Efficient Approximate Bayesian Computation Coupled With Markov Chain Monte Carlo Without Likelihood

In genetic counseling for cancer risk, the probability of carrying a mutation of a cancer-causing gene plays an important role. Family history of various cancers is important in calculating this probability. BRCAPRO is a widely used software for calculating the probability of carrying mutations in BRCA1 and BRCA2 genes given the family history of breast and ovarian cancer in first- and second-degree relatives. BRCAPRO uses an analytical (exact) calculational procedure. Using Markov chain Monte Carlo (MCMC) methods, we extend BRCAPRO to handle, in principle, any type of cancer, family history, any number of genes and alleles that each gene may have. When the information used in this MCMC approach is the same as for BRCAPRO (two genes: BRCA1 and BRCA2; two cancers: breast and ovarian; first- and second-degree relatives only), the two approaches give essentially the same answer. Extending the model to include (1) prostate cancer, (2) two mutated alleles of BRCA2, namely, mutations in Ovarian Cancer Cluster Region (OCCR) and non-OCCR region, and (3) relatives of degree greater than second-degree, leads to different carrier probabilities. The MCMC approach is a useful tool in building a comprehensive model to give accurate estimates of carrier probabilities. Such an approach will be even more important as additional information about the genetics of various cancers becomes available.

We present a new technique for statistical static timing analysis (SSTA) based on Markov chain Monte Carlo (MCMC), that allows fast and accurate estimation of the right-hand tail of the delay distribution. A ¿naive¿ MCMC approach is inadequate for SSTA. Several modifications and enhancements, presented in this paper, enable application of MCMC to SSTA. Moreover, such an approach overcomes inherent limitations of techniques such as importance sampling and Quasi-Monte Carlo. Our results on open source designs, with an independent delay variation model, demonstrate that our technique can obtain more than an order of magnitude improvement in computation time over simple Monte Carlo, given an estimation accuracy target at a point in the tail. Our approach works by providing a large number of samples in the region of interest. Open problems include extension of algorithm applicability to a broader class of synthesis conditions, and handling of correlated delay variations. In a broader context, this work aims to show that MCMC and associated techniques can be useful in rare event analyses related to circuits, particularly for high-dimensional problems.

Variational Bayes approximation of factor stochastic volatility models

Density-estimation likelihood-free inference (DELFI) has recently been\nproposed as an efficient method for simulation-based cosmological parameter\ninference. Compared to the standard likelihood-based Markov Chain Monte Carlo\n(MCMC) approach, DELFI has several advantages: it is highly parallelizable,\nthere is no need to assume a possibly incorrect functional form for the\nlikelihood and complicated effects (e.g the mask and detector systematics) are\neasier to handle with forward models. In light of this, we present two DELFI\npipelines to perform weak lensing parameter inference with lognormal\nrealizations of the tomographic shear field -- using the C_l summary statistic.\nThe first pipeline accounts for the non-Gaussianities of the shear field,\nintrinsic alignments and photometric-redshift error. We validate that it is\naccurate enough for Stage III experiments and estimate that O(1000) simulations\nare needed to perform inference on Stage IV data. By comparing the second DELFI\npipeline, which makes no assumption about the functional form of the\nlikelihood, with the standard MCMC approach, which assumes a Gaussian\nlikelihood, we test the impact of the Gaussian likelihood approximation in the\nMCMC analysis. We find it has a negligible impact on Stage IV parameter\nconstraints. Our pipeline is a step towards seamlessly propagating all\ndata-processing, instrumental, theoretical and astrophysical systematics\nthrough to the final parameter constraints.\n

