Bayesian framework

Visibility in architectural layouts affects human navigation, so a suitable representation of visibility context is useful in understanding human activity. Motivated by studies of spatial behavior, we use a set of features from visibility analysis to represent spatial context in the interpretation of human activity. An agent's goal, belief about the world, trajectory and visible layout are considered to be random variables that evolve with time during the agent's movement, and are modeled in a Bayesian framework. We design a search-based task in a sprite-world, and compare the results of our framework to those of human subject experiments. Our findings confirm that knowledge of spatial layout improves human interpretations of the trajectories (implying that visibility context is useful in this task). Since our framework demonstrates performance close to that of human subjects with knowledge of spatial layout, our findings confirm that our model makes adequate use of visibility context. In addition, the representation we use for visibility context allows our model to generalize well when presented with new scenes.

Petroleum reservoir models are vital tools to help engineers in making field development decisions. Uncertainty of reservoir models in predicting future performance of a field needs to be quantified for risk management practices. Rigorous optimisation and uncertainty quantification of the reservoir simulation models are the two important steps in any reservoir engineering study. These steps facilitate decision making and have a direct impact on technical and financial performance of oil and gas companies. Optimisation of reservoir models to match past petroleum production datahistory matching -entails tuning the simulation model parameters to reproduce dynamic data profiles observed at the production wells. History matching is an inverse problem with non-unique solution; thus, different combinations of reservoir model parameters can provide a good match to the data. Multiple history matched reservoir models are used to quantify uncertainty of future hydrocarbon production from a field. Recently application of evolutionary and swarm intelligence algorithms to history matching problems has become very popular. Stochastic sampling algorithms are used to explore the model parameter space and to find good fitting models. Exploration/exploitation of the search space is essential to obtain a diverse set of history matched reservoir models. Diverse solutions from different regions of the search space represent different possible realizations of the reservoir model and are essential for realistic uncertainty quantification of reservoir performance in the future. This chapter compares the application of four recent stochastic optimisation methods: Ant Colony Optimisation, Differential Evolution, Particle Swarm Optimisation and the Neighbourhood Algorithm for the problem of history matching. The algorithms are integrated within a Bayesian framework to quantify uncertainty of the predictions.

The development of effective techniques for knowledge representation and reasoning (KRR) is a crucial aspect of successful intelligent systems. Different representation paradigms, as well as their use in dedicated reasoning systems, have been extensively studied in the past. Nevertheless, new challenges, problems, and issues have emerged in the context of knowledge representation in Artificial Intelligence (AI), involving the logical manipulation of increasingly large information sets (see for example Semantic Web, BioInformatics and so on). Improvements in storage capacity and performance of computing infrastructure have also affected the nature of KRR systems, shifting their focus towards representational power and execution performance. Therefore, KRR research is faced with a challenge of developing knowledge representation structures optimized for large scale reasoning. This new generation of KRR systems includes graph-based knowledge representation formalisms such as Bayesian Networks (BNs), Semantic Networks (SNs), Conceptual Graphs (CGs), Formal Concept Analysis (FCA), CPnets, GAI-nets, all of which have been successfully used in a number of applications. The goal of this workshop is to bring together the researchers involved in the development and application of graph-based knowledge representation formalisms and reasoning techniques.

New application of the Full Bayesian Significance Test (FBST) for precise hypotheses is presented. The FBST is an alternative to significance tests or, equivalently, to p-values. In the FBST we compute the evidence of the precise hypothesis. This evidence is the complement of the probability of a credible set "tangent" to the sub-manifold (of the parameter space) that defines the null hypothesis. We use the FBST to compare coefficients of variation, in applications arising in finance and industrial engineering.

We propose a nonlinear method for learning the low-dimensional pose of a robot from high-dimensional panoramic images. The panoramic images are assumed to lie on a nonlinear low-dimensional appearance manifold that is embedded in a high-dimensional image space. We demonstrate that the local geometry of a point and its nearest neighbors on this manifold can be used to project the point onto a low-dimensional coordinate space. Using this embedding, the unknown camera position can be estimated from a novel panoramic image. We show how the image-based position measurements can be integrated with odometry information in a Bayesian framework to yield an online estimate of a robot's position. Results from simulated data show that the proposed method outperforms other appearance-based models based upon principal components analysis and kernel density estimation.

