The geo-structures embedded in the multiple variable strata could be significantly affected by the geological uncertainty. The quantitative evaluation of geological uncertainty and its influence on ...the structural safety of embedded tunnels are seldom studied in the past. This paper aims to analyse the effect of geological uncertainty on the structural performance of tunnel using the proposed stochastic geological modelling framework. The geological uncertainty is characterized using an improved coupled Markov chain model based on sparse limited boreholes. A mapping approach is presented to solve the mesh asymmetry problem between the simulated strata and the numerical tunnel model. The tunnel structural performance analysis is then conducted based on the combined model considering the geological uncertainty and tunnel structure. A geological uncertainty index (GUI) is proposed to quantitatively evaluate the level of uncertainty of each borehole and the whole site. The effect of the borehole layout scheme on uncertainty evaluation of factor of safety of tunnel structure is investigated by a large number of stratigraphic realizations. Boreholes collected from Norway with relatively more considerable variability and from Shanghai with relatively more minor variability are adopted as case studies to illustrate the proposed probabilistic analysis framework. The results show that the boreholes with larger GUI values and closer to tunnel locations have a greater weight to affect the embedded tunnel structural performance in uncertain geological strata.
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We develop a new Bayesian modelling framework for the class of higher‐order, variable‐memory Markov chains, and introduce an associated collection of methodological tools for exact inference with ...discrete time series. We show that a version of the context tree weighting alg‐orithm can compute the prior predictive likelihood exa‐ctly (averaged over both models and parameters), and two related algorithms are introduced, which identify the a posteriori most likely models and compute their exact posterior probabilities. All three algorithms are deterministic and have linear‐time complexity. A family of variable‐dimension Markov chain Monte Carlo samplers is also provided, facilitating further exploration of the posterior. The performance of the proposed methods in model selection, Markov order estimation and prediction is illustrated through simulation experiments and real‐world applications with data from finance, genetics, neuroscience and animal communication. The associated algorithms are implemented in the R package BCT.
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43.
The probabilistic model checker Storm Hensel, Christian; Junges, Sebastian; Katoen, Joost-Pieter ...
International journal on software tools for technology transfer,
08/2022, Volume:
24, Issue:
4
Journal Article
Peer reviewed
Open access
We present the probabilistic model checker
Storm
.
Storm
supports the analysis of discrete- and continuous-time variants of both Markov chains and Markov decision processes.
Storm
has three major ...distinguishing features. It supports multiple input languages for Markov models, including the
Jani
and
Prism
modeling languages, dynamic fault trees, generalized stochastic Petri nets, and the probabilistic guarded command language. It has a modular setup in which solvers and symbolic engines can easily be exchanged. Its Python API allows for rapid prototyping by encapsulating
Storm
’s fast and scalable algorithms. This paper reports on the main features of
Storm
and explains how to effectively use them. A description is provided of the main distinguishing functionalities of
Storm
. Finally, an empirical evaluation of different configurations of
Storm
on the QComp 2019 benchmark set is presented.
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We study a mixing condition for entangled Markov chains, so-called ψ-mixing property. We prove that every entangled Markov chain, whose Markov operators satisfy the Markov–Dobrushin condition, is ...ψ-mixing. Moreover, we show the restriction of the underlying QMC to the diagonal algebra gives rise to a classical mixing Markov chains with the same exponential rate of convergence.
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We analyze dynamical large deviations of quantum trajectories in Markovian open quantum systems in their full generality. We derive a quantum level-2.5 large deviation principle for these systems, ...which describes the joint fluctuations of time-averaged quantum jump rates and of the time-averaged quantum state for long times. Like its level-2.5 counterpart for classical continuous-time Markov chains (which it contains as a special case), this description is both explicit and complete, as the statistics of arbitrary time-extensive dynamical observables can be obtained by contraction from the explicit level-2.5 rate functional we derive. Our approach uses an unraveled representation of the quantum dynamics which allows these statistics to be obtained by analyzing a classical stochastic process in the space of pure states. For quantum reset processes we show that the unraveled dynamics is semi-Markovian and derive bounds on the asymptotic variance of the number of quantum jumps which generalize classical thermodynamic uncertainty relations. We finish by discussing how our level-2.5 approach can be used to study large deviations of nonlinear functions of the state, such as measures of entanglement.
