Inference Of Model Parameters Research Articles

Improving estimates of waning immunity rates in stochastic SIRS models with a hierarchical framework

As most disease causing pathogens require transmission from an infectious individual to a susceptible individual, continued persistence of the pathogen within the population requires the replenishment of susceptibles through births, immigration, or waning immunity.Consider the introduction of an unknown infectious disease into a fully susceptible population where it is not known how long immunity is conferred once an individual recovers from infection. If, initially, the prevalence of disease increases (that is, the infection takes off), the number of infectives will usually decrease to a low level after the first major outbreak. During this post-outbreak period, the disease dynamics may be influenced by stochastic effects and there is a non-zero probability that the epidemic will die out. Die out in this period following the first major outbreak is known as an epidemic fade-out. If the disease does not die out, the susceptible population may be replenished by the waning of immunity, and a second wave may start.In this study, we investigate if the rate of waning immunity (and other epidemiological parameters) can be reliably estimated from multiple outbreak data, in which some outbreaks display epidemic fade-out and others do not. We generated synthetic outbreak data from independent simulations of stochastic SIRS models in multiple communities. Some outbreaks faded-out and some did not. We conducted Bayesian parameter estimation under two alternative approaches: independently on each outbreak and under a hierarchical framework. When conducting independent estimation, the waning immunity rate was poorly estimated and biased towards zero when an epidemic fade-out was observed. However, under a hierarchical approach, we obtained more accurate and precise posterior estimates for the rate of waning immunity and other epidemiological parameters. The greatest improvement in estimates was obtained for those communities in which epidemic fade-out was observed.Our findings demonstrate the feasibility and value of adopting a Bayesian hierarchical approach for parameter inference for stochastic epidemic models.

Free-field characterization of locally reacting sound absorbers using Bayesian inference with sequential frequency transfer

The in situ absorption characteristics of sound-absorbing samples are generally estimated inversely from sound field measurements above the sample’s surface. However, the entire measurement process is subject to numerous sources of uncertainty, which cannot be accounted for using deterministic inference methods. This paper introduces a Bayesian framework, including sequential frequency transfer to infer point estimates and uncertainty ranges of the frequency-dependent surface admittance, the corresponding sound absorption coefficient and the associated measurement and model uncertainty. The inference is conducted in two phases: in the initial phase, the absorption characteristics and the measurement and model uncertainty at a predefined initial frequency are inferred based on a weakly informative prior. Extensive prior predictive checks are conducted to find the best trade-off between a weak level of informativeness of the prior and physically meaningful predictions of the sound field above the absorber. In the sequential phase, the posterior mean at an analyzed frequency serves as the prior mean at the subsequent frequency. The framework is applied to simulated as well as real free-field measurements of the specific impedance above two different rock wool samples. The measurements are conducted with a combined pressure-particle velocity probe and the samples are assumed to exhibit local reaction behavior. For the investigated samples, a minimum number of four individual measurements of the specific impedance already allows for an accurate estimation of the frequency-dependent absorption characteristics and the associated measurement and model uncertainty, particularly for frequencies above 600 Hz. Due to the proposed sequential frequency transfer, the computational effort of the sampling-based Bayesian inference at a discrete frequency is significantly reduced. This paves the way for efficient inference of frequency-dependent model parameters while overcoming the curse of dimensionality associated with the inference of stochastic processes. The proposed framework lays the foundation for accurate and efficient inference of frequency-dependent parameters in models beyond the field of acoustics.

A Class of Hierarchical Multivariate Wiener Processes for Modeling Dependent Degradation Data

In engineering practice, many products exhibit multiple and dependent degrading performance characteristics (PCs). It is common to observe that these PCs’ initial measurements are nonconstant and sometimes correlated with the subsequent degradation rate, which typically varies from one unit to another. To accommodate the unit-wise heterogeneity, PC-wise dependency, and “initiation-growth” correlation, this article proposes a broad class of multi-dimensional degradation models under a framework of hierarchical multivariate Wiener processes. These models incorporate dual multi-normally distributed random effects concerning the initial values and degradation rates. To infer model parameters, expectation-maximization (EM) algorithms and several tools for model validation and selection are developed. Various simulation studies are carried out to assess the performance of the inference method and to compare different models. Two case studies are conducted to demonstrate the applicability of the proposed methodology. The online supplementary materials of this article contain derivations of EM estimators, additional numerical results, and R codes.

