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We consider asymptotic approximations to joint posterior distributions in situations where the full conditional distributions referred to in Gibbs sampling are asymptotically normal. Our development focuses on problems where data augmentation facilitates simpler calculations, but results hold more generally. Asymptotic mean vectors are obtained as simultaneous solutions to fixed point equations...

In prediction problems with more predictors than observations, it can sometimes be helpful to use a joint probability model, π(Y,X), rather than a purely conditional model, π(Y | X), where Y is a scalar response variable and X is a vector of predictors. This approach is motivated by the fact that in many situations the marginal predictor distribution π(X) can provide useful information about th...

Kolmogorov in 1965 proposed two related measures of information content (alternately, measures of complexity) based on the size of a program which when processed by a suitable algorithm (machine) yields the desired object. The main emphasis was placed on a conditional complexity measure. In this paper a simple variation of the (restricted) conditional complexity measure investigated by Martin-L...

In many engineering situations, we need to make decisions under uncertainty. In some cases, we know the probabilities pi of different situations i; these probabilities should add up to 1. In other cases, we only have expert estimates of the degree of possibility μi of different situations; in accordance with the possibility theories, the largest of these degrees should be equal to 1. In practic...

Bayesian networks (BNs) are useful for coding conditional independence statements between a given set of measurement variables. On the other hand, event trees (ETs) are convenient for representing asymmetric structure and how situations unfold. In this paper we report the development of a new graphical framework for discrete probability models called the Chain Event Graph (CEG). The class of CE...

We present a new, novel approach to obtaining a network’s connectivity. More specifically, we show that there exists a relationship between a network’s graph isoperimetric properties and its conditional connectivity. A network’s connectivity is the minimum number of nodes, whose removal will cause the network disconnected. It is a basic and important measure for the network’s reliability, hence...

A key function of categories is to help predictions about unobserved features of objects. At the same time, humans often find themselves in situations where the categories of the objects they perceive are uncertain. How do people make predictions about unobserved features in such situations? We propose a rational model that solves this problem. Our model complements existing models in that it i...

People can often outperform statistical methods and machine learning algorithms in situations that involve making inferences about the relationship between causes and effects. While people are remarkably good at causal reasoning in many situations, there are several instances where they deviate from expected responses. This paper examines three situations where judgments related to causal infer...

The fact that individuals will most likely behave differently in different situations begets the introduction of conditional strategies. Inspired by this, we study the evolution of cooperation in the spatial public goods game, where, besides unconditional cooperators and defectors, also different types of conditional cooperators compete for space. Conditional cooperators will contribute to the ...