PROBABILISTIC MODELLING OF EARTHQUAKE OCCURRENCE: FIRST EXAMPLES OF DATA INTEGRATION WITHIN A BAYESIAN FRAMEWORK

PROBABILISTIC MODELLING OF EARTHQUAKE OCCURRENCE: FIRST EXAMPLES OF DATA INTEGRATION WITHIN A BAYESIAN FRAMEWOR

Using instruments in the study of animate beings:Della Porta’s and Bacon’s experiments with plants

In this paper, I explain Francis Bacon's use of plants as philosophical instruments in the context of his Historia vitae et mortis. My main claim is that Bacon experimented with plants in order to obtain knowledge about the hidden processes of nature, knowledge that could be transferred to the human case and used for the prolongation of life. Bacon's experiments were based on Giambattista della Porta's reports from the Magia naturalis, but I show how a different metaphysics and research method made Bacon systematically rework, reconceptualise, and put to divergent uses the results of the same experimental reports

Reading Scepticism Historically. Scepticism, Acatalepsia and the Fall of Adam in Francis Bacon

The first part of this paper will provide a reconstruction of Francis Bacon’s interpretation of Academic scepticism, Pyrrhonism, and Dogmatism, and its sources throughout his large corpus. It shall also analyze Bacon’s approach against the background of his intellectual milieu, looking particularly at Renaissance readings of scepticism as developed by Guillaume Salluste du Bartas, Pierre de la Primaudaye, Fulke Greville, and John Davies. It shall show that although Bacon made more references to Academic than to Pyrrhonian Scepticism, like most of his contemporaries, he often misrepresented and mixed the doctrinal components of both currents. The second part of the paper shall offer a complete chronological survey of Bacon’s assessment of scepticism throughout his writings. Following the lead of previous studies by other scholars, I shall support the view that, while he approved of the state of doubt and the suspension of judgment as a provisional necessary stage in the pursuit of knowledge, he rejected the notion of acatalepsia. To this received reading, I shall add the suggestion that Bacon’s criticism of acatalepsia ultimately depends on his view of the historical conditions that surround human nature. I deal with this last point in the third part of the paper, where I shall argue that Bacon’s evaluation of scepticism relied on his adoption of a Protestant and Augustinian view of human nature that informed his overall interpretation of the history of humanity and nature, including the sceptical schools

All Alone in the Universe: Individuals in Descartes and Newton

In this paper we argue that the primary issue in Descartes' Principles of Philosophy, Part II, articles 1-40, is the problem of individuating bodies. We demonstrate that Descartes departs from the traditional quest for a principle of individuation, moving to a different strategy with the more modest aim of constructing bodies adequate to the needs of his cosmology. In doing this he meets with a series of difficulties, and this is precisely the challenge that Newton took up. We show that Descartes' questions and his strategy influenced not only Newton's account of physical bodies, but also the structure of his mechanics

Multisource data fusion and super-resolution from astronomical images

Abstract Virtual Observatories give us access to huge amounts of image data that are often redundant. Our goal is to take advantage of this redundancy by combining images of the same field of view into a single model. To achieve this goal, we propose to develop a multi-source data fusion method that relies on probability and band-limited signal theory. The target object is an image to be inferred from a number of blurred and noisy sources, possibly from different sensors under various conditions (i.e. resolution, shift, orientation, blur, noise...). We aim at the recovery of a compound model "image+uncertainties" that best relates to the observations and contains a maximum of useful information from the initial data set. Thus, in some cases, spatial super-resolution may be required in order to preserve the information. We propose to use a Bayesian inference scheme to invert a forward model, which describes the image formation process for each observation and takes into account some a priori knowledge (e.g. stars as point sources). This involves both automatic registration and spatial resampling, which are ill-posed inverse problems that are addressed within a rigorous Bayesian framework. The originality of the work is in devising a new technique of multi-image data fusion that provides us with super-resolution, self-calibration and possibly model selection capabilities. This approach should outperform existing methods such as resample-and-add or drizzling since it can handle different instrument characteristics for each input image and compute uncertainty estimates as well. Moreover, it is designed to also work in a recursive way, so that the model can be updated when new data become available. Key words: Model-based data fusion, uncertainties, generative models, inverse problems, signal reconstruction, super-resolution, spatial resampling, resolution-limited, B-Splines Email addresses: [email protected] (A. Jalobeanu, J.A. Gutiérrez), [email protected] (E. Slezak). URLs: lsiit-miv.u-strasbg.fr/paseo (A. Jalobeanu, J.A. Gutiérrez), www.obs-nice.fr/cassiopee (E. Slezak)

Multisource data fusion for bandlimited signals: a Bayesian perspective.

Abstract. We consider data fusion as the reconstruction of a single model from multiple data sources. The model is to be inferred from a number of blurred and noisy observations, possibly from different sensors under various conditions. It is all about recovering a compound object, signal+uncertainties, that best relates to the observations and contains all the useful information from the initial data set. We wish to provide a flexible framework for bandlimited signal reconstruction from multiple data. In this paper, we focus on a general approach involving forward modeling (prior model, data acquisition) and Bayesian inference. The proposed method is valid for n-D objects (signals, images or volumes) with multidimensional spatial elements. For the sake of clarity, both formalism and test results will be shown in 1D for single band signals. The main originality lies in seeking an object with a prescribed bandwidth, hence our choice of a B-Spline representation. This ensures an optimal sampling in both signal and frequency spaces, and allows for a shift invariant processing. The model resolution, the geometric distortions, the blur and the regularity of the sampling grid can be arbitrary for each sensor. The method is designed to handle realistic Gauss+Poisson noise. We obtained promising results in reconstructing a super-resolved signal from two blurred and noisy shifted observations, using a Gaussian Markov chain as a prior. Practical applications are under development within the SpaceFusion project. For instance, in astronomical imaging, we aim at a sharp, well-sampled, noise-free and possibly super-resolved image. Virtual Observatories could benefit from such a way to combine large numbers of multispectral images from various sources. In planetary imaging or remote sensing, a 3D image formation model is needed; nevertheless, this can be addressed within the same framework