Modelling as a way of organising knowledge

The paper is motivated by the need of to address a new the old topic of operational research and hard (but also soft) systems science: what is the role of mathematical modelling, how does it relate to knowledge, to creativity, to human concerns? Such a need arises because of the great change observed today, of informational revolution, of transition towards knowledge-based economy, towards networked organization of our social and economic life. During last 50 years operational research, mathematical modelling and computerised techniques of model analysis and optimisation contributed essentially to the change of perception of contemporary world, characteristic for the current informational revolution indicating the change of civilisation eras. These contributions have been noted during these years inside operational research, but analysed mostly from so-called soft systems thinking perspective. Main contributions to the actual formation of the new era, however, came from the hard systems research, in particular, as we shall show, from mathematical modelling in applications to the development of technological systems.     

A Sequent Calculus for Propositional Dynamic Logic for Agents with Interactions

We consider a propositional dynamic logic for agents with interactions such as known commitment, no learning, and perfect recall. For this logic, we present a sequent calculus with a restricted cut rule and prove the soundness and completeness for the calculus.__________Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 2, pp. 261–269, April–June, 2005.     

Beyond mathematical content knowledge: A mathematician's knowledge needed for teaching an inquiry-oriented differential equations course

In this research report we examine knowledge other than content knowledge needed by a mathematician in his first use of an inquiry-oriented curriculum for teaching an undergraduate course in differential equations. Collaboratively, the mathematician and two mathematics education researchers identified the challenges faced by the mathematician as he began to adopt reform-minded teaching practices. Our analysis reveals that responding to those challenges entailed formulating and addressing particular instructional goals, previously unfamiliar to the instructor. From a cognitive analytical perspective, we argue that the instructor's knowledge — or lack of knowledge — influenced his ability to set and accomplish his instructional goals as he planned for, reflected on, and enacted instruction. By studying the teaching practices of a professional mathematician, we identify forms of knowledge apart from mathematical content knowledge that are essential to reform-oriented teaching, and we highlight how knowledge acquired through more traditional instructional practices may fail to support research-based forms of student-centered teaching.     

多源验前信息下先验分布的稳健融合方法

根据多种先验分布与似然函数尾部特性的比较,给出了多源验前信息下先验分布的稳健融合方法.讨论了由该方法得到的融合先验分布的后验稳健性问题.最后的数值例子表明,由该方法得到的融合先验分布具有较好的稳健性,进一步验证了该方法的有效性.     

Some remarks on Bayesian inference for one-way ANOVA models

We consider the standard one-way ANOVA model; it is well-known that classical statistical procedures are based on a scalar non-centrality parameter. In this paper we explore both marginal likelihood and integrated likelihood functions for this parameter and we show that they exactly lead to the same answer. On the other hand, we prove that a fully Bayesian testing procedure may provide different conclusions, depending on what is considered to be the real quantity of interest in the model or, said differently, which are the competing hypotheses. We illustrate these issues via a real data example.     

Bayesian prediction based on a class of shrinkage priors for location-scale models

A class of shrinkage priors for multivariate location-scale models is introduced. We consider Bayesian predictive densities for location-scale models and evaluate performance of them using the Kullback–Leibler divergence. We show that Bayesian predictive densities based on priors in the introduced class asymptotically dominate the best invariant predictive density.     

广义自回归模型参数的收缩估计

运用经典方法结合参数的先验信息得到了广义一阶自回归模型中自相关系数的收缩估计的闭式表达式,它是通常极大似然估计与先验均值的加权平均,在适当的先验信息下优于原来的估计.     

BAYESIAN LOCAL INFLUENCE ASSESSMENTS IN A GROWTH CURVE MODEL WITH GENERAL COVARIANCE STRUCTURE

1 IntroductionThe problem of how to deal With local influence assessment in a growth curve model withgeneral covariance structure is very important. There are two main reasons why this is so. First,although the growth curve model can be viewed as a generalizetion of classical linear regressionmodel in some wad, as pointed out by for etc.[1], two models are substantially different andthe former is much more complicated than the latter. Secondly3 it is not generally the case withlocally influen…     

Multicriteria estimation of probabilities on basis of expert non-numeric,non-exact and non-complete knowledge

A new method of alternatives’ probabilities estimation under deficiency of expert numeric information (obtained from different sources) is proposed. The method is based on the Bayesian model of uncertainty randomization. Additional non-numeric, non-exact, and non-complete expert knowledge (NNN-knowledge, NNN-information) is used for final estimation of the alternatives’ probabilities. An illustrative example demonstrates the proposed method application to forecasting of oil shares price with the use of NNN-information obtained from different experts (investment firms).     

Why contextualists cannot know they are right: Self-refuting implications of contextualism

Conversational contextualism in epistemology is characterized by four main theses: 1. the indexicality of knowledge claims thesis; 2. the attributor contextualism thesis; 3. the conversational contextualism thesis, and 4. the main thesis of contextualism according to which a knowledge claim can be true in one context and false in another context in which more stringent standards for knowledge are operant. It is argued that these theses taken together generate problems for contextualism. In particular, it is shown that there is no context in which the contextualist can truthfully claim to know her theory is true. Since these results were obtained only with principles the contextualist cannot give up—like the principle of epistemic closure and the principle that knowledge implies truth—it seems that contextualism is in need of a thoroughgoing revision if it is to become a successful epistemic theory.