Imprecise probability models for inference in exponential families

When considering sampling models described by a distribution from an exponential family, it is possible to create two types of imprecise probability models. One is based on the corresponding conjugate distribution and the other on the corresponding predictive distribution. In this paper, we show how these types of models can be constructed for any (regular, linear, canonical) exponential family, such as the centered normal distribution. To illustrate the possible use of such models, we take a look at credal classification. We show that they are very natural and potentially promising candidates for describing the attributes of a credal classifier, also in the case of continuous attributes

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Using imprecise continuous time Markov chains for assessing the reliability of power networks with common cause failure and non-immediate repair.

We explore how imprecise continuous time Markov chains can improve traditional reliability models based on precise continuous time Markov chains. Specifically, we analyse the reliability of power networks under very weak statistical assumptions, explicitly accounting for non-stationary failure and repair rates and the limited accuracy by which common cause failure rates can be estimated. Bounds on typical quantities of interest are derived, namely the expected time spent in system failure state, as well as the expected number of transitions to that state. A worked numerical example demonstrates the theoretical techniques described. Interestingly, the number of iterations required for convergence is observed to be much lower than current theoretical bounds

Epistemic irrelevance in credal networks : the case of imprecise Markov trees

We replace strong independence in credal networks with the weaker notion of epistemic irrelevance. Focusing on directed trees, we show how to combine local credal sets into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is essentially linear in the number of nodes, is formulated entirely in terms of coherent lower previsions. We supply examples of the algorithm's operation, and report an application to on-line character recognition that illustrates the advantages of our model for prediction

Completing an uncertainty criterion of classification

We present a variation of a method of classification based in uncertainty on credal set. Similarly to its origin it use the imprecise Dirichlet model to create the credal set and the same uncertainty measures. It take into account sets of two variables to reduce the uncertainty and to seek the direct relations between the variables in the data base and the variable to be classified. The success are equivalent to the success of the first method except in those where there are a direct relations between some variables that decide the value of the variable to be classified where we have a notable improvement

Flexible shrinkage in high-dimensional Bayesian spatial autoregressive models

This article introduces two absolutely continuous global-local shrinkage priors to enable stochastic variable selection in the context of high-dimensional matrix exponential spatial specifications. Existing approaches as a means to dealing with overparameterization problems in spatial autoregressive specifications typically rely on computationally demanding Bayesian model-averaging techniques. The proposed shrinkage priors can be implemented using Markov chain Monte Carlo methods in a flexible and efficient way. A simulation study is conducted to evaluate the performance of each of the shrinkage priors. Results suggest that they perform particularly well in high-dimensional environments, especially when the number of parameters to estimate exceeds the number of observations. For an empirical illustration we use pan-European regional economic growth data.Comment: Keywords: Matrix exponential spatial specification, model selection, shrinkage priors, hierarchical modeling; JEL: C11, C21, C5

A robust Bayesian land use model for crop rotations

Often, in dynamical systems, such as farmers’ crop choices, the dynamics are driven by external non-stationary factors, such as rainfall and agricultural input and output prices. Such dynamics can be modelled by a non-stationary stochastic process, where the transition probabilities are functions of such external factors. We propose using a multinomial logit model for these transition probabilities, and investigate the problem of estimating the parameters of this model from data. We adapt the work of Chen and Ibrahim to propose a conjugate prior distribution for the parameters of the multinomial logit model. Inspired by the imprecise Dirichlet model, we will perform a robust Bayesian analysis by proposing a fairly broad class of prior distributions, in order to accommodate scarcity of data and lack of strong prior expert opinion. We discuss the computation of bounds for the posterior transition probabilities, using a variety of calculation methods. These sets of posterior transition probabilities mean that our land use model consists of a non-stationary imprecise stochastic process. We discuss computation of future events in this process. Finally, we use our novel land use model to investigate real-world data. We investigate the impact of external variables on the posterior transition probabilities, and investigate a scenario for future crop growth. We also use our model to solve a hypothetical yet realistic policy problem