Bayesian Parameter Inference Research Articles

Adsorption of Praziquantel Enantiomers on Chiral Cellulose Tris 3-Chloro, 4-Methylphenylcarbamate by Frontal Analysis: Fisherian and Bayesian Parameter Estimation and Inference

Adsorption of Praziquantel Enantiomers on Chiral Cellulose Tris 3-Chloro, 4-Methylphenylcarbamate by Frontal Analysis: Fisherian and Bayesian Parameter Estimation and Inference

Bayesian inference in epidemics: linear noise analysis.

This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the Bayesian model's convergence with increasing amounts of data under measurement limitations. Depending on how weakly informative the disease measurements are, we offer a kind of 'best case' as well as a 'worst case' analysis where, in the former case, we assume that the prevalence is directly accessible, while in the latter that only a binary signal corresponding to a prevalence detection threshold is available. Both cases are studied under an assumed so-called linear noise approximation as to the true dynamics. Numerical experiments test the sharpness of our results when confronted with more realistic situations for which analytical results are unavailable.

Characterizing Sparse Asteroid Light Curves with Gaussian Processes

Abstract In the era of wide-field surveys like the Zwicky Transient Facility and the Rubin Observatory’s Legacy Survey of Space and Time, sparse photometric measurements constitute an increasing percentage of asteroid observations, particularly for asteroids newly discovered in these large surveys. Follow-up observations to supplement these sparse data may be prohibitively expensive in many cases, so to overcome these sampling limitations, we introduce a flexible model based on Gaussian processes to enable Bayesian parameter inference of asteroid time-series data. This model is designed to be flexible and extensible, and can model multiple asteroid properties such as the rotation period, light-curve amplitude, changing pulse profile, and magnitude changes due to the phase-angle evolution at the same time. Here, we focus on the inference of rotation periods. Based on both simulated light curves and real observations from the Zwicky Transient Facility, we show that the new model reliably infers rotational periods from sparsely sampled light curves and generally provides well-constrained posterior probability densities for the model parameters. We propose this framework as an intermediate method between fast but very limited-period detection algorithms and much more comprehensive but computationally expensive shape-modeling based on ray-tracing codes.

Providing Evidence for the Null Hypothesis in Functional Magnetic Resonance Imaging Using Group-Level Bayesian Inference.

Classical null hypothesis significance testing is limited to the rejection of the point-null hypothesis; it does not allow the interpretation of non-significant results. This leads to a bias against the null hypothesis. Herein, we discuss statistical approaches to ‘null effect’ assessment focusing on the Bayesian parameter inference (BPI). Although Bayesian methods have been theoretically elaborated and implemented in common neuroimaging software packages, they are not widely used for ‘null effect’ assessment. BPI considers the posterior probability of finding the effect within or outside the region of practical equivalence to the null value. It can be used to find both ‘activated/deactivated’ and ‘not activated’ voxels or to indicate that the obtained data are not sufficient using a single decision rule. It also allows to evaluate the data as the sample size increases and decide to stop the experiment if the obtained data are sufficient to make a confident inference. To demonstrate the advantages of using BPI for fMRI data group analysis, we compare it with classical null hypothesis significance testing on empirical data. We also use simulated data to show how BPI performs under different effect sizes, noise levels, noise distributions and sample sizes. Finally, we consider the problem of defining the region of practical equivalence for BPI and discuss possible applications of BPI in fMRI studies. To facilitate ‘null effect’ assessment for fMRI practitioners, we provide Statistical Parametric Mapping 12 based toolbox for Bayesian inference.

Optimal Cosmic Microwave Background Lensing Reconstruction and Parameter Estimation with SPTpol Data

