Likelihood Evaluation Research Articles

Bayesian inference for damage identification based on analytical probabilistic model of scattering coefficient estimators and ultrafast wave scattering simulation scheme

Ultrasonic Guided Waves (GW) actuated by piezoelectric transducers installed on structures have proven to be sensitive to small structural defects, with acquired scattering signatures being dependent on the damage type. This study presents a generic framework for probabilistic damage characterization within complex structures, based on physics-rich information on ultrasound wave interaction with existent damage. To this end, the probabilistic model of wave scattering properties estimated from measured GWs is inferred based on absolute complex-valued ratio statistics. Based on the probabilistic model, the likelihood function connecting the scattering properties predicted by a computational model containing the damage parametric description and the scattering estimates is formulated within a Bayesian system identification framework to account for measurement noise and modelling errors. The Transitional Monte Carlo Markov Chain (TMCMC) is finally employed to sample the posterior probability density function of the updated parameters. However, the solution of a Bayesian inference problem often requires repeated runs of “expensive-to-evaluate” Finite Element (FE) simulations, making the inversion procedure firmly demanding in terms of runtime and computational resources. To overcome the computational challenges of repeated likelihood evaluations, a cheap and fast Kriging surrogate model built and based on a set of training points generated with an experiment design strategy in tandem with a hybrid Wave and Finite Element (WFE) computational scheme is proposed in this study. In each “numerical experiment”, the training outputs (i.e. ultrasound scattering properties) are efficiently computed using the hybrid WFE scheme which combines conventional FE analysis with periodic structure theory. By establishing the relationship between the training outputs and damage characterization parameters statistically, the surrogate model further enhances the computational efficiency of the exhibited scheme. Two case studies including one numerical example and an experimental one are presented to verify the accuracy and efficiency of the proposed algorithm.

Improved component-based methods for mixture risk assessment are key to characterize complex chemical pollution in surface waters

The present monitoring and assessment of water quality problems fails to characterize the likelihood that complex mixtures of chemicals affect water quality. The European collaborative project SOLUTIONS suggests that this likelihood can be estimated, amongst other methods, with improved component-based methods (CBMs). The use of CBMs is a well-established practice in the WFD, as one of the lines of evidence to evaluate chemical pollution on a per-chemical basis. However, this is currently limited to a pre-selection of 45 and approximately 300 monitored substances (priority substances and river basin-specific pollutants, respectively), of which only a few actually co-occur in relevant concentrations in real-world mixtures. Advanced CBM practices are therefore needed that consider a broader, realistic spectrum of chemicals and thereby improve the assessment of mixture impacts, diagnose the causes of observed impacts and provide more useful water management information. Various CBMs are described and illustrated, often representing improvements of well-established methods. Given the goals of the WFD and expanding on current guidance for risk assessment, these improved CBMs can be applied to predicted or monitored concentrations of chemical pollutants to provide information for management planning. As shown in various examples, the outcomes of the improved CBMs allow for the evaluation of the current likelihood of impacts, of alternative abatement scenarios as well as the expected consequences of future pollution scenarios. The outputs of the improved CBMs are useful to underpin programmes of measures to protect and improve water quality. The combination of CBMs with effect-based methods (EBMs) might be especially powerful to identify as yet underinvestigated emerging pollutants and their importance in a mixture toxicity context. The present paper has been designed as one in a series of policy briefs to support decisions on water quality protection, monitoring, assessment and management under the European Water Framework Directive (WFD).

Likelihood evaluation of models with occasionally binding constraints

SummaryApplied researchers interested in estimating key parameters of dynamic stochastic general equilibrium models face an array of choices regarding numerical solution and estimation methods. We focus on the likelihood evaluation of models with occasionally binding constraints. We document how solution approximation errors and likelihood misspecification, related to the treatment of measurement errors, can interact and compound each other.