The prominent role of monetary policy in the U.S. interwar depression has been conventional wisdom since Friedman and Schwartz (1963). This paper presents evidence on both the surprise and the systematic components of monetary policy between 1929 and 1933. Doubts surrounding GDP estimates for the 1920s would call into question conventional VAR techniques. We therefore adopt the FAVAR methodology of

The prominent role of monetary policy in the U.S. interwar depression has been conventional wisdom since . This paper presents evidence on both the surprise and the systematic components of monetary policy between 1929 and 1933. Doubts surrounding GDP estimates for the 1920s would call into question conventional VAR techniques. We therefore adopt the FAVAR methodology of , aggregating a large number of time series into a few factors and inserting these into a monetary policy VAR. We work in a Bayesian framework and apply MCMC methods to obtain the posteriors. Employing the generalized sign restriction approach toward identification of Amir Ahmadi and Uhlig (2008), we find the effects of monetary policy shocks to have been moderate. To analyze the systematic policy component, we back out the monetary policy reaction function and its response to aggregate supply and demand shocks. Results broadly confirm the Friedman/Schwartz view about restrictive monetary policy, but indicate only moderate effects. We further analyze systematic policy through conditional forecasts of key time series at critical junctures, taken with and without the policy instrument. Effects are again quite moderate. Our results caution against a predominantly monetary interpretation of the Great Depression.

This is the author's final draft. The publisher's official version is available electronically from:<http://onlinelibrary.wiley. com/journal/10.1111/%28ISSN%291835-2561>.The main purpose of this paper is to introduce the Dempster-Shafer theory (“DS” theory) of belief functions for managing uncertainties, specifically in the auditing and information systems domains. We illustrate the use of DS theory by deriving a fraud risk assessment formula for a simplified version of a model developed by Srivastava, Mock, and Turner (2007). In our formulation, fraud risk is the normalized product of four risks: risk that management has incentives to commit fraud, risk that management has opportunities to commit fraud, risk that management has an attitude to rationalize committing fraud, and the risk that auditor’s special procedures will fail to detect fraud. We demonstrate how to use such a model to plan for a financial audit where management fraud risk is assessed to be high. In a...

The phenomenon of soil liquefaction can be an induced effect of earthquake shaking where the saturated soil loses some or all of its bearing capacity and stiffness. Likewise, the increase of water pressure in the soil pores under the seismic wave causes a decrease of the shear strength. As a result, the soil becomes liquefied and susceptible to producing permanent deformations. The phenomenon of liquefaction is generally unpredictable, and neglecting it can influence the stability of structures and infrastructure foundations. Since the 1964 Alaska and Niigata earthquakes, more research works have been conducted to assess land liquefaction vulnerability. This study is undertaken in this field, whose objective, on the one hand, is to signal the phenomenon of liquefaction in the north of Morocco as a geo-technical part known for its instability and, on the other hand, to study the semi-empirical methods to adequately evaluate the liquefaction potential while specifying the most appropriate method for our case study. Similarly, the study is based on data derived from experimental results of in-situ tests applied to the embankment crossing the valley of "Oued Gharifa" on a high-speed rail line section from KP 228+400 to KP 229+375. Moreover, this research aims to show and discuss the evaluation of liquefaction potential of the experimental results of the CPT (cone penetration test) using three semi-empirical methods, namely the Juang method, the Olsen method, and the Robertson method. In doing so, we are going to compare the application results of the three semiempirical methods in light of evaluating the liquefaction likelihood of the studied area, taking into account the nature of the soil, the variation of the safety coefficient, and the liquefaction potential for each method as well.

We propose combining advanced statistical approaches with data mining techniques to build classifiers to enhance decision-making models for the job assignment problem. Adaptive Generalized Estimation Equation (AGEE) approaches with Gibbs sampling under Bayesian framework and adaptive Bayes classifiers based on the estimations of AGEE models which uses modified Naive Bayes algorithm are proposed. The proposed classifiers have several important features. Firstly, it accounts for the correlation among the outputs and the indeterministic subjective noise into the estimation of parameters. Secondly, it reduces the number of attributes used to predict the class. Moreover, it drops the assumption of independence made by the Naive Bayes classifier. We apply our techniques to the problem of assigning jobs to Navy officers, with the goal of enhancing happiness for both the Navy and the officers. The classification results were compared with nearest neighbor, Multi-Layer Perceptron and Support Vector Machine approaches.