Abstract We perform the first simultaneous Bayesian parameter inference and optimal reconstruction of the gravitational lensing of the cosmic microwave background (CMB), using 100 deg2 of polarization observations from the SPTpol receiver on the South Pole Telescope. These data reach noise levels as low as 5.8 μK arcmin in polarization, which are low enough that the typically used quadratic estimator (QE) technique for analyzing CMB lensing is significantly suboptimal. Conversely, the Bayesian procedure extracts all lensing information from the data and is optimal at any noise level. We infer the amplitude of the gravitational lensing potential to be A ϕ = 0.949 ± 0.122 using the Bayesian pipeline, consistent with our QE pipeline result, but with 17% smaller error bars. The Bayesian analysis also provides a simple way to account for systematic uncertainties, performing a similar job as frequentist “bias hardening” or linear bias correction, and reducing the systematic uncertainty on A ϕ due to polarization calibration from almost half of the statistical error to effectively zero. Finally, we jointly constrain A ϕ along with A L, the amplitude of lensing-like effects on the CMB power spectra, demonstrating that the Bayesian method can be used to easily infer parameters both from an optimal lensing reconstruction and from the delensed CMB, while exactly accounting for the correlation between the two. These results demonstrate the feasibility of the Bayesian approach on real data, and pave the way for future analysis of deep CMB polarization measurements with SPT-3G, Simons Observatory, and CMB-S4, where improvements relative to the QE can reach 1.5 times tighter constraints on A ϕ and seven times lower effective lensing reconstruction noise.

Adaptive Semiparametric Bayesian Differential Equations Via Sequential Monte Carlo

Nonlinear differential equations (DEs) are used in a wide range of scientific problems to model complex dynamic systems. The differential equations often contain unknown parameters that are of scientific interest, which have to be estimated from noisy measurements of the dynamic system. Generally, there is no closed-form solution for nonlinear DEs, and the likelihood surface for the parameter of interest is multi-modal and very sensitive to different parameter values. We propose a Bayesian framework for nonlinear DE systems. A flexible nonparametric function is used to represent the dynamic process such that expensive numerical solvers can be avoided. A sequential Monte Carlo algorithm in the annealing framework is proposed to conduct Bayesian inference for parameters in DEs. In our numerical experiments, we use examples of ordinary differential equations and delay differential equations to demonstrate the effectiveness of the proposed algorithm. We developed an R package that is available at https://github.com/shijiaw/smcDE. Supplementary files for this article are available online.

Inferring the effect of interventions on COVID-19 transmission networks

Countries around the world implement nonpharmaceutical interventions (NPIs) to mitigate the spread of COVID-19. Design of efficient NPIs requires identification of the structure of the disease transmission network. We here identify the key parameters of the COVID-19 transmission network for time periods before, during, and after the application of strict NPIs for the first wave of COVID-19 infections in Germany combining Bayesian parameter inference with an agent-based epidemiological model. We assume a Watts–Strogatz small-world network which allows to distinguish contacts within clustered cliques and unclustered, random contacts in the population, which have been shown to be crucial in sustaining the epidemic. In contrast to other works, which use coarse-grained network structures from anonymized data, like cell phone data, we consider the contacts of individual agents explicitly. We show that NPIs drastically reduced random contacts in the transmission network, increased network clustering, and resulted in a previously unappreciated transition from an exponential to a constant regime of new cases. In this regime, the disease spreads like a wave with a finite wave speed that depends on the number of contacts in a nonlinear fashion, which we can predict by mean field theory.

On two exponential populations under a joint adaptive type-II progressive censoring

In this paper, we introduce a new joint adaptive Type-II progressive censoring (JAPC) scheme for independent samples from two different populations. We place two independent samples simultaneously on a life testing experiment. It is assumed that the lifetime of the experimental units of the populations follow exponential distribution with mean and , respectively. The maximum likelihood estimators of the unknown parameters and their exact distributions are derived. Based on the exact distributions of the maximum likelihood estimators, approximate confidence intervals are constructed. Further, the Bayesian inference of the model parameters is considered under a very flexible Beta-Gamma prior. We obtain Bayes estimators and associated credible intervals of the unknown parameters under squared error loss function. Extensive simulations are performed to see the effectiveness of the proposed estimation methods. A real dataset is considered for implementing the proposed model on it. Also we use the variable neighbourhood search (VNS) method to derive the optimal censoring scheme of the model in the Bayesian framework.

Bayesian inference of a non-local proliferation model.

From a systems biology perspective, the majority of cancer models, although interesting and providing a qualitative explanation of some problems, have a major disadvantage in that they usually miss a genuine connection with experimental data. Having this in mind, in this paper, we aim at contributing to the improvement of many cancer models which contain a proliferation term. To this end, we propose a new non-local model of cell proliferation. We select data that are suitable to perform Bayesian inference for unknown parameters and we provide a discussion on the range of applicability of the model. Furthermore, we provide proof of the stability of posterior distributions in total variation norm which exploits the theory of spaces of measures equipped with the weighted flat norm. In a companion paper, we provide detailed proof of the well-posedness of the problem and we investigate the convergence of the escalator boxcar train (EBT) algorithm applied to solve the equation.