Sequential Monte Carlo Samplers with Independent Markov Chain Monte Carlo Proposals

Sequential Monte Carlo (SMC) methods for sampling from the posterior of static Bayesian models are flexible, parallelisable and capable of handling complex targets. However, it is common practice to adopt a Markov chain Monte Carlo (MCMC) kernel with a multivariate normal random walk (RW) proposal in the move step, which can be both inefficient and detrimental for exploring challenging posterior distributions. We develop new SMC methods with independent proposals which allow recycling of all candidates generated in the SMC process and are embarrassingly parallelisable. A novel evidence estimator that is easily computed from the output of our independent SMC is proposed. Our independent proposals are constructed via flexible copula-type models calibrated with the population of SMC particles. We demonstrate through several examples that more precise estimates of posterior expectations and the marginal likelihood can be obtained using fewer likelihood evaluations than the more standard RW approach.

Parallelized inference for gravitational-wave astronomy

Bayesian inference is the workhorse of gravitational-wave astronomy, for example, determining the mass and spins of merging black holes, revealing the neutron star equation of state, and unveiling the population properties of compact binaries. The science enabled by these inferences comes with a computational cost that can limit the questions we are able to answer. This cost is expected to grow. As detectors improve, the detection rate will go up, allowing less time to analyze each event. Improvement in low-frequency sensitivity will yield longer signals, increasing the number of computations per event. The growing number of entries in the transient catalog will drive up the cost of population studies. While Bayesian inference calculations are not entirely parallelizable, key components are embarrassingly parallel: calculating the gravitational waveform and evaluating the likelihood function. Graphical processor units (GPUs) are adept at such parallel calculations. We report on progress porting gravitational-wave inference calculations to GPUs. Using a single code - which takes advantage of GPU architecture if it is available - we compare computation times using modern GPUs (NVIDIA P100) and CPUs (Intel Gold 6140). We demonstrate speed-ups of $\sim 50 \times$ for compact binary coalescence gravitational waveform generation and likelihood evaluation and more than $100\times$ for population inference within the lifetime of current detectors. Further improvement is likely with continued development. Our python-based code is publicly available and can be used without familiarity with the parallel computing platform, CUDA.

INFERNO: Inference-Aware Neural Optimisation

Complex computer simulations are commonly required for accurate data modelling in many scientific disciplines, making statistical inference challenging due to the intractability of the likelihood evaluation for the observed data. Furthermore, sometimes one is interested on inference drawn over a subset of the generative model parameters while taking into account model uncertainty or misspecification on the remaining nuisance parameters. In this work, we show how non-linear summary statistics can be constructed by minimising inference-motivated losses via stochastic gradient descent such that they provide the smallest uncertainty for the parameters of interest. As a use case, the problem of confidence interval estimation for the mixture coefficient in a multi-dimensional two-component mixture model (i.e. signal vs background) is considered, where the proposed technique clearly outperforms summary statistics based on probabilistic classification, a commonly used alternative which does not account for the presence of nuisance parameters.

Unbiased approximations of products of expectations

SummaryWe consider the problem of approximating the product of $n$ expectations with respect to a common probability distribution $\mu$. Such products routinely arise in statistics as values of the likelihood in latent variable models. Motivated by pseudo-marginal Markov chain Monte Carlo schemes, we focus on unbiased estimators of such products. The standard approach is to sample $N$ particles from $\mu$ and assign each particle to one of the expectations; this is wasteful and typically requires the number of particles to grow quadratically with the number of expectations. We propose an alternative estimator that approximates each expectation using most of the particles while preserving unbiasedness, which is computationally more efficient when the cost of simulations greatly exceeds the cost of likelihood evaluations. We carefully study the properties of our proposed estimator, showing that in latent variable contexts it needs only ${O} (n)$ particles to match the performance of the standard approach with ${O}(n^{2})$ particles. We demonstrate the procedure on two latent variable examples from approximate Bayesian computation and single-cell gene expression analysis, observing computational gains by factors of about 25 and 450, respectively.

Likelihood Evaluation of Models with Occasionally Binding Constraints

Applied researchers interested in estimating key parameters of DSGE models face an array of choices regarding numerical solution and estimation methods. We focus on the likelihood evaluation of models with occasionally binding constraints. We document how solution approximation errors and likelihood misspecification, related to the treatment of measurement errors, can interact and compound each other.