In geotechnical engineering, and in the particular case of underground works, a great number of uncertainties arise due to the lack of knowledge of the involved formations and their variability. Geomechanical parameters are one of the main issues in the underground works design. In the initial stages, the available information about the rock masses characteristics is scarce. As the project advances to other stages more and more information from different sources becomes available and can be used for updating the geomechanical model. Bayesian methodologies use probability as the main tool to deal with uncertainty and manage to reduce it using new data via the Bayes theorem. In this work, a part of a developed Bayesian framework to the updating of the deformability modulus (E) in an underground structure is presented. Assuming E as a random variable, data from LFJ tests is used to obtain a posterior and less uncertain distribution of E. This approach led to good results and considerable uncertainty reduction and increased reliability. The developed Bayesian framework constitutes a rational and structured way of dealing with data with different sources and uncertainty levels.

Robots that are able to acquire an accurate model of their environment are regarded as fulfilling a major precondition of truly autonomous mobile vehicles. To learn a map of the environment, three problems need to be addressed simultaneously, namely exploration, mapping, and localization. In this work, we present an integrated solution to these three problems. To solve the simultaneous localization and mapping (SLAM) problem, our approach uses a highly efficient variant of algorithm proposed by Murphy and colleagues . In this algorithm, a Rao-Blackwellized particle filter (RBPF) is used to efficiently represent the joint posterior about possible maps and trajectories taken by the robot. The key contribution of our approach is an efficient decision-theoretic algorithm for computing vantage points that reduce the expected uncertainty in the RBPF. The approaches mostly related to our work have been presented by Makarenko et al. [3] and Bourgault et al. . They use an Extended Kalman Filter (EKF) to solve the SLAM problem and introduce a utility function which trades-off the cost of exploring new terrain with the potential reduction of uncertainty by measuring at selected positions. A similar technique has been applied by Sim et al. [5], who consider actions to guide the robot back to a known place in order to reduce the pose uncertainty of the vehicle during exploration. In contrast to our work, these approaches assume that the environment contains landmarks that can be uniquely determined during mapping. Our approach, in contrast, learns occupancy grid maps and thus is not restricted to environments with pre-defined landmarks. Compared to previous approaches, the novelty of the work reported here is that our algorithm simultaneously considers the uncertainty in the trajectory and in the map while building accurate occupancy grids. Based on an efficient scheme for computing the uncertainty of the joint posterior, we apply decisiontheoretic framework for choosing appropriate actions. Thereby, we utilize the properties of the Rao-Blackwellization. In brief, the uncertainty of an RBPF is determined by its entropy, which consists of two components. Whereas the first one computes the uncertainty over the trajectory taken by the robot, the second calculates the uncertainty of the individual maps weighted by the likelihood of the corresponding particles. We also demonstrate how the filter can be used to efficiently simulate possible measurements to be obtained along a path through already mapped terrain. To determine potential actions, we consider different action types including actions that collect sensor information about unknown areas as well as actions designed to re-visit known places to reduce the pose uncertainty of the vehicle. To finally select an action, we take into account the potential measurements gathered along the path of the robot as well as the cost for carrying out this action. Our approach has been implemented and tested in the real world and in simulation. Experimental results suggest that our approach leads to a robust exploration behavior that produces highly accurate grid maps. Furthermore, we illustrate the advantages of our action selection technique over previous approaches.

Theories of decision making are often formulated in terms of deterministic axioms, which do not account for stochastic variation that attends empirical data. This study presents a Bayesian inference framework for dealing with fallible data. The Bayesian framework provides readily applicable statistical procedures addressing typical inference questions that arise when algebraic axioms are tested against empirical data. The key idea of the Bayesian framework is to employ a prior distribution representing the parametric order constraints implied by a given axiom. Modern methods of Bayesian computation such as Markov chain Monte Carlo are used to estimate the posterior distribution, which provides the information that allows an axiom to be evaluated. Specifically, we adopt the Bayesian p-value as the criterion to assess the descriptive adequacy of a given model (axiom) and we use the deviance information criterion (DIC) to select among a set of candidate models. We illustrate the Bayesian framework by testing well-known axioms of decision making, including the axioms of monotonicity of joint receipt and stochastic transitivity.

This paper is a systematic review of the methodology for person fit research targeted specifically at methodologists in training. I analyze the ways in which researchers in the area of person fit have conducted simulation studies for parametric and nonparametric unidimensional IRT models since the seminal review paper by . I specifically review how researchers have operationalized different types of aberrant responding for particular testing conditions in order to compare these simulation design characteristics with features of the real-life testing situations for which person fit analyses are officially reported. I discuss the alignment between the theoretical and practical work and the implications for future simulation work and guidelines for best practice.

