Distributed Verification of Rare Properties using Importance Splitting Observers

Rare properties remain a challenge for statistical model checking (SMC) due to the quadratic scaling of variance with rarity. We address this with a variance reduction framework based on lightweight importance splitting observers. These expose the model-property automaton to allow the construction of score functions for high performance algorithms. The confidence intervals defined for importance splitting make it appealing for SMC, but optimising its performance in the standard way makes distribution inefficient. We show how it is possible to achieve equivalently good results in less time by distributing simpler algorithms. We first explore the challenges posed by importance splitting and present an algorithm optimised for distribution. We then define a specific bounded time logic that is compiled into memory-efficient observers to monitor executions. Finally, we demonstrate our framework on a number of challenging case studies

Cross-entropy optimisation of importance sampling parameters for statistical model checking

Statistical model checking avoids the exponential growth of states associated with probabilistic model checking by estimating properties from multiple executions of a system and by giving results within confidence bounds. Rare properties are often very important but pose a particular challenge for simulation-based approaches, hence a key objective under these circumstances is to reduce the number and length of simulations necessary to produce a given level of confidence. Importance sampling is a well-established technique that achieves this, however to maintain the advantages of statistical model checking it is necessary to find good importance sampling distributions without considering the entire state space. Motivated by the above, we present a simple algorithm that uses the notion of cross-entropy to find the optimal parameters for an importance sampling distribution. In contrast to previous work, our algorithm uses a low dimensional vector of parameters to define this distribution and thus avoids the often intractable explicit representation of a transition matrix. We show that our parametrisation leads to a unique optimum and can produce many orders of magnitude improvement in simulation efficiency. We demonstrate the efficacy of our methodology by applying it to models from reliability engineering and biochemistry.Comment: 16 pages, 8 figures, LNCS styl

Evolutionary design of a full–envelope flight control system for an unstable fighter aircraft

The use of an evolutionary algorithm in the framework of H∞ control theory is being considered as a means for synthesizing controller gains that minimize a weighted combination of the infinite-norm of the sensitivity function (for disturbance attenuation requirements) and complementary sensitivity function (for robust stability requirements) at the same time. The case study deals with the stability and control augmentation of an unstable high-performance jet aircraft. Constraints on closed-loop response are also enforced, that represent typical requirements on airplane handling qualities, that makes the control law synthesis process more demanding. Gain scheduling is required, in order to obtain satisfactory performance over the whole flight envelope, so that the synthesis is performed at different reference trim conditions, for several values of the dynamic pressure, Q, used as the scheduling parameter. Nonetheless, the dynamic behaviour of the aircraft may exhibit significant variations when flying at different altitudes h, even for the same value of the dynamic pressure, so that a trade-off is required between different feasible controllers synthesized for a given value of Q, but different h. A multi-objective search is thus considered for the determination of the best suited solution to be introduced in the scheduling of the control law. The obtained results are then tested on a longitudinal nonlinear model of the aircraft

EI: A Program for Ecological Inference

The program EI provides a method of inferring individual behavior from aggregate data. It implements the statistical procedures, diagnostics, and graphics from the book A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data (King'97). Ecological inference, as traditionally defined, is the process of using aggregate (i.e., "ecological") data to infer discrete individual-level relationships of interest when individual-level data are not available. Ecological inferences are required in political science research when individual-level surveys are unavailable (e.g., local or comparative electoral politics), unreliable (racial politics), insufficient (political geography), or infeasible (political history). They are also required in numerous areas of ma jor significance in public policy (e.g., for applying the Voting Rights Act) and other academic disciplines ranging from epidemiology and marketing to sociology and quantitative history.

Using simulation studies to evaluate statistical methods

Simulation studies are computer experiments that involve creating data by pseudorandom sampling. The key strength of simulation studies is the ability to understand the behaviour of statistical methods because some 'truth' (usually some parameter/s of interest) is known from the process of generating the data. This allows us to consider properties of methods, such as bias. While widely used, simulation studies are often poorly designed, analysed and reported. This tutorial outlines the rationale for using simulation studies and offers guidance for design, execution, analysis, reporting and presentation. In particular, this tutorial provides: a structured approach for planning and reporting simulation studies, which involves defining aims, data-generating mechanisms, estimands, methods and performance measures ('ADEMP'); coherent terminology for simulation studies; guidance on coding simulation studies; a critical discussion of key performance measures and their estimation; guidance on structuring tabular and graphical presentation of results; and new graphical presentations. With a view to describing recent practice, we review 100 articles taken from Volume 34 of Statistics in Medicine that included at least one simulation study and identify areas for improvement.Comment: 31 pages, 9 figures (2 in appendix), 8 tables (1 in appendix

Evolutionary design of a full-envelope full-authority flight control system for an unstable high-performance aircraft

The use of an evolutionary algorithm in the framework of H1 control theory is being considered as a means for synthesizing controller gains that minimize a weighted combination of the infinite norm of the sensitivity function (for disturbance attenuation requirements) and complementary sensitivity function (for robust stability requirements) at the same time. The case study deals with a complete full-authority longitudinal control system for an unstable high-performance jet aircraft featuring (i) a stability and control augmentation system and (ii) autopilot functions (speed and altitude hold). Constraints on closed-loop response are enforced, that representing typical requirements on airplane handling qualities, that makes the control law synthesis process more demanding. Gain scheduling is required, in order to obtain satisfactory performance over the whole flight envelope, so that the synthesis is performed at different reference trim conditions, for several values of the dynamic pressure, used as the scheduling parameter. Nonetheless, the dynamic behaviour of the aircraft may exhibit significant variations when flying at different altitudes, even for the same value of the dynamic pressure, so that a trade-off is required between different feasible controllers synthesized at different altitudes for a given equivalent airspeed. A multiobjective search is thus considered for the determination of the best suited solution to be introduced in the scheduling of the control law. The obtained results are then tested on a longitudinal non-linear model of the aircraft

Distinguishing niche and neutral processes: issues in variation partitioning statistical methods and further perspectives

Variance partitioning methods, which are built upon multivariate statistics, have been widely applied in different taxa and habitats in community ecology. Here, I performed a literature review on the development and application of the methods, and then discussed the limitation of available methods and the difficulties involved in sampling schemes. The central goal of the work is then to propose some potential practical methods that might help to overcome different issues of traditional least-square-based regression modeling. A variety of regression models has been considered for comparison. In initial simulations, I identified that generalized additive model (GAM) has the highest accuracy to predict variation components. Therefore, I argued that other advanced regression techniques, including the GAM and related models, could be utilized in variation partitioning for better quantifying the aggregation scenarios of species distribution.Comment: 19 pages; 4 figure