Reduction of apparent temporal variations of tidal parameters by a proper local response model

We describe a new harmonic tidal analysis method, which constrains the solution to be near a reference model. This regularization stabilizes the linear regression, allowing us to infer model parameters for each tidal harmonic. This overcomes the need to create a priori groupings of harmonics. The inversion is done iteratively by adjusting the reference model to reduce the data misfit. The frequency dependence of the solution is thus data-driven. We find models for the different spherical degrees independently. Our procedure allows narrow-band variations of the tidal admittance. We test the hypothesis that some of the temporal variations of tidal parameters found in previous studies were caused by inappropriate body tide models in combination with a priori wave grouping. We determine a local response model from 11.5 years of data recorded by the superconducting gravimeter SG056 at Black Forest Observatory (BFO, Schiltach). Using this as an a priori model in a non-regularized moving window analysis of wave groups composed from summed harmonics, we find that periodic variations of groups M1, K1, mu 2, N2, L2, and S2 are reduced by up to a factor of 7 compared to earlier studies. Some variations previously seen in the M2 group are captured as well.

Bayesian model calibration for diblock copolymer thin film self-assembly using power spectrum of microscopy data and machine learning surrogate

Identifying parameters of computational models from experimental data, or model calibration, is fundamental for assessing and improving the predictability and reliability of computer simulations. In this work, we propose a method for Bayesian calibration of models that predict morphological patterns of diblock copolymer (Di-BCP) thin film self-assembly while accounting for various sources of uncertainties in pattern formation and data acquisition. This method extracts the azimuthally-averaged power spectrum (AAPS) of the top-down microscopy characterization of Di-BCP thin film patterns as summary statistics for Bayesian inference of model parameters via the pseudo-marginal method. We derive the analytical and approximate form of a conditional likelihood for the AAPS of image data. We demonstrate that AAPS-based image data reduction retains the mutual information, particularly on important length scales, between image data and model parameters while being relatively agnostic to the aleatoric uncertainties associated with the random long-range disorder of Di-BCP patterns. Additionally, we propose a phase-informed prior distribution for Bayesian model calibration. Furthermore, reducing image data to AAPS enables us to efficiently build surrogate models to accelerate the proposed Bayesian model calibration procedure. We present the formulation and training of two multi-layer perceptrons for approximating the parameter-to-spectrum map, which enables fast integrated likelihood evaluations. We validate the proposed Bayesian model calibration method through numerical examples, for which the neural network surrogate delivers a fivefold reduction of the number of model simulations performed for a single calibration task.

Large deviations for the Pearson family of ergodic diffusion processes involving a quadratic diffusion coefficient and a linear force

The Pearson family of ergodic diffusions with a quadratic diffusion coefficient and a linear force is characterized by explicit dynamics of their integer moments and by explicit relaxation of spectral properties towards their steady state. Besides the Ornstein–Uhlenbeck process with a Gaussian steady state, other representative examples of the Pearson family are the square root or the Cox–Ingersoll–Ross process converging towards the gamma distribution, the Jacobi process converging towards the beta distribution, the reciprocal gamma process (corresponding to an exponential functional of the Brownian motion) that converges towards the inverse-gamma distribution, the Fisher–Snedecor process and the Student process. The last three steady states display heavy tails. The goal of the present paper is to analyze the large deviation properties of these various diffusion processes in a unified framework. We first consider level 1 concerning time-averaged observables over a large time window T. We write the first rescaled cumulants for generic observables and identify specific observables whose large deviations can be explicitly computed from the dominant eigenvalue of the appropriate deformed generator. The explicit large deviations at level 2 concerning the time-averaged density are then used to analyze the statistical inference of model parameters from data on a very long stochastic trajectory in order to obtain the explicit rate function for the two inferred parameters of the Pearson linear force.