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In the absence of recent admixture between species, bipartitions of individuals in gene trees that are shared across loci can potentially be used to infer the presence of two or more species. This ...approach to species delimitation via molecular sequence data has been constrained by the fact that genealogies for individual loci are often poorly resolved and that ancestral lineage sorting, hybridization, and other population genetic processes can lead to discordant gene trees. Here we use a Bayesian modeling approach to generate the posterior probabilities of species assignments taking account of uncertainties due to unknown gene trees and the ancestral coalescent process. For tractability, we rely on a user-specified guide tree to avoid integrating over all possible species delimitations. The statistical performance of the method is examined using simulations, and the method is illustrated by analyzing sequence data from rotifers, fence lizards, and human populations.
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The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when ...sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis-Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with alternative sampling approaches. MATLAB code that is available from http://www.ucl.ac.uk/statistics/research/rmhmc allows replication of all the results reported.
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Space-based high-contrast imaging mission concepts for studying rocky exoplanets in reflected light are currently under community study. We develop an inverse modeling framework to estimate the ...science return of such missions given different instrument design considerations. By combining an exoplanet albedo model, instrument noise model, and ensemble Markov chain Monte Carlo sampler, we explore retrievals of atmospheric and planetary properties for Earth twins as a function of signal-to-noise ratio (S/N) and resolution (R). Our forward model includes Rayleigh-scattering, single-layer water clouds with patchy coverage, and pressure-dependent absorption due to water vapor, oxygen, and ozone. We simulate data at R = 70 and 140 from 0.4 to 1.0 m with S/N = 5, 10, 15, and 20 at 550 nm (i.e., for HabEx/LUVOIR-type instruments). At these same S/Ns, we simulate data for WFIRST paired with a starshade, which includes two photometric points between 0.48 and 0.6 m and R = 50 spectroscopy from 0.6 to 0.97 m. Given our noise model for WFIRST-type detectors, we find that weak detections of water vapor, ozone, and oxygen can be achieved with observations with at least R = 70/S/N = 15 or R = 140/S/N = 10 for improved detections. Meaningful constraints are only achieved with R = 140/S/N = 20 data. The WFIRST data offer limited diagnostic information, needing at least S/N = 20 to weakly detect gases. Most scenarios place limits on planetary radius but cannot constrain surface gravity and, thus, planetary mass.
The design of an energy management strategy for a hybrid electric vehicle typically requires an estimate of requested power from the driver. If the driving cycle is not known a priori, stochastic ...methods, such as a Markov chain driver model (MCDM), must be employed. For tracked vehicles, the steering power, which is related to vehicle angular velocity, is a significant component of the driver demand. In this paper, a three-dimensional (3-D) MCDM incorporating angular velocity for a tracked vehicle is proposed. Based on the nearest-neighborhood method, an online transition probability matrix (TPM)-updating algorithm is implemented for the 3-D MCDM. Simulation results show that the TPM is able to update online and adapt to the changing driving conditions. Moreover, the adaptability of the online TPM updating algorithm to the change in driving is validated via a stochastic dynamic programming approach for a series hybrid tracked vehicle. Results show that the online updating for the MCDM's TPM is competent for adapting to the changing driving conditions.
•A two-stage shock model with self-healing mechanism is proposed.•Reliability indices are derived via the finite Markov chain imbedding approach.•Three maintenance policies are proposed.
In this ...paper, a two-stage shock model with self-healing mechanism is proposed as an extension of cumulative shock and delta-shock models. A change point is introduced to describe the two-stage failure process of a system and defined as the moment when the cumulative number of valid shocks reaches d. Before the change point, the system can heal the damage caused by a valid shock when the number of delta-invalid shocks reaches k in the trailing run of invalid shocks. Equivalently, the damage caused by previous i valid shocks can be healed when the number of delta-invalid shocks falls in ik,(i+1)k) in the run of invalid shocks. The system loses self-healing ability when it reaches the change point, and then fails when the cumulative number of valid shocks reaches a prefixed value n (n > d). Based on the established model, the finite Markov chain imbedding approach is employed to obtain the probability mass function, the distribution function and the mean of shock length. Three preventive maintenance policies are proposed for the system under different monitoring conditions, and corresponding optimization models are constructed to determine the optimal quantities. Finally, numerical examples are given for the proposed model.
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