they condition on observed data. Having reviewed the general theoretical framework, we discuss the implications for statistical graphics and exploratory data analysis, with the goal being to unify exploratory data analysis with more formal statistical methods based on probability models. We interpret various graphical displays as posterior predictive checks and discuss how Bayesian inference can be used to determine reference distributions. The goal of this work is not to downgrade descriptive statistics, or to suggest they be replaced by Bayesian modeling, but rather to suggest how exploratory data analysis fits into the probability‐modeling paradigm. We conclude with a discussion of the implications for practical Bayesian inference. In particular, we anticipate that Bayesian software can be generalized to draw simulations of replicated data and parameters from their posterior predictive distribution, and these can in turn be used to calibrate EDA graphs.     

Ambiguity, measurability and multiple priors

Summary.  The paper provides a notion of measurability for Multiple Prior Models characterized by nonatomic countably additive priors. A notable feature of our definition of measurability is that an event is measurable if and only if it is unambiguous in the sense of Ghirardato, Maccheroni and Marinacci [6]. In addition, the paper contains a thorough description of the basic properties of the family of measurable/unambiguous sets, of the measure defined on those and of the dependence of the class of measurable sets on the set of priors. The latter is obtained by means of an application of Lyapunovpua1p2pkenkr2/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s convexity theorem.Received: 26 August 2004, Revised: 7 September 2004, JEL Classification Numbers:   D81.I am grateful to Alp Atakan, Emel Filiz, Paolo Ghirardato, Fabio Maccheroni, Massimo Marinacci, Marco Scarsini and to a referee for comments and suggestions.     

浅论4p与4c的互补应用

4c理论是4p理论的发展，它们之间既有区别，各自又具有局限性。在市场经济条件下，企业营销单纯靠4c理论或4p理论的指导已不能适应市场的发展。只有互相结合，实现互补应用，才能发挥其巨大的作用，为企业提供尖锐的利器，使其立于不败之地。     

p2: a random effects model with covariates for directed graphs

A random effects model is proposed for the analysis of binary dyadic data that represent a social network or directed graph, using nodal and/or dyadic attributes as covariates. The network structure is reflected by modeling the dependence between the relations to and from the same actor or node. Parameter estimates are proposed that are based on an iterated generalized least-squares procedure. An application is presented to a data set on friendship relations between American lawyers.     

新岩石物理参数研究

对于非常规的储层,例如页岩气,它的储层区是脆性的。在描述不同岩石物理的参数中,杨氏模量E是衡量岩石的脆性的。计算杨氏模量E时,需要有效密度,而计算密度时需要的大偏移距地震资料通常是很难得到的。针对这种情况提出了一种新岩石物理参数E,即杨氏模量和密度的乘积,通过与属性的对比体现其在AVO叠前反演中的优势。