The effect on cosmological parameter estimation of a parameter dependent covariance matrix

Cosmological large-scale structure analyses based on two-point correlation functions often assume a Gaussian likelihood function with a fixed covariance matrix. We study the impact on cosmological parameter estimation of ignoring the parameter dependence of this covariance matrix, focusing on the particular case of joint weak-lensing and galaxy clustering analyses. Using a Fisher matrix formalism (calibrated against exact likelihood evaluation in particular simple cases), we quantify the effect of using a parameter dependent covariance matrix on both the bias and variance of the parameters. We confirm that the approximation of a parameter-independent covariance matrix is exceptionally good in all realistic scenarios. The information content in the covariance matrix (in comparison with the two point functions themselves) does not change with the fractional sky coverage. Therefore the increase in information due to the parameter dependent covariance matrix becomes negligible as the number of modes increases. Even for surveys covering less than 1% of the sky, this effect only causes a bias of up to of order 10% of the statistical uncertainties, with a misestimation of the parameter uncertainties at the same level or lower. The effect will only be smaller with future large-area surveys. Thus for most analyses the effect of a parameter-dependent covariance matrix can be ignored both in terms of the accuracy and precision of the recovered cosmological constraints.

Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models

ABSTRACTA computationally simple approach to inference in state space models is proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation of an intractable likelihood by matching summary statistics for the observed data with statistics computed from data simulated from the true process, based on parameter draws from the prior. Draws that produce a “match” between observed and simulated summaries are retained, and used to estimate the inaccessible posterior. With no reduction to a low-dimensional set ofsufficient statistics being possible in the state space setting, we define the summaries as the maximum of an auxiliary likelihood function, and thereby exploit the asymptotic sufficiency of this estimator for the auxiliary parameter vector. We derive conditions under which this approach—including a computationally efficient version based on the auxiliary score—achieves Bayesian consistency. To reduce the well-documented inaccuracy of ABC in multiparameter settings, we propose the separate treatment of each parameter dimension using an integrated likelihood technique. Three stochastic volatility models for which exact Bayesian inference is either computationally challenging, or infeasible, are used for illustration. We demonstrate that our approach compares favorably against an extensive set of approximate and exact comparators. An empirical illustration completes the article. Supplementary materials for this article are available online.

Probabilistic evaluation of vegetation drought likelihood and its implications to resilience across India

Abstract Vegetation distribution and growth are significantly affected by changing climate conditions. Understanding the response of vegetation to hydroclimatic disturbances such as droughts is crucial in context of climate change. The sensitivity of terrestrial ecosystem to drought is difficult to measure because of problems related to drought quantification, variable response of vegetation types and changing climate-vegetation dynamics. Since, India is hugely dependent on its vegetation and cropland, identifying the impact of droughts on vegetation is essential. In this study, we estimate the likelihood of vegetation droughts across India in changing scenarios of temperature, precipitation and soil moisture content. We also study the resilience of vegetation cover to disturbances induced by a dry condition. From the investigation, it is observed that at least half the area of 16 out of 24 major river basins is facing high chances of vegetation droughts due to lowered soil moisture levels. The croplands are most likely to be affected by drought, which is of paramount concern for country's food security. Further investigation suggests that at least one-third area of 18 river basins is non-resilient to vegetation droughts. Moreover, >50% of each vegetation type is non-resilient, which points out the fragility of country's terrestrial ecosystems. This study facilitates the understanding of vegetation drought hotspot regions, factors risking the terrestrial ecosystem and their ability to withstand such conditions. These findings provide useful insights for policy makers to develop effective strategies for vegetation drought mitigation and sustainable ecosystem management.

