In this paper, we show that the conditional transform with respect to the Gaussian process involving the first variation can be expressed in terms of the conditional transform without the first variation. We then use this result to obtain various integration formulas involving the conditional $diamond$-product and the first variation.

Ramsey’s test for conditionals seems to be in conflict with the so-called Thomason conditionals. A Thomason conditional is a conditional in which either the antecedent or the consequent is a statement about the reasoning agent’s own beliefs. Several authors have pointed out that resolving the apparent conflict is to be sought by abandoning the belief revision interpretation of the Ramsey test i...

We present Bayesian analyses of matrix-variate normal data with conditional independencies induced by graphical model structuring of the characterizing covariance matrix parameters. This framework of matrix normal graphical models includes prior specifications, posterior computation using Markov chain Monte Carlo methods, evaluation of graphical model uncertainty and model structure search. Ext...

Context-specific independence (CSI) refers to conditional independencies that are true only in specific contexts. It has been found useful in various inference algorithms for Bayesian networks. This paper studies the role of CSI in general. We provide a characterization of the computational leverages offered by CSI without referring to particular inference algorithms. We identify the issues tha...

Research suggests that students in certain contexts who are “metacognitively aware learners” demonstrate better academic performance (Shraw & Dennison, 1994; Md. Yunus & Ali, 2008). In this research, the metacognitive levels for two classes of differential equations students were studied. Students completed a survey adapted from the Metacognitive Awareness Inventory (MAI) (Shraw & Dennison, 199...

This paper sets out to give a natural pragmatic explanation of several aspects of the interpretation of singular indefinite noun phrases. We develop a uniform account of characteristic features of their use which have been dealt with only partly in other semantic paradigms (in particular the dynamic, the E-type and the choice function one). We give an intuitive motivation for the familiar disco...

The probability calculus provides an attractive canonical form for reasoning but its use requires numerous estimates of chance. Some of the estimates needed in artificial systems can be recorded individually or via Bayesian networks. Others can be tabulated as relative frequencies from stored data. For the shifting contexts of commonsense reasoning, however, the latter sources are likely to pro...

Standard economic theory assumes individuals make decisions over a set of risky domains according to their own risk preferences which are stable across these decision contexts. The validity of this assumption of context-invariant risk preference has led to debate in the literature. We exploit latent class analysis to identify conditional on predicted and realized risk how heterogeneity in risk ...