Multivariate analysis of fMRI data has benefited substantially from advances in machine learning. Most recently, a range of probabilistic latent variable models applied to fMRI data have been successful in a variety of tasks, including identifying similarity patterns in neural data (Representational Similarity Analysis and its empirical Bayes variant, RSA and BRSA; Intersubject Functional Connectivity, ISFC), combining multi-subject datasets (Shared Response Mapping; SRM), and mapping between brain and behavior (Joint Modeling). Although these methods share some underpinnings, they have been developed as distinct methods, with distinct algorithms and software tools. We show how the matrix-variate normal (MN) formalism can unify some of these methods into a single framework. In doing so, we gain the ability to reuse noise modeling assumptions, algorithms, and code across models. Our primary theoretical contribution shows how some of these methods can be written as instantiations of t...

Multivariate analysis of fMRI data has benefited substantially from advances in machine learning. Most recently, a range of probabilistic latent variable models applied to fMRI data have been successful in a variety of tasks, including identifying similarity patterns in neural data, combining multi-subject datasets, and mapping between brain and behavior. Although these methods share some underpinnings, they have been developed as distinct methods, with distinct algorithms and software tools. We show how the matrixvariate normal (MN) formalism can unify some of these methods into a single framework. In doing so, we gain the ability to reuse noise modeling assumptions, algorithms, and code across models. Our primary theoretical contribution shows how some of these methods can be written as instantiations of the same model, allowing us to generalize them to flexibly modeling structured residual covariances. Our formalism permits novel model variants and improved estimation strategies for SRM and RSA using substantially fewer parameters. We empirically demonstrate advantages of our two new methods: for MN-RSA, we show up to 10x improvement in runtime, up to 6x improvement in RMSE, and more conservative behavior under the null. For MN-SRM, our method grants a modest improvement to out-of-sample reconstruction while relaxing the orthonormality constraint

An inverse model using atmospheric CO 2 observations from a European network of stations to reconstruct daily CO 2 fluxes and their uncertainties over Europe at 50 km resolution has been developed within a Bayesian framework. We use the pseudo-data approach in which we try to recover known fluxes using a range of perturbations to the input. In this study, the focus is put on the sensitivity of flux accuracy to the inverse setup, varying the prior flux errors, the pseudo-data errors and the network of stations. We show that, under a range of assumptions about prior error and data error we can recover fluxes reliably at the scale of 1000 km and 10 days. At smaller scales the performance is highly sensitive to details of the inverse set-up. The use of temporal correlations in the flux domain appears to be of the same importance as the spatial correlations. We also note that the use of simple, isotropic correlations on the prior flux errors is more reliable than the use of apparently physically-based errors. Finally, increasing the European atmospheric network density improves the area with significant error reduction in the flux retrieval.

The proposed work uses fixed lag smoothing on the interactive multiple model-integrated probabilistic data association algorithm (IMM-IPDA) to enhance its performance. This approach makes use of the advantages of the fixed lag smoothing algorithm to track the motion of a maneuvering target while it is surrounded by clutter. The suggested method provides a new mathematical foundation in terms of smoothing for mode probabilities in addition to the target trajectory state and target existence state by including the smoothing advantages. The suggested fixed lag smoothing IMM-IPDA (FLs IMM-IPDA) method’s root mean square error (RMSE), true track rate (TTR), and mode probabilities are compared to those of other recent algorithms in the literature in this study. The results clearly show that the proposed algorithm outperformed the already-known methods in the literature in terms of these above parameters of interest.

We propose an application of a Bayesian methodology to dynamic MR images of protons J-coupled to 13 C nuclei for monitoring the in vivo 13 C-glucose uptake of mouse brain. The very low population of these protons and the random noise make the analysis of these images extremely difficult. The proposed method restores the images and provides an bactivationQ map of the mouse brain by means of a hypothesis testing procedure. The restoration step is performed in the Bayesian framework so that among the other advantages of a stochastic approach, it is possible to model spatial and temporal information about neighboring pixels. This leads to a restoration procedure able to reduce the noise level while preserving the information about the edges of signal areas. Based on the restored images, the testing procedure provides us with a reliable map of pixels characterized by the 13 C-glucose uptake.