Bayesian Estimation for Stochastic Gene Expression Using Multifidelity Models

The finite state projection (FSP) approach to solving the chemical master equation has enabled successful inference of discrete stochastic models to predict single-cell gene regulation dynamics. Unfortunately, the FSP approach is highly computationally intensive for all but the simplest models, an issue that is highly problematic when parameter inference and uncertainty quantification takes enormous numbers of parameter evaluations. To address this issue, we propose two new computational methods for the Bayesian inference of stochastic gene expression parameters given single-cell experiments. We formulate and verify an adaptive delayed acceptance Metropolis-Hastings (ADAMH) algorithm to utilize with reduced Krylov-basis projections of the FSP. We then introduce an extension of the ADAMH into a hybrid scheme that consists of an initial phase to construct a reduced model and a faster second phase to sample from the approximate posterior distribution determined by the constructed model. We test and compare both algorithms to an adaptive Metropolis algorithm with full FSP-based likelihood evaluations on three example models and simulated data to show that the new ADAMH variants achieve substantial speedup in comparison to the full FSP approach. By reducing the computational costs of parameter estimation, we expect the ADAMH approach to enable efficient data-driven estimation for more complex gene regulation models.

Associating host galaxy candidates to massive black hole binaries resolved by pulsar timing arrays

We propose a novel methodology to select host galaxy candidates of future pulsar timing array (PTA) detections of resolved gravitational waves (GWs) from massive black hole binaries (MBHBs). The method exploits the physical dependence of the GW amplitude on the MBHB chirp mass and distance to the observer, together with empirical MBH mass-host galaxy correlations, to rank potential host galaxies in the mass-redshift plane. This is coupled to a null-stream based likelihood evaluation of the GW amplitude and sky position in a Bayesian framework that assigns to each galaxy a probability of hosting the MBHB generating the GW signal. We test our algorithm on a set of realistic simulations coupling the likely properties of the first PTA resolved GW signal to synthetic all-sky galaxy maps. For a foreseeable PTA sky-localization precision of 100 squared degrees, we find that the GW source is hosted with 50% (90%) probability within a restricted number of <50 (<500) potential hosts. These figures are orders of magnitude smaller than the total number of galaxies within the PTA sky error-box, enabling extensive electromagnetic follow-up campaigns on a limited number of targets.

Random switching exponential smoothing: A new estimation approach

The random switching exponential smoothing as introduced by Sbrana and Silvestrini (International Journal of Production Economics, 156, 2014: 283–294) is a flexible forecasting model that can be used for time series with a (changing) trending behaviour. The estimation method originally proposed by these authors works only when some restrictive conditions on the parameters are met, therefore preventing its use in several practical applications. This paper presents a new, fast and efficient approach for estimating the random switching exponential smoothing model. The new method relies on the algebraic link between the model's structural parameters and the steady-state Kalman gain vector. This link simplifies the likelihood evaluation and thus reduces the computational burden. The finite-sample properties of the new estimation method are assessed in a Monte Carlo experiment and its out-of-sample forecasting performance is explored in an empirical evaluation exercise employing time series for wholesalers' inventories and sales in the United States. These series represent important business cycle indicators. Results show that both estimation methods perform broadly the same in simulations and in forecasting, over both short-term and longer-term horizons. However, despite the equal accuracy and forecasting performance, contrary to the originally proposed method, the new estimation approach can always be used, with no exceptions. In addition, its simplicity is a strong point in its favour for practitioners and forecasters working in business and industry.

Survey of amplitude‐aided multi‐target tracking methods

An amplitude-aided multi-target tracking (MTT) exploits amplitude as well as spatial features for MTT. Compared to MTT using a spatial feature only, it can maintain its performance even in densely cluttered environment because more accurate association is achieved by using both features for likelihood evaluation between tracks and measurements. Therefore, the goal of this study is to review the state-of-the-art amplitude-aided MTT methods and compare each other extensively. For a fair comparison, a unified MTT framework is developed, and various methods are implemented and compared based on the same framework. On the challenging visual MTT datasets, the implemented methods are evaluated for several aspects such as accuracy, speed, sensitivity, and stability. Moreover, this study presents a summary of the extensive evaluation and guideline to select an appropriate method for amplitude-aided tracking.