A step towards digital operations—A novel grey-box approach for modelling the heat dynamics of ultra-low temperature freezing chambers

Ultra-low temperature (ULT) freezers store perishable bio-contents and have high energy consumption, which highlight a demand for reliable methods for intelligent surveillance and smart energy management. This study introduces a novel grey-box modelling approach based on stochastic differential equations to describe the heat dynamics of the ULT freezing chambers. The proposed modelling approach only requires temperature data measured by the embedded sensors and uses data from the regular operation periods for model identification. The model encompasses three states: chamber temperature, envelope temperature, and local evaporator temperature. Special attention is given to the local evaporator temperature state, which is modelled as a time-variant system, to characterise the time delay and dynamic variations in cooling intensity.The model has three states, of which a time-variant model with nonlinear input for the local evaporator temperature state is specifically established to adapt to the variation of the cooling intensity at the position of the embedded chamber control probe. Two ULT freezers with different operational patterns are modelled. The unknown model parameters are estimated using the maximum likelihood method. The results demonstrate that the models can accurately predict the chamber temperature measured by the control probe (RMSE <0.19°C) and are promising to be applied for forecasting future states. In addition, the model for local evaporator temperature can effectively adapt to different operational patterns and provide insight into the local evaporation cooling supply status. The proposed approach greatly promotes the practical feasibility of grey-box modelling of the heat dynamics for ULT freezers and is a step forward in future digital operationscan serve several potential digital applications. A major limitation of the modelling approach is the low identifiability, which can potentially be addressed by inferring model parameters based on relative parameter changes.

Unlabelled landmark matching via Bayesian data selection, and application to cell matching across imaging modalities

We consider the problem of landmark matching between two unlabelled point sets, in particular where the number of points in each cloud may differ, and where points in each cloud may not have a corresponding match. We invoke a Bayesian framework to identify the transformation of coordinates that maps one cloud to the other, alongside correspondence of the points. This problem necessitates a novel methodology for Bayesian data selection, simultaneous inference of model parameters, and selection of the data which leads to the best fit of the model to the majority of the data. We apply this to a problem in developmental biology where the landmarks correspond to segmented cell centres, where potential death or division of cells can lead to discrepancies between the point-sets from each image. We validate the efficacy of our approach using in silico tests and a microinjected fluorescent marker experiment. Subsequently we apply our approach to the matching of cells between real time imaging and immunostaining experiments, facilitating the combination of single-cell data between imaging modalities. Furthermore our approach to Bayesian data selection is broadly applicable across data science, and has the potential to change the way we think about fitting models to data.

Topic-Clustering Model with Temporal Distribution for Public Opinion Topic Analysis of Geospatial Social Media Data

Analysis of the spatiotemporal distribution of online public opinion topics can help understand the hotspots of public concern. The topic model is employed widely in public opinion topic clustering for social media data. In order to handle topic-clustering of low-quality geospatial social media data, such as microblog data, with short text and timeliness characteristics, this study proposed a Dirichlet multinomial mixture over time (DMMOT) model to cluster microblog topic for public opinion analysis. The DMMOT model assumes that a single document belongs to a single topic, in line with the characteristics of a short text, and it introduces the probability distribution of “topic-time” in the process of topic generation. The model parameter inference process was presented in detail by exploring the Gibbs sampling method. Results generated using the DMMOT model in case study show that the “topic-word” distribution is semantically aggregated within various topics, and “topic-time” distribution clustered within a time window under each topic. Furthermore, the characteristics of the trend of each topic over time are basically consistent with the corresponding trend of topic in reality in terms of content. These indicate that the DMMOT model improves topic clustering for short text to some extent. Furthermore, the DMMOT model performed well in both temporal and spatial analysis of public opinion topics based on microblog data.

Tree-based data filtering for online user-generated reviews

Analysis of online user-generated reviews has attracted extensive attention with broad applications in recent years. However, the high-volume and low-value density of online reviews bring challenges to a timely and effective data utilization. To address that challenge, this work proposes an unsupervised review filtering method based on the inherent tree-structured hierarchies among review data that reflect the general-to-specific characteristics of various quality aspects discussed in reviews. In particular, the reviews with aspects distributed near the leaf nodes of the tree are capable of providing more specific and detailed information about the examined product, which is more likely to be reserved after the tree-based filtering. To enable an effective extraction of aspect hierarchies from a broad variety of review corpora, a Bayesian nonparametric hierarchical topic model has been constructed and incorporated with an enhanced Pólya urn scheme. The approximate inference of model parameters is obtained by an efficient collapsed Gibbs sampling procedure. The proposed method can enhance the layered effect of individual reviews according to their general-to-specific characteristics and reserve an information-rich subset filtered from the raw review corpus. The merits of the proposed method have been elaborated by case studies on two real-world data sets and an extensive simulation study.