Multiplicative update algorithms have encountered a great success to solve optimization problems with nonnegativity constraints, such as the famous non-negative matrix factorization (NMF) and its many variants. However, despite several years of research on the topic, the understanding of their convergence properties is still to be improved. In reference [1], we show that Lyapunov's stability theory provides a very enlightening viewpoint on the problem. We prove the exponential or asymptotic stability of the solutions to general optimization problems with non-negative constraints, including the particular case of supervised NMF, and finally study the more difficult case of unsupervised NMF. The theoretical results presented in the paper are confirmed by numerical simulations involving both supervised and unsupervised NMF, and the convergence speed of NMF multiplicative updates is investigated. In this supporting document, we present the proofs of some theoretical results presented in . This document, written as a sequel of [1], is not intended to be read separately.

Probabilistic Latent Component Analysis (PLCA) is a tool similar to Non-negative Matrix Factorization (NMF), which is used to model non-negative data such as non-negative time-frequency representations of audio. In this paper, we put forward a trick to help the corresponding parameter estimation algorithm to converge toward more meaningful solutions, based on the new concept of brakes. The idea is to control the convergence rate of the parameters of a PLCA-based model within the estimation algorithm: the parameters which are known to be properly initialized are braked in order to stay close to their initial values, whereas the other ones keep a regular convergence rate. This is an effective way to better account for a relevant initialization. In this paper, these brakes are implemented in the framework of PLCA, and they are tested in an application of multipitch estimation. Results show that the use of brakes can significantly influence the decomposition and thus the performance, ma...

The estimation of remaining useful life (RUL) of a faulty component is at the centre of system prognostics and health management. It gives operators a potent tool in decision making by quantifying how much time is left until functionality is lost. RUL prediction needs to contend with multiple sources of errors, like modelling inconsistencies, system noise and degraded sensor fidelity, which leads to unsatisfactory performance from classical techniques like autoregressive integrated moving average (ARIMA) and extended Kalman filtering (EKF). The Bayesian theory of uncertainty management provides a way to contain these problems. The relevance vector machine (RVM), the Bayesian treatment of the well known support vector machine (SVM), a kernel-based regression/classification technique, is used for model development. This model is incorporated into a particle filter (PF) framework, where statistical estimates of noise and anticipated operational conditions are used to provide estimates ...

The estimation of remaining useful life (RUL) of a faulty component is at the center of system prognostics and health management. It gives operators a potent tool in decision making by quantifying how much time is left until functionality is lost. This is especially true for aerospace systems, where unanticipated subsystem downtime may lead to catastrophic failures. RUL prediction needs to contend with multiple sources of error like modeling inconsistencies, system noise and degraded sensor fidelity. Bayesian theory of uncertainty management provides a way to contain these problems by integrating out the nuisance variables. We use the Relevance Vector Machine (RVM), for model development. RVM is a Bayesian treatment of the well known Support Vector Machine (SVM), a kernel-based regression/classification technique. This model is next used in a Particle Filter (PF) framework. Statistical estimates of the noise in the system and anticipated operational conditions are processed to provide estimates of RUL in the form of a probability density function (PDF). Validation of this approach on experimental data collected from Li-ion batteries is presented.

Prezentam o metoda generală de aplicare a inferenţei Bayesiene pentru repartiţii bidimensionale definite de copule. In această lucrare considerăm cazul în care ambele repartiţii marginale sunt Weibull sau exponenţiale dar metoda poate fi extinsă şi la alte repartiţii. Pentru determinarea repartiţiei posterioare se folosesc tehnici de simulare Markov chain Monte Carlo. We present a general methodology for performing Bayesian inference on copula models. Here we discuss the case in which each marginal distribution is Weibull or Exponential but the approach can be generalized to other distributions. We solve the computational problem associated with sampling from the posterior distribution using Markov chain Monte Carlo. We illustrate the method with simulated data in order to assess its efficiency.

The stochastic multi-armed bandit problem captures the fundamental exploration vs. exploitation tradeoff inherent in online decision-making in uncertain settings. However, in several applications, the traditional objective of maximizing the expected sum of rewards obtained can be inappropriate. Motivated by the problem of optimizing job assignments to groom novice workers with unknown trainability in labor platforms, we consider a new objective in the classical setup. Instead of maximizing the expected total reward from $T$ pulls, we consider the vector of cumulative rewards earned from each of the $K$ arms at the end of $T$ pulls, and aim to maximize the expected value of the $highest$ cumulative reward. This corresponds to the objective of grooming a single, highly skilled worker using a limited supply of training jobs. For this new objective, we show that any policy must incur a regret of $\Omega(K^{1/3}T^{2/3})$ in the worst case. We design an explore-then-commit policy featurin...