Cardiorenal and endocrine effects of synthetic canine BNP1-32 in dogs with compensated congestive heart failure caused by myxomatous mitral valve disease.

BackgroundThe effects of synthetic brain natriuretic peptide (BNP1‐32) on cardiorenal and renin angiotensin aldosterone system in dogs with naturally occurring congestive heart failure (CHF) are unknown.ObjectivesTo evaluate the cardiorenal and endocrine effects of SC administered synthetic canine BNP1‐32, with or without furosemide, in dogs with CHF caused by myxomatous mitral valve disease (MMVD).AnimalsSeven client‐owned male dogs with compensated American College of Veterinary Internal Medicine stage C CHF caused by MMVD on chronic treatment with furosemide, benazepril, and pimobendan.MethodsA single‐dose, crossover, pilot study. Each dog received a dose of BNP1‐32 (5 μg/kg), furosemide (2 mg/kg), and both BNP1‐32/furosemide (5 μg/kg and 2 mg/kg, respectively) SC with a 2‐week washout period among each treatment. Between‐ and within‐treatment effects were evaluated using linear mixed modeling with restricted maximum likelihood estimation and evaluation of least square differences.ResultsRapid absorption of BNP1‐32 and a corresponding rise in urinary cyclic guanosine monophosphate excretion was observed at 1‐2 hours after any treatment containing BNP1‐32 (P < .05). However, BNP1‐32 did not influence measured cardiorenal variables. Plasma aldosterone concentrations were below quantifiable levels in majority of the samples.Conclusions and Clinical ImportanceNo beneficial cardiorenal effects were detected. It is possible that dogs with chronic CHF have a reduction in natriuretic peptide responsiveness.

Evaluation of Likelihood of Failure of Topsides Piping on an Offshore Drilling Installation Due to Corrosion–Erosion Using Fuzzy Logic–Possibilistic Approach

Corrosion and erosion are common degradation mechanisms associated with offshore drilling installations. These degradation mechanisms lead to failures in piping and other equipments resulting in loss of containment. In order to develop inspection–maintenance programs for these installations, engineers need to estimate rates of associated degradation mechanisms. Unfortunately, due to the complexities involved, it is often difficult to develop models that can accurately predict the rates of degradation mechanisms in operational installations. Luckily, development of risk-based inspection programs does not require accurate prediction models. It often suffices to have models that can give approximate predictions, but models should be robust enough to be applicable for analysis under different operating conditions of the plants, and can incorporate subjective knowledge available with inspection engineers. This paper presents a methodology to estimate likelihood of failure of a pressurized mud system piping subjected to internal corrosion and erosion. The methodology consists of two parts (a) fuzzy logic approach for estimating the rate of degradation of equipment walls subjected to corrosion and erosion; and (b) possibilistic approach for calculating possibility of failure and necessity of failure.

Parallel likelihood calculation for phylogenetic comparative models: The SPLITT C++ library

Abstract Phylogenetic comparative models (PCMs) have been used to study macroevolutionary patterns, to characterize adaptive phenotypic landscapes, to quantify rates of evolution, to measure trait heritability, and to test various evolutionary hypotheses. A major obstacle to applying these models has been the complexity of evaluating their likelihood function. Recent works have shown that for many PCMs, the likelihood can be obtained in time proportional to the size of the tree based on post‐order tree traversal, also known as pruning. Despite this progress, inferring complex multi‐trait PCMs on large trees remains a time‐intensive task. Here, we study parallelizing the pruning algorithm as a generic technique for speeding‐up PCM‐inference. We implement several parallel traversal algorithms in the form of a generic C++ library for Serial and Parallel LIneage Traversal of Trees (SPLITT). Based on SPLITT, we provide examples of parallel likelihood evaluation for several popular PCMs, ranging from a single‐trait Brownian motion model to complex multi‐trait Ornstein‐Uhlenbeck and mixed Gaussian phylogenetic models. Using the phylogenetic Ornstein–Uhlenbeck mixed model (POUMM) as a showcase, we run benchmarks on up to 24 CPU cores, reporting up to an order of magnitude parallel speed‐up for the likelihood calculation on simulated balanced and unbalanced trees of up to 100,000 tips with up to 16 traits. Noticing that the parallel speed‐up depends on multiple factors, the SPLITT library is capable to automatically select the fastest traversal strategy for a given hardware, tree‐topology, and data. Combining SPLITT likelihood calculation with adaptive Metropolis sampling on real data, we show that the time for Bayesian POUMM inference on a tree of 10,000 tips can be reduced from several days to less than an hour. We conclude that parallel pruning effectively accelerates the likelihood calculation and, thus, the statistical inference of Gaussian phylogenetic models. For time‐intensive Bayesian inferences, we recommend combining this technique with adaptive Metropolis sampling. Beyond Gaussian models, the parallel tree traversal can be applied to numerous other models, including discrete trait and birth–death population dynamics models. Currently, SPLITT supports multi‐core shared memory architectures, but can be extended to distributed memory architectures as well as graphical processing units.