Statistically Valid Variational Bayes Algorithm for Ising Model Parameter Estimation

Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant in the likelihood. Here, we use a pseudo-likelihood instead, to study the Bayesian estimation of two-parameter, inverse temperature and magnetization, Ising model with a fully specified coupling matrix. We develop a computationally efficient variational Bayes procedure for model estimation. Under the Gaussian mean-field variational family, we derive posterior contraction rates of the variational posterior obtained under the pseudo-likelihood. We also discuss the loss incurred due to variational posterior over true posterior for the pseudo-likelihood approach. Extensive simulation studies validate the efficacy of mean-field Gaussian and bivariate Gaussian families as the possible choices of the variational family for inference of Ising model parameters. Supplementary materials for this article are available online.

Retracted: Self-consistent models of Earth’s mantle and core from long-period seismic and tidal constraints

SUMMARYIn this study, we inverted a large set of normal-mode centre-frequencies and quality (attenuation) factors, including astronomic-geodetic data (mass, moment of inertia and tidal response), using self-consistently built models of the radial elastic and anelastic seismic structure of the Earth. The mantle models are constructed using petrologic phase equilibria in combination with a laboratory-based viscoelastic model that connects dissipation from seismic to tidal periods, whereas seismic properties for a well-mixed and homogeneous core are computed using equations-of-state. Relative to the preliminary seismic reference model (PREM), we find that for the models to fit the observations, mantle P- and S-wave velocities have to be slightly faster and slower, respectively, while outer-core P-wave velocity is slower on account of a different velocity gradient, whereas inner-core velocity structure is similar, within the uncertainties of the inferred model parameters. In terms of density, we find that the lower mantle is less dense and the outer core more dense than PREM, while the inner core is similar to PREM. To study the impact of the inferred mantle seismic velocity structure, we computed P- and S-wave traveltimes and compared these to the observations of globally-averaged P- and S-wave traveltimes from the reprocessed ISC catalogue that resulted in an excellent match. In an attempt to further refine the seismic P-wave velocity structure of the outer core, we also considered multiple core–mantle-boundary underside-reflected body wave traveltime data. Although the match to the underside reflections clearly improves as a result of a steeper velocity gradient in the outer core relative to the normal-modes- and astronomic-geodetic-data-only case, subtle differences nevertheless persist that appear to support a change in velocity gradient in the outermost core, evocative of a stably-stratified layer. The laboratory-based viscoelastic model considered here resolves the anelastic response of Earth’s mantle from long-period seismic (∼100 s) to tidal (18.6 yr) periods, accounting for both normal-mode and tidal dissipation measurements. Finally, as a potential means of refining core composition, we considered the density contrast across the inner-core boundary (ICB) based on our inverted models. The most probable ICB density difference found here is 0.3–0.45 g cm−3, which is in the lower range of earlier body-wave- and normal-mode-based predictions. This suggests that the compositional heterogeneity associated with light-element partitioning, which is considered the principal driving mechanism for the compositional convection that powers the geodynamo, may be less effective than previously thought, calling for exsolution of solids from the liquid outer core as a possible additional source of energy. This would also help address the problem of a young inner core.

CONNECT: a neural network based framework for emulating cosmological observables and cosmological parameter inference

Bayesian parameter inference is an essential tool in modern cosmology, and typically requires the calculation of 105–106 theoretical models for each inference of model parameters for a given dataset combination. Computing these models by solving the linearised Einstein-Boltzmann system usually takes tens of CPU core-seconds per model, making the entire process very computationally expensive.In this paper we present connect, a neural network framework emulating class computations as an easy-to-use plug-in for the popular sampler MontePython. connect uses an iteratively trained neural network which emulates the observables usually computed by class. The training data is generated using class, but using a novel algorithm for generating favourable points in parameter space for training data, the required number of class-evaluations can be reduced by two orders of magnitude compared to a traditional inference run. Once connect has been trained for a given model, no additional training is required for different dataset combinations, making connect many orders of magnitude faster than class (and making the inference process entirely dominated by the speed of the likelihood calculation).For the models investigated in this paper we find that cosmological parameter inference run with connect produces posteriors which differ from the posteriors derived using class by typically less than 0.01–0.1 standard deviations for all parameters. We also stress that the training data can be produced in parallel, making efficient use of all available compute resources. The connect code is publicly available for download on GitHub (https://github.com/AarhusCosmology/connect_public).

