In statistical inference, we infer the population parameter based on the realization of sample statistics. This can be considered in the framework of inductive inference. We show, in Chen (1993), that if we measure a parameter by the possibility (or belief) measure, we can have an inductive inference similar to the Bayesian inference in belief update. In this article we apply this inference to ...

Reference Evapotranspiration (ET0) is a basic parameter for determination of irrigation program. It is one of the most important factors in water resources management and considers as a requirement for every irrigation and drainage plans. Because of the spatial variations of ET0, it is necessary to use from intrapolation methods in order to estimation of this parameter in regional studie. Using...

The Research Center for Human Development in Dakar (CRDH) with the technical assistance of ICF Macro and the National Malaria Control Programme (NMCP) conducted in 2008/2009 the Senegal Malaria Indicator Survey (SMIS), the first nationally representative household survey collecting parasitological data and malaria-related indicators. In this paper, we present spatially explicit parasitaemia ris...

In this paper, we show that a hierarchical Bayesian modelling approach to sequential learning leads to many interesting attributes such as regularisation and automatic relevance determination. We identify three inference levels within this hierarchy, namely model selection, parameter estimation and noise estimation. In environments where data arrives sequentially, techniques such as cross-valid...

We show that a hierarchical Bayesian modeling approach allows us to perform regularization in sequential learning. We identify three inference levels within this hierarchy: model selection, parameter estimation, and noise estimation. In environments where data arrive sequentially, techniques such as cross validation to achieve regularization or model selection are not possible. The Bayesian app...

13 Approximate Bayesian inference on the basis of summary statistics is well14 suited to complex problems for which the likelihood is either mathematically 15 or computationally intractable. However the methods that use rejection suf16 fer from the curse of dimensionality when the number of summary statistics 17 is increased. Here we propose a machine-learning approach to the estimation 18 of t...

Existing formulations for optical flow estimation and image segmentation have used Bayesian Networks and Markov Random Field (MRF) priors to impose smoothness of segmentation. These approaches typically focus on estimation in a single time slice based on two consecutive images. We develop a motion segmentation framework for a continuous stream of images using inference in a corresponding Dynami...

The ill-posed nature of the MEG (or related EEG) source localization problem requires the incorporation of prior assumptions when choosing an appropriate solution out of an infinite set of candidates. Bayesian approaches are useful in this capacity because they allow these assumptions to be explicitly quantified using postulated prior distributions. However, the means by which these priors are ...