Risk assessment on rabies entry through hunting dog movement with semi-quantitative approach to Sumatera Island, Indonesia.

Objective:The objective of this study was to assess the risk of rabies entry through the movement of hunting dog from Garut District to Sumatera Island with a semi-quantitative approach.Materials and Methods:Rabies entry assessment used the standard risk analysis according to the World Organization for Animal Health, with a semi-quantitative approach referring to Australian Biosecurity. Risk estimation calculation used Microsoft Excel and probabilities were estimated using Monte Carlo stochastic simulation modeling with @Risk (Palisade Corporation).Results:Risk estimation were considered as “very low” with a 0.02 (90%; 0.01–0.03) probability. The probability of undetected rabies-infected dog during Veterinary Certificate issuance [node probability (NP4)] was considered as the highest, with “moderate” likelihood and 0.63 (90%; 0.51–0.75) of probability value. The number of dog movement to Sumatera reached 27,000 heads per year which 5,050 heads of them come from Garut District. There were 2 of 100 dogs from Garut District entered to Sumatera possibly infected by rabies. The five highest parameters most determinant of the risk were dog vaccination before transported (0.66), dog obtained from other District (0.41), vaccination program (0.32), serologically test (0.27), and history of vaccination (0.23).Conclusion:Risk estimation from assessing on rabies entry to Sumatera through hunting dogs movement from Garut District was considered “very low.” Risk mitigation is focused on the highest parameters that contribute the most to risk based on the results of the sensitivity analysis. Semi-quantitative likelihood evaluations can consider the volume of dog traffic which is an important issue in risk analysis which is not easy to get with a simpler qualitative approach.

150-Gb/s SEFDM IM/DD transmission using log-MAP Viterbi decoding for short reach optical links.

Spectral efficient frequency division multiplexing (SEFDM) can improve the spectral efficiency for next-generation optical and wireless communications. In this work, we apply SEFDM in beyond 100-Gb/s optical intensity modulation and direct detection transmissions and propose a low-complexity logarithmic-maximum-a-posteriori (log-MAP) Viterbi decoding algorithm to achieve the maximum likelihood (ML) detection. We evaluate the likelihood of detections using a posteriori probability instead of Euclidean distance by taking both noise and inter-carrier interference into consideration. In order to balance the performance and complexity, we then employ Viterbi decoding principle to retain only certain paths with ML detections (a.k.a., the surviving paths) while discarding the others during the decoding procedure. Results show that the proposed log-MAP Viterbi decoding scheme achieves optimal performance due to the precise likelihood evaluation, which guarantees the retention of the global ML detection. By using the proposed decoding scheme, the data rate of SEFDM signals can reach 150-Gb/s in a 2-km standard single mode fiber transmission, using only 28-GHz bandwidth and 16-QAM modulation. Experimental results show that the 16-QAM modulated SEFDM signal with a bandwidth compression factor of 0.8 outperforms 32-QAM modulated OFDM, while both signals have the same bandwidth (28-GHz) and data rate (140-Gb/s), which demonstrate the superiority of SEFDM in optical short reach applications.