This paper presents a generative statistical approach for the automatic three-dimensional (3D) extraction and reconstruction of unfoliaged deciduous trees from terrestrial wide-baseline image sequences. Unfoliaged trees are difficult to reconstruct from images due to partially weak contrast, background clutter, occlusions, and particularly the possibly varying order of branches in images from different viewpoints. This work combines generative modeling by L-systems and a statistical approach for maximum a posteriori (MAP) estimation for the reconstruction of the 3D branching structure of trees. Background estimation is conducted by means of gray scale morphology to provide a good basis of generative modeling. A Gaussian likelihood function based on intensity differences is employed to evaluate the hypotheses. The target tree is classified into three typical branching types after the extraction of the first level of branches and specific Production Rules of an L-system are used. Generic prior distributions for parameters are refined based on already extracted branches in a Bayesian framework and are integrated into the MAP estimation. By these means most of the branching structure besides the tiny twigs can be reconstructed. The results are presented in form of VRML models and show the potential of the approach.

It is presented in the paper, a contribution to the field of human-machine interaction a system that has the ability to analyze emotional content of human movements, using as basis a technique known as Laban Movement Analysis. This work searches for computational approaches to quantify human qualities like emotion and expression and explores new functionalities towards implementation of more advanced surveillance systems or perception system for social robots. Human body parts are tracked using both vision and magnetic trackers, generating trajectories. Laban Analysis concept is used to extract useful features from those trajectories to classify human movements. To solve the problem of classification a Bayesian framework was adopted, as it offers an intuitive approach to learning and classification. The descriptor opens a wide range of possibilities to analyze the emotional content and expressiveness of gestures.

This paper describes a method for asking statistical questions about a large text corpus. We exemplify the method by addressing the question, "What percentage of Federal Register documents are real documents, of possible interest to a text researcher or analyst?" We estimate an answer to this question by evaluating 200 documents selected from a corpus of 45,820 Federal Register documents. Stratified sampling is used to reduce the sampling uncertainty of the estimate from over 3100 documents to fewer than 1000. The stratification is based on observed characteristics of real documents, while the sampling procedure incorporates a Bayesian version of Neyman allocation. A possible application of the method is to establish baseline statistics used to estimate recall rates for information retrieval systems.

This paper describes a method for asking statistical questions about a large text corpus. We exemplify the method by addressing the question," What percentage of Federal Register documents are real documents, of possible interest to a text researcher or analyst ...

The structural approach to joint inversion, entailing common boundaries or gradients, offers a flexible way to invert diverse types of surface-based and/or crosshole geophysical data. The cross-gradients function has been introduced as a means to construct models in which spatial changes in two models are parallel or anti-parallel. Inversion methods that use such structural constraints also provide estimates of non-linear and non-unique field-scale relationships between model parameters. Here, we invert jointly crosshole radar and seismic traveltimes for structurally similar models using an iterative non-linear traveltime tomography algorithm. Application of the inversion scheme to synthetic data demonstrates that it better resolves lithological boundaries than the individual inversions. Tests of the scheme on observed radar and seismic data acquired within a shallow aquifer illustrate that the resultant models have improved correlations with flowmeter data than with models based on individual inversions. The highest correlation with the flowmeter data is obtained when the joint inversion is combined with a stochastic regularization operator, where the vertical integral scale is estimated from the flowmeter data. Point-spread functions shows that the most significant resolution improvements of the joint inversion is in the horizontal direction. To determine petrophysical properties, state variables, and structural boundaries, it may be necessary to combine information provided by models obtained from different geophysical data (e.g., . Interpretation of several individually inverted data sets can be illuminating, but the results are usually affected by the resolution limitations of each model. For consistent interpretations of multiple geophysical models, it would be advantageous to have inversion tools that have similar formulations of the inverse problem regardless of the type of geophysical data being inverted. This would allow models to be coupled, as long as the data have comparable spatial support. By joint inversion, we refer to coupled models that are obtained by simultaneously minimizing a misfit function that includes the data misfit of each data type. Joint inversion can improve the resolution of each geophysical model and provide models that are consistent with each other and therefore easier to interpret (e.g., ). is not yet a standard tool in geophysical applications, mainly because robust and well-established petrophysical models that can be used to couple the models are usually only available for certain geophysical parameters, such as compressional and shear wave slownesses . Furthermore, petrophysical models often apply only in restricted geological settings (e.g., . In addition, the parameters of petrophysical models can seldom be adequately constrained by individual field data sets, such that fairly strong assumptions are required to couple models based on their petrophysical properties. To avoid introducing questionable petrophysical models, joint inversion methods have been developed for layered (1D) structures that are expected to have coincident layer boundaries and constant properties within each layer (e.g., Monteiro Santos et al., 2006). A

