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R.: Specification and analysis of distributed objectbased stochastic hybrid systems
 In: HSCC
, 2006
"... Abstract. In practice, many stochastic hybrid systems are not autonomous: they are objects that communicate with other objects by exchanging messages through an asynchronous medium such as a network. Issues such as: how to compositionally specify distributed objectbased stochastic hybrid systems ..."
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Cited by 14 (1 self)
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Abstract. In practice, many stochastic hybrid systems are not autonomous: they are objects that communicate with other objects by exchanging messages through an asynchronous medium such as a network. Issues such as: how to compositionally specify distributed objectbased stochastic hybrid systems (OBSHS), how to formally model them, and how to verify their properties seem therefore quite important. This paper addresses these issues by: (i) defining a mathematical model for such systems that can be naturally regarded as a generalized stochastic hybrid system (GSHS) in the sense of [7]; (ii) proposing a formal OBSHS specification language in which system transitions are specified in a modular way by probabilistic rewrite rules; and (iii) showing how these systems can be subjected to statistical model checking analysis to verify their probabilistic temporal logic properties. 1
Deriving Probability Density Functions from Probabilistic Functional Programs
"... Abstract. The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic functional programs to density functions has only ..."
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Cited by 8 (1 self)
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Abstract. The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic functional programs to density functions has only recently been developed. In this work, we present a density compiler for a probabilistic language with discrete and continuous distributions, and discrete observations, and provide a proof of its soundness. The compiler greatly reduces the development effort of domain experts, which we demonstrate by solving inference problems from various scientific applications, such as modelling the global carbon cycle, using a standard Markov chain Monte Carlo framework. 1
Possibilistic and Probabilistic AbstractionBased Model Checking
 Process Algebra and Probabilistic Methods, Performance Modeling and Veri Second Joint International Workshop PAPMPROBMIV 2002, volume 2399 of Lecture Notes in Computer Science
, 2002
"... models whose verification results transfer to the abstracted models for a logic with unrestricted use of negation and quantification. This framework is novel in that its models have quantitative or probabilistic observables and state transitions. Properties of a quantitative temporal logic have meas ..."
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Cited by 5 (3 self)
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models whose verification results transfer to the abstracted models for a logic with unrestricted use of negation and quantification. This framework is novel in that its models have quantitative or probabilistic observables and state transitions. Properties of a quantitative temporal logic have measurable denotations in these models. For probabilistic models such denotations approximate the probabilistic semantics of full LTL. We show how predicatebased abstractions specify abstract quantitative and probabilistic models with finite state space. 1
Characterizing the EilenbergMoore Algebras for a Monad of Stochastic Relations
, 2004
"... We investigate the category of EilenbergMoore algebras for the Giry monad associated with stochastic relations over Polish spaces with continuous maps as morphisms. The algebras are characterized through convex partitions of the space of all probability measures. Examples are investigated, and it ..."
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Cited by 1 (0 self)
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We investigate the category of EilenbergMoore algebras for the Giry monad associated with stochastic relations over Polish spaces with continuous maps as morphisms. The algebras are characterized through convex partitions of the space of all probability measures. Examples are investigated, and it is shown that finite spaces usually do not have algebras at all.
Categories for Imperative Semantics PLDG Seminar
"... The aim of these notes is to provide an introduction to category theory, and a motivation for its use in denotational semantics. I will do this by showing how to apply it to give an abstract semantics to a simple imperative language. These notes are loosely based ..."
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The aim of these notes is to provide an introduction to category theory, and a motivation for its use in denotational semantics. I will do this by showing how to apply it to give an abstract semantics to a simple imperative language. These notes are loosely based
A ModelLearner Pattern for Bayesian Reasoning Andrew D. Gordon (Microsoft Research and University of Edinburgh) Mihhail Aizatulin (Open University)
"... A Bayesian model is based on a pair of probability distributions, known as the prior and sampling distributions. A wide range of fundamental machine learning tasks, including regression, classification, clustering, and many others, can all be seen as Bayesian models. We propose a new probabilistic ..."
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A Bayesian model is based on a pair of probability distributions, known as the prior and sampling distributions. A wide range of fundamental machine learning tasks, including regression, classification, clustering, and many others, can all be seen as Bayesian models. We propose a new probabilistic programming abstraction, a typed Bayesian model, based on a pair of probabilistic expressions for the prior and sampling distributions. A sampler for a model is an algorithm to compute synthetic data from its sampling distribution, while a learner for a model is an algorithm for probabilistic inference on the model. Models, samplers, and learners form a generic programming pattern for modelbased inference. They support the uniform expression of common tasks including model testing, and generic compositions such as mixture models, evidencebased model averaging, and mixtures of experts. A formal semantics supports reasoning about model equivalence and implementation correctness. By developing a series of examples and three learner implementations based on exact inference, factor graphs, and Markov chain Monte Carlo, we demonstrate the broad applicability of this new programming pattern.
MFPS 2009 Categories of Timed Stochastic Relations
"... Stochastic behavior—the probabilistic evolution of a system in time—is essential to modeling the complexity of realworld systems. It enables realistic performance modeling, qualityofservice guarantees, and especially simulations for biological systems. Languages like the stochastic pi calculus ha ..."
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Stochastic behavior—the probabilistic evolution of a system in time—is essential to modeling the complexity of realworld systems. It enables realistic performance modeling, qualityofservice guarantees, and especially simulations for biological systems. Languages like the stochastic pi calculus have emerged as effective tools to describe and reason about systems exhibiting stochastic behavior. These languages essentially denote continuoustime stochastic processes, obtained through an operational semantics in a probabilistic transition system. In this paper we seek a more descriptive foundation for the semantics of stochastic behavior using categories and monads. We model a firstorder imperative language with stochastic delay by identifying probabilistic choice and delay as separate effects, modeling each with a monad, and combining the monads to build a model for the stochastic language.
Natural Transformations as Rewrite Rules and Monad Composition
, 2004
"... Eklund et al. [6] present a graphical technique aimed at simplifying the verification of various categorytheoretic constructions, notably the composition of monads. In this note we take a different approach involving string rewriting. We show that a given tuple (T, µ, η) is a monad if and only if T ..."
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Eklund et al. [6] present a graphical technique aimed at simplifying the verification of various categorytheoretic constructions, notably the composition of monads. In this note we take a different approach involving string rewriting. We show that a given tuple (T, µ, η) is a monad if and only if T is a terminal object in a certain category of functors and natural transformations, and that this fact can be established by proving confluence of a certain string rewriting system. We illustrate the technique on the monad composition problem of Eklund et al. 1