Bayesian Dependency Modelling and Inference for PBPK Model Parameters: A Nimble Approach

Bayesian Dependency Modelling and Inference for PBPK Model Parameters: A Nimble Approach

Abstract 139: Exploiting interactions between ploidy and host physiology

Abstract Whole-genome doubling facilitates rapid tumor evolution and is a hallmark of many cancers, including Glioblastoma (GBM) where it has an incidence of ~14%. GBM remains uniformly lethal, with a median overall survival of 14-16 months, despite aggressive therapy. In people aged 65 and above, prognosis is even more dismal, with median survival of less than 7 months. While comorbidities explain some of the increased age-related risk, age-related changes in the tumor microenvironment likely also contribute. Aging brains have higher incidence of polyploidy (Pearson r=0.80; P=0.031; Nandakumar et al., 2021), hypoxia related gene expression (Pearson r =0.22, P =0.008) and Glucose levels (Ding et al., 2021) as well as decreased stiffness (Hiscox et al., 2018). The average ploidy of 20 different cancer types correlates with the Oxygen levels recorded in their respective tissue of origin (Spearman r = 0.66, P = 0.002). Together these results suggest that availability of metabolic substrates in the GBM environment drives different cell fate decisions in cancer cells of different ploidy and shapes GBM disease initiation. We address this hypothesis with integrated in-vitro and in-silico experiments and multi-omic and imaging analysis of primary and recurrent GBM. We genetically engineered cell lines to obtain diploid and tetraploid lineages for each and tested how exposure to variable gradients of glucose, hypoxia and phosphate affect their migratory patterns. We performed RNA-seq and WGS of multiple regions obtained from two patient-matched primary and recurrent GBM. Pre- and post-surgery MRI data was available from both surgeries and registered to a T1 map Atlas to quantify stiffness and oxygenation in the brain. This data was used to calibrate a Stochastic State-Space Model (S3MB) we developed to recapitulate re-growth of enhancing primary tumor margins into the respective recurrent tumor. The model domain is initiated from MRI data and consists of 4mm3 voxels. Each voxel state is defined by 8+ variables that are updated over time: Stiffness, Oxygen, Phosphate, Glucose, Vasculature, Dead cells, migrating cells and proliferating cells of various ploidies. In-vitro results, multi-omics results and similarity between observed and simulated recurrent tumors were used to infer model parameters (resource consumption-, migration-, death and proliferation rates). Running the model backwards in time, we predict the local point of origin (LPO) of each GBM. We found that resource availability in the predicted LPO was correlated to WGD status, suggesting conditions in the local environment in which a GBM originates shape the outcome of an early competition between diploid and tetraploid cells. Citation Format: Noemi Andor. Exploiting interactions between ploidy and host physiology [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 139.

Inference of astrophysical parameters with a conditional invertible neural network

Conditional Invertible Neural Networks (cINNs) provide a new technique for the inference of free model parameters by enabling the creation of posterior distributions. With these distributions, the mean parameter values, their uncertainties and the correlations between the parameters can be estimated. In this contribution, we summarize the functionality of cINNs, which are based on normalizing flows, and present the application of this new method to a scenario from astroparticle physics. We show that it is possible to constrain properties of the currently unknown sources of ultra-high-energy cosmic rays and compare the posterior distributions obtained with the network to those acquired using the classic Markov Chain Monte Carlo method.