We propose a new method in which a generative network (GN) set within a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and estimate the corresponding uncertainties associated with the states and parameters of a numerical physical simulation. We train the GN using only unconditional simulations of the discretized PDE model. A GN is used here to exploit the ability of these methods to generate realistic outputs from complex probability distributions, such as the ones that represent the possible states and parameters of a physical problem. We compare the proposed method with the gold standard Markov chain Monte Carlo (MCMC). Additionally, we suggest the use of a novel type of time-stepping regularization to improve the representativeness of the physical solution, and we present a new way of evaluating the GN training, taking advantage of the real/generated sample structure. We apply the proposed approaches to a spatio-temporal compartmental model in epidemiology. The results show that the proposed GN-based ROM can efficiently quantify uncertainty and accurately match the measurements and the gold standard. This is achieved using only a limited number of unconditional simulations from the full-order numerical PDE model (40 simulations). The GN-based ROM operates 60 times faster than the gold standard (MCMC), while producing uncertainties that closely match those generated by the MCMC approach. The proposed method is a general framework for quantifying uncertainties in numerical physical simulations and is not restricted to the specific physics of this application.

Medical imaging systems are commonly assessed and optimized by use of objective measures of image quality (IQ). The Ideal Observer (IO) performance has been advocated to provide a figure-of-merit for use in assessing and optimizing imaging systems because the IO sets an upper performance limit among all observers. When joint signal detection and localization tasks are considered, the IO that employs a modified generalized likelihood ratio test maximizes observer performance as characterized by the localization receiver operating characteristic (LROC) curve. Computations of likelihood ratios are analytically intractable in the majority of cases. Therefore, sampling-based methods that employ Markov-Chain Monte Carlo (MCMC) techniques have been developed to approximate the likelihood ratios. However, the applications of MCMC methods have been limited to relatively simple object models. Supervised learning-based methods that employ convolutional neural networks have been recently developed to approximate the IO for binary signal detection tasks. In this paper, the ability of supervised learning-based methods to approximate the IO for joint signal detection and localization tasks is explored. Both background-known-exactly and background-known-statistically signal detection and localization tasks are considered. The considered object models include a lumpy object model and a clustered lumpy model, and the considered measurement noise models include Laplacian noise, Gaussian noise, and mixed Poisson-Gaussian noise. The LROC curves produced by the supervised learning-based method are compared to those produced by the MCMC approach or analytical computation when feasible. The potential utility of the proposed method for computing objective measures of IQ for optimizing imaging system performance is explored.

Bayesian identification of a cracked plate using a population-based Markov Chain Monte Carlo method

The recent proliferation of Markov Chain Monte Carlo (MCMC) approaches has led to the use of the Bayesian inference in a wide variety of fields, including reliability engineering. With the current (and future) proliferation of new products, old problems continue to hamper us, while new challenges keep appearing. In Bayesian reliability, these include but are not limited to: (1) achieving and making use of prior information; (2) applying small data sets or system operating/environmental (SOE) data with big and complex data; and (3) making posterior inferences from high-dimensional numerical integration. To deal with old problems while meeting new challenges, this paper proposes an improved procedure for Bayesian reliability inference with MCMC, discussing modern reliability data and noting some applications where the Bayesian reliability approach with MCMC can be used. It also explores opportunities to use Bayesian reliability models to create stronger statistical methods from prior to posterior. Finally, it outlines some practical concerns and remaining challenges for future research.

Simple mechanistic epidemic models are widely used for forecasting and parameter estimation of infectious diseases based on noisy case reporting data. Despite the widespread application of models to emerging infectious diseases, we know little about the comparative performance of standard computational-statistical frameworks in these contexts. Here we build a simple stochastic, discrete-time, discrete-state epidemic model with both process and observation error and use it to characterize the effectiveness of different flavours of Bayesian Markov chain Monte Carlo (MCMC) techniques. We use fits to simulated data, where parameters (and future behaviour) are known, to explore the limitations of different platforms and quantify parameter estimation accuracy, forecasting accuracy, and computational efficiency across combinations of modeling decisions (e.g. discrete vs. continuous latent states, levels of stochasticity) and computational platforms (JAGS, NIMBLE, Stan).