Zeus: a python implementation of ensemble slice sampling for efficient Bayesian parameter inference

ABSTRACT We introduce zeus, a well-tested Python implementation of the Ensemble Slice Sampling (ESS) method for Bayesian parameter inference. ESS is a novel Markov chain Monte Carlo (MCMC) algorithm specifically designed to tackle the computational challenges posed by modern astronomical and cosmological analyses. In particular, the method requires only minimal hand-tuning of 1−2 hyperparameters that are often trivial to set; its performance is insensitive to linear correlations and it can scale up to 1000s of CPUs without any extra effort. Furthermore, its locally adaptive nature allows to sample efficiently even when strong non-linear correlations are present. Lastly, the method achieves a high performance even in strongly multimodal distributions in high dimensions. Compared to emcee, a popular MCMC sampler, zeus performs 9 and 29 times better in a cosmological and an exoplanet application, respectively.

Least-informative priors for 0νββ decay searches

Bayesian parameter inference techniques require a choice of prior distribution which can strongly impact the statistical conclusions drawn. We discuss the construction of least-informative priors for neutrinoless double beta decay searches. Such priors attempt to be objective by maximizing the information gain from an experimental setup. In a parametrization using the lightest neutrino mass $m_l$ and an effective Majorana phase parameter $\Phi$, we construct such a prior using two different approaches and compare them with the standard flat and logarithmic priors in $m_l$.

The Poisson Nadarajah-Haghighi Distribution: Different Methods of Estimation

Estimation of parameters of Poisson Nadarajah-Haghighi (PNH) distribution from the frequentist and Bayesian point of view is discussed in this article. To this end, we briefly described ten different frequentist approaches, namely, the maximum likelihood estimators, percentile based estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators, minimum spacing absolute distance estimators, minimum spacing absolute-log distance estimators, Cramér-von Mises estimators, Anderson-Darling estimators and right-tail Anderson-Darling estimators. To assess the performance of different estimators, Monte Carlo simulations are done for small and large samples. The performance of the estimators is compared in terms of their bias, root mean squares error, average absolute difference between the true and estimated distribution functions, and the maximum absolute difference between the true and estimated distribution functions of the estimates using simulated data. For the Bayesian inference of the unknown parameters, we use Metropolis–Hastings (MH) algorithm to calculate the Bayes estimates and the corresponding credible intervals. Results from the simulation study suggests that among the considered classical methods of estimation, weighted least squares and the maximum product spacing estimators uniformly produces the least biases of the estimates with least root mean square errors. However, Bayes estimates perform better than all other estimates. Finally, we discuss a practical data set to show the application of the distribution.

Evapotranspiration and Crop Coefficient of Ratoon Rice Crop Determined by Water Depth Observation and Bayesian Inference

Actual crop evapotranspiration (ET) and crop coefficient (Kc) of ratoon rice crop, which are necessary for irrigation planning, have been hardly reported. ET can be directly measured by lysimeter and eddy covariance but it is expensive, so it remains difficult to determine ET, especially in developing countries. The focus of this study was to evaluate the ET and Kc of ratoon cropping in a tropical region of Myanmar using a simplified method. Our method combined the manual observation of water depth in concrete paddy tanks and the ET model estimation using Bayesian parameter inference. The ET and Kc could be determined using this method with an incomplete observation dataset. The total ET of ratoon was 60–70% less than that of the main crop, but this difference was mainly attributed to climate conditions in each cultivation. The Kc regression curve between transplanted rice and ratoon crops was different because of the tillering traits. The results suggest that irrigation scheduling of ratoon cropping in the initial growth stage should take high crop water requirements into account. In addition, the productivity of ratoon crop is equivalent to transplanted rice, which was determined for cultivation in experiment conditions of small concrete tanks. Therefore, further study on ratoon in Myanmar is necessary for clarifying the viability of ratoon cropping.

