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Bayesian analysis for Markov jump processes (MJPs) is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding, thus its applicability is limited to a small class of problems. In this paper, we describe the application of Riemann manifold Markov chain Monte Carlo (MCMC) methods using an approximation to the likelihood of the MJP that is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient whereas the convergence rate and mixing of the chains allow for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.

Bat echolocation call identification methods are important in developing efficient cost-effective methods for large-scale bioacoustic surveys for global biodiversity monitoring and conservation planning. Such methods need to provide interpretable probabilistic predictions of species since they will be applied across many different taxa in a diverse set of applications and environments. We develop such a method using a multinomial probit likelihood with independent Gaussian process priors and study its feasibility on a data set from an on-going study of 21 species, five families and 1800 bat echolocation calls collected from Mexico, a hotspot of bat biodiversity. We propose an efficient approximate inference scheme based on the expectation propagation algorithm and observe that the overall methodology significantly improves on currently adopted approaches to bat call classification by providing an approach which can be easily generalized across different species and call types and is fully probabilistic. Implementation of this method has the potential to provide robust species identification tools for biodiversity acoustic bat monitoring programmes across a range of taxa and spatial scales.

The development of an intra-abdominal bile collection (biloma) is an infrequent complication of laparoscopic cholecystectomy (LC). These bilomas develop in the subhepatic space most often secondary to iatrogenic injury of the extrahepatic ducts. We present a case of hepatic subcapsular biloma following LC and we discuss its etiology and management. Early diagnosis is crucial and percutaneous drainage under CT guidance should be employed to resolve this complication.

Bayesian analysis for Markov jump processes (MJPs) is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding, thus its applicability is limited to a small class of problems. In this paper, we describe the application of Riemann manifold Markov chain Monte Carlo (MCMC) methods using an approximation to the likelihood of the MJP that is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient whereas the convergence rate and mixing of the chains allow for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.

Searching for information is a recurring problem that almost everyone has faced at some point. Being in a library looking for a book, searching through newspapers and magazines for an old article or searching through emails for an old conversation with a colleague are some examples of the searching activity. These are some of the many situations where someone; the “user”; has some vague idea of the information he is looking for; an “information need”; and is searching through a large number of documents, emails or articles; “information items”; to find the most “relevant” item for his purpose. In this thesis we study the problem of retrieving images from large image archives. We consider two different approaches for image retrieval. The first approach is content based image retrieval where the user is searching images using a query image. The second approach is semantic retrieval where the users expresses his query using keywords. We proposed a unified framework to treat both approaches using generative probabilistic models in order to rank and classify images with respect to user queries. The methodology presented in this Thesis is evaluated on a real image collection and compared against state of the art methods.

Bayesian analysis for Markov jump processes is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding thus its applicability is limited to a small class of problems. In this paper we describe the application of Riemann manifold MCMC methods using an approximation to the likelihood of the Markov jump process which is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient while the convergence rate and mixing of the chains allows for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.

Hamiltonian Monte Carlo (HMC) improves the computational efficiency of the Metropolis algorithm by reducing its random walk behavior. Riemannian Manifold HMC (RMHMC) further improves HMC's performance by exploiting the geometric properties of the parameter space. However, the geometric integrator used for RMHMC involves implicit equations that require costly numerical analysis (e.g., fixed-point iteration). In some cases, the computational overhead for solving implicit equations undermines RMHMC's benefits. To avoid this problem, we propose an explicit geometric integrator that replaces the momentum variable in RMHMC by velocity. We show that the resulting transformation is equivalent to transforming Riemannian Hamilton dynamics to Lagrangian dynamics. Experimental results show that our method improves RMHMC's overall computational efficiency. All computer programs and data sets are available online (http://www.ics.uci.edu/~babaks/Site/Codes.html) in order to allow replications of the results reported in this paper.

This chapter contains sections titled: Introduction Markov chain Monte Carlo Methods Finite Gaussian mixture models Experiments Discussion Acknowledgements Appendix References

Human activities and climate change constitute the contemporary catalyst for natural processes and their impacts, i.e., geo-environmental hazards. Globally, natural catastrophic phenomena and hazards, such as drought, soil erosion, quantitative and qualitative degradation of groundwater, frost, flooding, sea level rise, etc., are intensified by anthropogenic factors. Thus, they present rapid increase in intensity, frequency of occurrence, spatial density, and significant spread of the areas of occurrence. The impact of these phenomena is devastating to human life and to global economies, private holdings, infrastructure, etc., while in a wider context it has a very negative effect on the social, environmental, and economic status of the affected region. Geospatial technologies including Geographic Information Systems, Remote Sensing—Earth Observation as well as related spatial data analysis tools, models, databases, contribute nowadays significantly in predicting, preventing, researching, addressing, rehabilitating, and managing these phenomena and their effects. This review attempts to mark the most devastating geo-hazards from the view of environmental monitoring, covering the state of the art in the use of geospatial technologies in that respect. It also defines the main challenge of this new era which is nothing more than the fictitious exploitation of the information produced by the environmental monitoring so that the necessary policies are taken in the direction of a sustainable future. The review highlights the potential and increasing added value of geographic information as a means to support environmental monitoring in the face of climate change. The growth in geographic information seems to be rapidly accelerated due to the technological and scientific developments that will continue with exponential progress in the years to come. Nonetheless, as it is also highlighted in this review continuous monitoring of the environment is subject to an interdisciplinary approach and contains an amount of actions that cover both the development of natural phenomena and their catastrophic effects mostly due to climate change.