Rapid estimation of the coseismic fault model for medium-to-large-sized earthquakes is key for disaster response. To estimate the coseismic fault model for large earthquakes, the Geospatial Information Authority of Japan and Tohoku University have jointly developed a real-time GEONET analysis system for rapid deformation monitoring (REGARD). REGARD can estimate the single rectangular fault model and slip distribution along the assumed plate interface. The single rectangular fault model is useful as a first-order approximation of a medium-to-large earthquake. However, in its estimation, it is difficult to obtain accurate results for model parameters due to the strong effect of initial values. To solve this problem, this study proposes a new method to estimate the coseismic fault model and model uncertainties in real time based on the Bayesian inversion approach using the Markov Chain Monte Carlo (MCMC) method. The MCMC approach is computationally expensive and hyperparameters should be defined in advance via trial and error. The sampling efficiency was improved using a parallel tempering method, and an automatic definition method for hyperparameters was developed for real-time use. The calculation time was within 30 s for 1 × 106 samples using a typical single LINUX server, which can implement real-time analysis, similar to REGARD. The reliability of the developed method was evaluated using data from recent earthquakes (2016 Kumamoto and 2019 Yamagata-Oki earthquakes). Simulations of the earthquakes in the Sea of Japan were also conducted exhaustively. The results showed an advantage over the maximum likelihood approach with a priori information, which has initial value dependence in nonlinear problems. In terms of application to data with a small signal-to-noise ratio, the results suggest the possibility of using several conjugate fault models. There is a tradeoff between the fault area and slip amount, especially for offshore earthquakes, which means that quantification of the uncertainty enables us to evaluate the reliability of the fault model estimation results in real time.

Applying Bayesian Model Averaging to mechanistic models: An example and comparison of methods

We present a flow law for dislocation‐dominated creep in wet quartz derived from compiled experimental and field‐based rheological data. By integrating the field‐based data, including independently calculated strain rates, deformation temperatures, pressures, and differential stresses, we add constraints for dislocation‐dominated creep at conditions unattainable in quartz deformation experiments. A Markov Chain Monte Carlo (MCMC) statistical analysis computes internally consistent parameters for the generalized flow law: = Aσne−(Q+VP)/RT. From this initial analysis, we identify different effective stress exponents for quartz deformed at confining pressures above and below ∼700 MPa. To minimize the possible effect of confining pressure, compiled data are separated into “low‐pressure” (<560 MPa) and “high‐pressure” (700–1,600 MPa) groups and reanalyzed using the MCMC approach. The “low‐pressure” data set, which is most applicable at midcrustal to lower‐crustal confining pressures, yields the following parameters: log(A) = −9.30 ± 0.66 MPa−n−r s−1; n = 3.5 ± 0.2; r = 0.49 ± 0.13; Q = 118 ± 5 kJ mol−1; and V = 2.59 ± 2.45 cm3 mol−1. The “high‐pressure” data set produces a different set of parameters: log(A) = −7.90 ± 0.34 MPa−n−r s−1; n = 2.0 ± 0.1; r = 0.49 ± 0.13; Q = 77 ± 8 kJ mol−1; and V = 2.59 ± 2.45 cm3 mol−1. Predicted quartz rheology is compared to other flow laws for dislocation creep; the calibrations presented in this study predict faster strain rates under geological conditions by more than 1 order of magnitude. The change in n at high confining pressure may result from an increase in the activity of grain size sensitive creep.

Bayesian statistical data assimilation for ecosystem models using Markov Chain Monte Carlo

The computer revolution has been driven by a sustained increase of computational speed of approximately one order of magnitude (a factor of ten) every 5 years since about 1950. In natural sciences, this has led to a continuous increase of the importance of computer simulations. Major enabling techniques are Markov Chain Monte Carlo (MCMC) and molecular dynamics (MD) simulations.This article deals with the MCMC approach. First, basic simulation techniques as well as methods for their statistical analysis are reviewed. Afterwards, the focus is on generalized ensembles and biased updating. These are two advanced techniques, which are of relevance for simulations of biomolecules or are expected to become relevant in that respect. In particular, we consider the multicanonical ensemble and the replica exchange method (also known as parallel tempering or method of multiple Markov chains).KeywordsMarkov Chain Monte CarloMonte CarloMarkov Chain Monte Carlo MethodLattice Gauge TheoryMetropolis AlgorithmThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Estimating the Cross-Sectional Market Response to an Endogenous Event: Naked vs. Underwritten Calls of Convertible Bonds