An Offline-Online Decomposition Method for Efficient Linear Bayesian Goal-Oriented Optimal Experimental Design: Application to Optimal Sensor Placement

Bayesian optimal experimental design (OED) plays an important role in minimizing model uncertainty with limited experimental data in a Bayesian framework. In many applications, rather than minimizing the uncertainty in the inference of model parameters, one seeks to minimize the uncertainty of a model-dependent quantity of interest (QoI). This is known as goal-oriented OED (GOOED). Here, we consider GOOED for linear Bayesian inverse problems governed by large-scale models represented by partial differential equations (PDE) that are computationally expensive to solve. In particular, we consider optimal sensor placement by maximizing an expected information gain (EIG) for the QoI. We develop an efficient method to solve such problems by deriving a new formulation of the goal-oriented EIG. Based on this formulation we propose an offline-online decomposition scheme that achieves significant computational reduction by computing all of the PDE-dependent quantities in an offline stage just once, and optimizing the sensor locations in an online stage without solving any PDEs. Moreover, in the offline stage we need only to compute low-rank approximations of two Hessian-related operators. The computational cost of these low-rank approximations, measured by the number of PDE solves, does not depend on the parameter or data dimensions for a large class of elliptic, parabolic, and sufficiently dissipative hyperbolic inverse problem that exhibit dimension-independent rapid spectra decay. We carry out detailed error analysis for the approximate goal-oriented EIG due to the low-rank approximations of the two operators. Furthermore, in the online stage we extend a swapping greedy method to optimize the sensor locations developed in our recent work that is demonstrated to be more efficient than a standard greedy method. We conduct a numerical experiment for a contaminant transport inverse problem with an infinite-dimensional parameter field to demonstrate the efficiency, accuracy, and both data- and parameter-dimension independence of the proposed algorithm.

Spatial evolution of human cultures inferred through Bayesian phylogenetic analysis.

Spatial distribution of human culture reflects both descent from the common ancestor and horizontal transmission among neighbouring populations. To analyse empirically documented geographical variations in cultural repertoire, we will describe a framework for Bayesian statistics in a spatially explicit model. To consider both horizontal transmission and mutation of the cultural trait in question, our method employs a network model in which populations are represented by nodes. Using algorithms borrowed from Bayesian phylogenetic analysis, we will perform a Markov chain Monte Carlo (MCMC) method to compute the posterior distributions of parameters, such as the rate of horizontal transmission and the mutation rates among trait variants, as well as the identity of trait variants in unobserved populations. Besides the inference of model parameters, our method enables the reconstruction of the genealogical tree of the focal trait, provided that the mutation rate is sufficiently small. We will also describe a heuristic algorithm to reduce the dimension of the parameter space explored in the MCMC method, where we simulate the coalescent process in the network of populations. Numerical examples show that our algorithms compute the posterior distribution of model parameters within a practical computation time, although the posterior distribution tends to be broad if we use uninformative priors.

Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems

This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian inference applications, a multielement Polynomial Chaos Expansion based Kriging metamodel is proposed. The developed surrogate model combines in a piecewise function an array of local Polynomial Chaos based Kriging metamodels constructed on a finite set of non-overlapping subdomains of the stochastic input space. Therewith, the presence of non-smoothness in the response of the forward model (e.g. nonlinearities and sparseness) can be reproduced by the proposed metamodel with minimum computational costs owing to its local adaptation capabilities. The model parameter inference is conducted through a Markov chain Monte Carlo approach comprising adaptive exploration and delayed rejection. The efficiency and accuracy of the proposed approach are validated through two case studies, including an analytical benchmark and a numerical case study. The latter relates the partial differential equation governing the hydrogen diffusion phenomenon of metallic materials in Thermal Desorption Spectroscopy tests.

An Approximate Bayesian Computation Approach for Modeling Genome Rearrangements.

The inference of genome rearrangement events has been extensively studied, as they play a major role in molecular evolution. However, probabilistic evolutionary models that explicitly imitate the evolutionary dynamics of such events, as well as methods to infer model parameters, are yet to be fully utilized. Here, we developed a probabilistic approach to infer genome rearrangement rate parameters using an Approximate Bayesian Computation (ABC) framework. We developed two genome rearrangement models, a basic model, which accounts for genomic changes in gene order, and a more sophisticated one which also accounts for changes in chromosome number. We characterized the ABC inference accuracy using simulations and applied our methodology to both prokaryotic and eukaryotic empirical datasets. Knowledge of genome-rearrangement rates can help elucidate their role in evolution as well as help simulate genomes with evolutionary dynamics that reflect empirical genomes.