This paper has two themes. First, we classify some effects which outliers in the data have on unit root inference. We show that, both in a classical and a Bayesian framework, the presence of additive outliers moves 'standard' inference towards stationarity. Second, we base inference on an independent Student-t instead of a Gaussian likelihood. This yields results that are less sensitive to the presence of outliers. Application to several time series with outliers reveals a negative correlation between the unit root and degrees of freedom parameter of the Student-t distribution. Therefore, imposing normality may incorrectly provide evidence against the unit root.

Motivated by applications such as visual surveillance and video monitoring, there has been a lot of interest in constructing cognitive vision systems capable of detecting and identifying actions and activities. Hidden Markov models (HMMs) are perhaps the most successful framework in perceptual computing for modeling and classifying dynamic behaviors, popular because they offer dynamic time warping, a training algorithm, and a clear Bayesian semantics. This work was motivated by the need of an efficient, robust, and real time HMM-based action recognizer, realistic in the sense that practical constraints such as the training set size are taken into account. Generalizing previous works, we formulate the main issues a recognizer should address, present a generic strategy to design such a recognizer, and formalize the conditions and the limitations on the features, as well as some important building steps and issues.

In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done by evaluating the marginal likelihood of the data given a candidate structure. This term can be computed in closed-form for standard parametric families (e.g., Gaussians), and can be approximated, at some computational cost, for some semi-parametric families (e.g., mixtures of Gaussians). We present a new family of continuous variable probabilistic networks that are based on Gaussian Process priors. These priors are semiparametric in nature and can learn almost arbitrary noisy functional relations. Using these priors, we can directly compute marginal likelihoods for structure learning. The resulting method can discover a wide range of functional dependencies in multivariate data. We develop the Bayesian score of Gaussian Process Networks and describe how to learn them from data. We present empirical results on artificial data as well as on real-life domains with non-linear dependencies.

In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done by evaluating the marginal likelihood of the data given a candidate structure. This term can be computed in closed-form for standard parametric families (e.g., Gaussians), and can be approximated, at some computational cost, for some semi-parametric families (e.g., mixtures of Gaussians). We present a new family of continuous variable probabilistic networks that are based on Gaussian Process priors. These priors are semiparametric in nature and can learn almost arbitrary noisy functional relations. Using these priors, we can directly compute marginal likelihoods for structure learning. The resulting method can discover a wide range of functional dependencies in multivariate data. We develop the Bayesian score of Gaussian Process Networks and describe how to learn them from data. We present empirical results on artificial data as well as on real-life domains with non-linear dependencies.

This paper considers a family of distributions constructed by a stochastic mixture of the order statistics of a sample of size two. Various properties of the proposed model are studied. We apply the model to extend the exponential and symmetric Laplace distributions. An extension to the bivariate case is considered.

Estimation of cetacean abundance or density using visual methods can be cost ineffective under many scenarios. Methods based on acoustic data have recently been proposed as an alternative, and could potentially be more effective for visually elusive species that produce loud sounds. Motivated by a data set of minke whale (\textit{Balaenoptera acutorostrata}) boing sounds detected at multiple hydrophones at the U.S. Navy's Pacific Missile Range Facility (PMRF), we present an approach to estimate density or abundance based on spatially explicit capture recapture (SECR) methods. We implement the proposed methods in both a likelihood and a Bayesian framework. The point estimates for abundance and detection parameters from both implementation methods are very similar and agree well with current knowledge about the species. The two implementation approaches are compared in a small simulation study. While the Bayesian approach might be easier to generalize, the likelihood approach is faster to implement (at least in simple cases like the one presented here) and more readily amenable to model selection. SECR methods seem to be a strong candidate for estimating density from acoustic data where recaptures of sound at multiple hydrophones/microphones are available, and we anticipate further development of related methodologies in the future.

Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially-explicit processes that evolve over time. Correspondingly, in recent years there has been a significant amount of research on new statistical methodology for such models. Although descriptive models that approach the problem from the second-order (covariance) perspective are important, and innovative work is being done in this regard, many real-world processes are dynamic, and it can be more efficient in some cases to characterize the associated spatio-temporal dependence by the use of dynamical models. The chief challenge with the specification of such dynamical models has been related to the curse of dimensionality. Even in fairly simple linear, first-order Markovian, Gaussian error settings, statistical models are often over parameterized. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters. In addition, this framework has allowed for the specification of science based parameterizations (and associated prior distributions) in which classes of deterministic dynamical models (e.g., partial differential equations (PDEs), integro-difference equations (IDEs), matrix models, and agent-based models) are used to guide specific parameterizations. Most of the focus for the application of such models in statistics has been in the linear case. The problems mentioned above with linear dynamic models are com-Communicated by Domingo Morales.

In this article we extend the work of and illustrate the use of an evidential reasoning approach for developing fraud risk analysis models under the Bayesian framework. New formulations facilitating fraud risk assessments are needed because decision tree approaches previously used to develop analytical models are not appropriate in complex situations involving several interrelated variables. To demonstrate the evidential reasoning approach, a fraud risk assessment formula is derived and illustrated. The fraud risk formula captures the impact of the presence or absence of and interrelationships between the three 'fraud triangle' risk factors: Incentives, Attitude and Opportunities. The formula includes the impact of risks and controls related to these three fraud risk factors as well as the impact of forensic audit procedures and relevant analytical and other procedures that provide evidence for the presence or absence of fraud. This formula may be used in audit practice both to help plan the audit and to assess fraud risk sequentially as audit evidence is obtained.

There is theoretical and experimental evidence that the spatial extent of mass neural activity is an important factor of brain response in neuroimaging studies. Direct estimation of the surface area of activated regions would importantly complement the quantitative analysis of amplitude variations of cortical currents. These latter are accessible at the regional scale through source modeling of magnetoencephalographic signals. Here we present a joint approach to the estimation of both the local spatial extent and amplitude variations of neural current sources. The technique operates in two consecutive steps: 1) the compact modeling of regional cortical currents using equivalent current multipoles and 2) the remapping of these latter back onto the cortical surface using a sparse-focal imaging model. This Multipole Cortical Remapping technique operates in a Bayesian framework. Performances are evaluated using extensive Monte-Carlo simulations and are complemented with real data from a somatosensory mapping MEG experiment.

The problem of selecting the correct subset of predictors within a linear model has received much attention in recent literature. Within the Bayesian framework, a popular choice of prior has been Zellner's g-prior which is based on the inverse of empirical covariance matrix of the predictors. An extension of the Zellner's prior is proposed in this article which allow for a power parameter on the empirical covariance of the predictors. The power parameter helps control the degree to which correlated predictors are smoothed towards or away from one another. In addition, the empirical covariance of the predictors is used to obtain suitable priors over model space. In this manner, the power parameter also helps to determine whether models containing highly collinear predictors are preferred or avoided. The proposed power parameter can be chosen via an empirical Bayes method which leads to a data adaptive choice of prior. Simulation studies and a real data example are presented to show how the power parameter is well determined from the degree of cross-correlation within predictors. The proposed modification compares favorably to the standard use of Zellner's prior and an intrinsic prior in these examples.

In this paper, we apply the Markov Chain Monte Carlo method, within the Bayesian framework, for the estimation of parameters appearing in the heat conduction model in metals under the condition of thermal non-equilibrium between electrons and lattice. Such non-equilibrium can be experimentally observed in a time scale of up to few picoseconds, during the heating of thin metal films with laser pulses of the order of femtoseconds. Simulated measurements containing random errors are used for the solution of the inverse problem. Results are presented for the simultaneous estimation of the electron-phonon coupling factor, the thermal conductivity and the heat capacity of the electron gas.

L’interprétation des images géoscientifiques est une tâche complexe en raison de la présence de sédiments, d’eau et de végétation qui masquent partiellement ou totalement les formations géologiques sous-jacentes. SFES2D est un outil multi-échelle spécifiquement conçu pour l’extraction et la sélection de caractéristiques spatiales et spectrales à des fins géologiques. Il intègre des méthodes avancées telles que l’Analyse en Composantes Principales (ACP), l’Analyse en Composantes Indépendantes (ACI) et la Transformée en Ondelettes Continue (TOC), optimisées par une approche bayésienne pour l’identification des linéaments curvilignes. Grâce à ses capacités de segmentation, SFES2D permet de générer rapidement des cartes pseudo-géologiques adaptées à diverses échelles d’analyse, allant de la cartographie de terrain à l’examen microscopique d’échantillons de roches.