Vine copula graphical models in the construction of biological networks

The copula Gaussian graphical model (CGGM) is one of the major mathematical models for high dimensional biological networks which provides a graphical representation, especially, for sparse networks. Basically, this model uses a regression of the Gaussian graphical model (GGM) whose precision matrix describes the conditional dependence between the variables to estimate the coefficients of the linear regression model. The Bayesian inference for the model parameters is used to overcome the dimensional limitation of GGM under sparse networks and small sample sizes. But from the application in bench-mark data sets, it is seen that although CGGM is successful in certain systems, it may not fit well for non-normal multivariate observations. In this study, we propose the vine copulas to relax the strict normality assumption of CGGM and to describe networks from a variety of copulas’ alternates besides the Gaussian copula. Accordingly, we evaluate the best fitted bivariate copula distribution for every pairwise gene and compute the estimated adjacency matrix which denotes the presence of an edge between the corresponding genes. We assess the performance of our proposed approach in three network data via distinct accuracy measures by comparing the outputs with the results of the CGGM.

Bayesian inference of root architectural model parameters from synthetic field data

Background and aimsCharacterizing root system architectures of field-grown crops is challenging as root systems are hidden in the soil. We investigate the possibility of estimating root architecture model parameters from soil core data in a Bayesian framework.MethodsIn a synthetic experiment, we simulated wheat root systems in a virtual field plot with the stochastic CRootBox model. We virtually sampled soil cores from this plot to create synthetic measurement data. We used the Markov chain Monte Carlo (MCMC) DREAM(ZS) sampler to estimate the most sensitive root system architecture parameters. To deal with the CRootBox model stochasticity and limited computational resources, we essentially added a stochastic component to the likelihood function, thereby turning the MCMC sampling into a form of approximate Bayesian computation (ABC).ResultsA few zero-order root parameters: maximum length, elongation rate, insertion angles, and numbers of zero-order roots, with narrow posterior distributions centered around true parameter values were identifiable from soil core data. Yet other zero-order and higher-order root parameters were not identifiable showing a sizeable posterior uncertainty.ConclusionsBayesian inference of root architecture parameters from root density profiles is an effective method to extract information about sensitive parameters hidden in these profiles. Equally important, this method also identifies which information about root architecture is lost when root architecture is aggregated in root density profiles.

Efficient Bayesian inference for large chaotic dynamical systems

Abstract. Estimating parameters of chaotic geophysical models is challenging due to their inherent unpredictability. These models cannot be calibrated with standard least squares or filtering methods if observations are temporally sparse. Obvious remedies, such as averaging over temporal and spatial data to characterize the mean behavior, do not capture the subtleties of the underlying dynamics. We perform Bayesian inference of parameters in high-dimensional and computationally demanding chaotic dynamical systems by combining two approaches: (i) measuring model–data mismatch by comparing chaotic attractors and (ii) mitigating the computational cost of inference by using surrogate models. Specifically, we construct a likelihood function suited to chaotic models by evaluating a distribution over distances between points in the phase space; this distribution defines a summary statistic that depends on the geometry of the attractor, rather than on pointwise matching of trajectories. This statistic is computationally expensive to simulate, compounding the usual challenges of Bayesian computation with physical models. Thus, we develop an inexpensive surrogate for the log likelihood with the local approximation Markov chain Monte Carlo method, which in our simulations reduces the time required for accurate inference by orders of magnitude. We investigate the behavior of the resulting algorithm with two smaller-scale problems and then use a quasi-geostrophic model to demonstrate its large-scale application.

Uncertainty Quantification and Bayesian Inference of Cloud Parameterization in the NCAR Single Column Community Atmosphere Model (SCAM6)

Uncertainty quantification (UQ) in weather and climate models is required to assess the sensitivity of their outputs to various parameterization schemes and thereby improve their consistency with observations. Herein, we present an efficient UQ and Bayesian inference for the cloud parameters of the NCAR Single Column Atmosphere Model (SCAM6) using surrogate models based on a polynomial chaos expansion. The use of a surrogate model enables to efficiently propagate uncertainties in parameters into uncertainties in model outputs. We investigated eight uncertain parameters: the auto-conversion size threshold for ice to snow (dcs), the fall speed parameter for stratiform cloud ice (ai), the fall speed parameter for stratiform snow (as), the fall speed parameter for cloud water (ac), the collection efficiency of aggregation ice (eii), the efficiency factor of the Bergeron effect (berg_eff), the threshold maximum relative humidity for ice clouds (rhmaxi), and the threshold minimum relative humidity for ice clouds (rhmini). We built two surrogate models using two non-intrusive methods: spectral projection (SP) and basis pursuit denoising (BPDN). Our results suggest that BPDN performs better than SP as it enables to filter out internal noise during the process of fitting the surrogate model. Five out of the eight parameters (namely dcs, ai, rhmaxi, rhmini, and eii) account for most of the variance in predicted climate variables (e.g., total precipitation, cloud distribution, shortwave and longwave cloud radiative effect, ice, and liquid water path). A first-order sensitivity analysis reveals that dcs contributes ~40–80% of the total variance of the climate variables, ai around 15–30%, and rhmaxi, rhmini, and eii around 5–15%. The second- and higher-order effects contribute ~7 and 20%, respectively. The sensitivity of the model to these parameters was further explored using response curves. A Markov chain Monte Carlo (MCMC) sampling algorithm was also implemented for the Bayesian inference of dcs, ai, as, rhmini, and berg_eff using cloud distribution data collected at the Southern Great Plains (USA). The inferred parameters suggest improvements in the global Climate Earth System Model (CESM2) simulations of the tropics and sub-tropics.

