Parameter Synthesis for Markov Models

Markov chain analysis is a key technique in reliability engineering. A practical obstacle is that all probabilities in Markov models need to be known. However, system quantities such as failure rates or packet loss ratios, etc. are often not---or only partially---known. This motivates considering parametric models with transitions labeled with functions over parameters. Whereas traditional Markov chain analysis evaluates a reliability metric for a single, fixed set of probabilities, analysing parametric Markov models focuses on synthesising parameter values that establish a given reliability or performance specification $\varphi$. Examples are: what component failure rates ensure the probability of a system breakdown to be below 0.00000001?, or which failure rates maximise reliability? This paper presents various analysis algorithms for parametric Markov chains and Markov decision processes. We focus on three problems: (a) do all parameter values within a given region satisfy $\varphi$?, (b) which regions satisfy $\varphi$ and which ones do not?, and (c) an approximate version of (b) focusing on covering a large fraction of all possible parameter values. We give a detailed account of the various algorithms, present a software tool realising these techniques, and report on an extensive experimental evaluation on benchmarks that span a wide range of applications.Comment: 38 page

Reachability in Parametric Interval Markov Chains using Constraints

Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are labeled with parametric intervals of probabilities. In this work, we study the difference between pIMCs and other Markov Chain abstractions models and investigate the two usual semantics for IMCs: once-and-for-all and at-every-step. In particular, we prove that both semantics agree on the maximal/minimal reachability probabilities of a given IMC. We then investigate solutions to several parameter synthesis problems in the context of pIMCs -- consistency, qualitative reachability and quantitative reachability -- that rely on constraint encodings. Finally, we propose a prototype implementation of our constraint encodings with promising results

SATMC: Spectral Energy Distribution Analysis Through Markov Chains

We present the general purpose spectral energy distribution (SED) fitting tool SED Analysis Through Markov Chains (SATMC). Utilizing Monte Carlo Markov Chain (MCMC) algorithms, SATMC fits an observed SED to SED templates or models of the user's choice to infer intrinsic parameters, generate confidence levels and produce the posterior parameter distribution. Here we describe the key features of SATMC from the underlying MCMC engine to specific features for handling SED fitting. We detail several test cases of SATMC, comparing results obtained to traditional least-squares methods, which highlight its accuracy, robustness and wide range of possible applications. We also present a sample of submillimetre galaxies that have been fitted using the SED synthesis routine GRASIL as input. In general, these SMGs are shown to occupy a large volume of parameter space, particularly in regards to their star formation rates which range from ~30-3000 M_sun yr^-1 and stellar masses which range from ~10^10-10^12 M_sun. Taking advantage of the Bayesian formalism inherent to SATMC, we also show how the fitting results may change under different parametrizations (i.e., different initial mass functions) and through additional or improved photometry, the latter being crucial to the study of high-redshift galaxies.Comment: 17 pages, 11 figures, MNRAS accepte

Combining vocal tract length normalization with hierarchial linear transformations

Recent research has demonstrated the effectiveness of vocal tract length normalization (VTLN) as a rapid adaptation technique for statistical parametric speech synthesis. VTLN produces speech with naturalness preferable to that of MLLR-based adaptation techniques, being much closer in quality to that generated by the original av-erage voice model. However with only a single parameter, VTLN captures very few speaker specific characteristics when compared to linear transform based adaptation techniques. This paper pro-poses that the merits of VTLN can be combined with those of linear transform based adaptation in a hierarchial Bayesian frame-work, where VTLN is used as the prior information. A novel tech-nique for propagating the gender information from the VTLN prior through constrained structural maximum a posteriori linear regres-sion (CSMAPLR) adaptation is presented. Experiments show that the resulting transformation has improved speech quality with better naturalness, intelligibility and improved speaker similarity. Index Terms — Statistical parametric speech synthesis, hidden Markov models, speaker adaptation, vocal tract length normaliza-tion, constrained structural maximum a posteriori linear regression 1

Automated Experiment Design for Data-Efficient Verification of Parametric Markov Decision Processes

We present a new method for statistical verification of quantitative properties over a partially unknown system with actions, utilising a parameterised model (in this work, a parametric Markov decision process) and data collected from experiments performed on the underlying system. We obtain the confidence that the underlying system satisfies a given property, and show that the method uses data efficiently and thus is robust to the amount of data available. These characteristics are achieved by firstly exploiting parameter synthesis to establish a feasible set of parameters for which the underlying system will satisfy the property; secondly, by actively synthesising experiments to increase amount of information in the collected data that is relevant to the property; and finally propagating this information over the model parameters, obtaining a confidence that reflects our belief whether or not the system parameters lie in the feasible set, thereby solving the verification problem.Comment: QEST 2017, 18 pages, 7 figure

Parameter-Independent Strategies for pMDPs via POMDPs

Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition probabilities to account for stochastic uncertainties of the environment such as noise or input disturbances. We study pMDPs with reachability objectives where the parameter values are unknown and impossible to measure directly during execution, but there is a probability distribution known over the parameter values. We study for the first time computing parameter-independent strategies that are expectation optimal, i.e., optimize the expected reachability probability under the probability distribution over the parameters. We present an encoding of our problem to partially observable MDPs (POMDPs), i.e., a reduction of our problem to computing optimal strategies in POMDPs. We evaluate our method experimentally on several benchmarks: a motivating (repeated) learner model; a series of benchmarks of varying configurations of a robot moving on a grid; and a consensus protocol.Comment: Extended version of a QEST 2018 pape