Robots are increasingly used to carry out critical missions in extreme environments that are hazardous for humans. This requires a high degree of operational autonomy under uncertain conditions, and poses new challenges for assuring the robot's safety and reliability. In this paper, we develop a framework for probabilistic model checking on a layered Markov model to verify the safety and reliability requirements of such robots, both at pre-mission stage and during runtime. Two novel estimators based on conservative Bayesian inference and imprecise probability model with sets of priors are introduced to learn the unknown transition parameters from operational data. We demonstrate our approach using data from a real-world deployment of unmanned underwater vehicles in extreme environments.
One of the initial methods to learn the transition probabilities of DTMC is in @cite_35 , which later has been retrofitted for CTMC @cite_13 and extended with ageing factors of collected data to accurately estimate time-varying transition probabilities @cite_26 . To reduce the noise and provide smooth estimates, a lightweight adaptive filter is proposed in @cite_10 . Whilst, above mentioned approaches yield point estimations, these can be affected by unquantified and potentially significant errors. The work in @cite_15 is the first to synthesise bounds for unknown transition parameters. However, it is based on the theory of simultaneous confidence intervals, which is fundamentally different to the Bayesian approach presented here which has the distinct advantage of being able to embed various forms of prior knowledge.
@cite_35 @cite_26 @cite_10 @cite_15 @cite_13
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We present a novel probabilistic approach for fitting a statistical model to an image. A 3D Morphable Model (3DMM) of faces is interpreted as a generative (Top-Down) Bayesian model. Random Forests are used as noisy detectors (Bottom-Up) for the face and facial landmark positions. The Top-Down and Bottom-Up parts are then combined using a Data-Driven Markov Chain Monte Carlo Method (DDMCMC). As core of the integration, we use the Metropolis-Hastings algorithm which has two main advantages. First, the algorithm can handle unreliable detections and therefore does not need the detectors to take an early and possible wrong hard decision before fitting. Second, it is open for integration of various cues to guide the fitting process. Based on the proposed approach, we implemented a completely automatic, pose and illumination invariant face recognition application. We are able to train and test the building blocks of our application on different databases. The system is evaluated on the Multi-PIE database and reaches state of the art performance. This paper proposes a novel abstraction technique for continuous-time Markov chains (CTMCs). Our technique fits within the realm of three-valued abstraction methods that have been used successfully for traditional model checking. The key idea is to apply abstraction on uniform CTMCs that are readily obtained from general CTMCs, and to abstract transition probabilities by intervals. It is shown that this provides a conservative abstraction for both true and false for a three-valued semantics of the branching-time logic CSL (Continuous Stochastic Logic). Experiments on an infinite-state CTMC indicate the feasibility of our abstraction technique. Markov chains with Labelled Transitions can be used to generate test cases in a model-based approach. These test cases are generated by random walks on the model according to probabilities associated with transitions. When these probabilities correspond to a usage profile, reliability may be estimated. However, in early stages of development, such probabilities are not easy to determine, thus default profiles must be considered. In such a case it may be interesting to target some coverage criteria rather to use classical uniform probability generation approach. In this paper we enrich an existing industrial tool based on usage profile with 3 possibilities to create default profiles that improve transition coverage. We report experiments that compare the improvement of the coverage rates by our approaches with respect to uniform probabilities on transitions from a given state, which is the current default profile. Received 28 May 2002; revised 18 September 2002; accepted 24 September 2002; published 14 February 2003. [1] When an inverse problem is solved to estimate an unknown function such as the hydraulic conductivity in an aquifer or the contamination history at a site, one constraint is that the unknown function is known to be everywhere nonnegative. In this work, we develop a statistically rigorous method for enforcing function nonnegativity in Bayesian inverse problems. The proposed method behaves similarly to a Gaussian process with a linear variogram (i.e., unrestricted Brownian motion) for parameter values significantly greater than zero. The method uses the method of images to define a prior probability density function based on reflected Brownian motion that implicitly enforces nonnegativity. This work focuses on problems where the unknown is a function of a single variable (e.g., time). A Markov chain Monte Carlo (MCMC) method, specifically, a highly efficient Gibbs sampler, is implemented to generate conditional realizations of the unknown function. The new method is applied to the estimation of the trichloroethylene (TCE) and perchloroethylene (PCE) contamination history in an aquifer at Dover Air Force Base, Delaware, based on concentration profiles obtained from an underlying aquitard. INDEX TERMS: 1831 Hydrology: Groundwater quality; 1869 Hydrology: Stochastic processes; 3260 Mathematical Geophysics: Inverse theory; KEYWORDS: stochastic inverse modeling, contaminant source identification, inference under constraints, Markov chain Monte Carlo (MCMC), Gibbs sampling, Bayesian inference