A neural network-aided Bayesian identification framework for multiscale modeling of nanocomposites

This work proposes a Bayesian framework for determining the mechanical properties of carbon based nanocomposites. In particular, Bayesian parameter inference is applied to learn the parameters that characterize the CNT/polymer interface in the microscale. These parameters are associated with great uncertainties and their characterization is a difficult task, since microscale measurements are costly and hard to obtain. To overcome this, the present study introduces a computational framework for updating the prior beliefs on the values of these parameters, by using measurements on large-scale structures comprised of the composite. In terms of modeling, the CNT/polymer interface is formulated with the cohesive zone model and a bilinear bond-slip constitutive law. Typically, predicting the response of such systems requires multiscale analysis approaches, such as the FE2 method, employed in this work. Despite its accuracy, FE2 is associated with immense computational demands for large-scale problems and, therefore, its application to the Bayesian setting, which requires multiple model evaluations, is prohibitive. To alleviate this cost, a surrogate modeling technique is developed which utilizes artificial neural networks, trained to predict the nonlinear stress–strain relationship of representative volume elements of the microstructure. The data set over which the neural network is trained, is obtained by analyzing a limited number of different RVE configurations using a detailed finite element analysis. The elaborated methodology is first validated through a numerical example from 2D elasticity, which demonstrated its high accuracy and its significant cost reduction capabilities. It is then applied to a more challenging large-scale problem from 3D elasticity. Even though this paper focuses on the characterization of the mechanical properties of composite materials, the proposed numerical procedure is generic and can be straightforwardly applied to other physically analogous phenomena related to nano-composite modeling, such as parameter identification in heat transfer or electrical conduction.

Rapid and robust parameter inference for binary mergers

The detection rate for compact binary mergers has grown as the sensitivity of the global network of ground based gravitational wave detectors has improved, now reaching the stage where robust automation of the analyses is essential. Automated low-latency algorithms have been developed that send out alerts when candidate signals are detected. The alerts include sky maps to facilitate electromagnetic follow up observations, along with probabilities that the system might contain a neutron star, and hence be more likely to generate an electromagnetic counterpart. Data quality issues, such as loud noise transients (glitches), can adversely affect the low-latency algorithms, causing false alarms and throwing off parameter estimation. Here a new analysis method is presented that is robust against glitches, and capable of producing fully Bayesian parameter inference, including sky maps and mass estimates, in a matter of minutes. Key elements of the method are wavelet-based de-noising, penalized maximization of the likelihood during the initial search, rapid sky localization using pre-computed inner products, and heterodyned likelihoods for full Bayesian inference.

Bayesian Inference of Ice Softness and Basal Sliding Parameters at Langjökull

We develop Bayesian statistical models that are designed for the inference of ice softness and basal sliding parameters, important glaciological quantities. These models are applied to Langjökull, the second largest temperate ice cap in Iceland at about 900 squared kilometers in area. The models make use of a relationship between physical parameters and ice velocity as stipulated by a shallow ice approximation that is generally applicable to Langjökull. The posterior distribution for ice softness concentrates around 18.2 × 10−25s−1Pa−3; moreover, spatially varying basal sliding parameters are inferred allowing for the decomposition of velocity into a deformation component and a sliding component, with spatial variation consistent with previous studies. Bayesian computation is conducted with a Gibbs sampling approach. The paper serves as an example of statistical inference for ice softness and basal sliding parameters at temperate, shallow glaciers using surface velocity data.