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

Steps Before Syntax: Helping Novice Programmers Solve Problems using the PCDIT Framework

Novice programmers often struggle with problem solving due to the high cognitive loads they face. Furthermore, many introductory programming courses do not explicitly teach it, assuming that problem solving skills are acquired along the way. In this paper, we present 'PCDIT', a non-linear problem solving framework that provides scaffolding to guide novice programmers through the process of transforming a problem specification into an implemented and tested solution for an imperative programming language. A key distinction of PCDIT is its focus on developing concrete cases for the problem early without actually writing test code: students are instead encouraged to think about the abstract steps from inputs to outputs before mapping anything down to syntax. We reflect on our experience of teaching an introductory programming course using PCDIT, and report the results of a survey that suggests it helped students to break down challenging problems, organise their thoughts, and reach working solutions

ESTIMATING THE PROBABILITY OF FALSE ALARM FOR A ZERO-BIT WATERMARKING TECHNIQUE

International audienceAssessing that a probability of false alarm is below a given significance level is a crucial issue in watermarking. We pro- pose an iterative and self-adapting algorithm which estimates very low probabilities of error. Some experimental investiga- tions validates its performance for a rare detection scenario where there exists a close form formula of the probability of false alarm. Our algorithm appears to be much quicker and more accurate than a classical Monte Carlo estimator. It even allows the experimental measurement of error exponents