Bayesian Parameter Estimation Research Articles

Estimation of step-stress life testing model using time-censoring: A Bayesian approach

Accelerated life tests (ALTs) of highly reliable products or materials are effective testing techniques to gather failure data rapidly in a limited time period. Also, partially accelerated life tests (PALTs) can enable us to achieve this goal without putting all test units under severe conditions. This article considers both frequent and Bayesian estimations of the step-stress PALTs model using time-censored data from generalized exponential distribution (GED). The maximum likelihood and Bayesian estimates of the model parameters are obtained. The posterior means and posterior variances are computed under the squared error (SE) loss function using Lindley’s procedure. The performance of the estimators is evaluated numerically for different parameter values and different sample sizes via their mean squared error (MSE). In addition, the average confidence intervals lengths (ACIL) of the model parameters are also obtained. For illustrative purposes, a simulation study is given.

Estimation and prediction for two-parameter Pareto distribution based on progressively double Type-II hybrid censored data

<abstract> <p>In this paper, a new censoring test plan called progressively double Type-II hybrid censoring scheme is introduced for the first time. Based on this type of censored data, the maximum likelihood estimates of the unknown parameters and reliability for the two-parameter Pareto distribution are obtained. Using the Bayesian method, the Bayesian estimates of the unknown parameters and reliability are obtained under the symmetric and asymmetric loss functions. The failure times of all withdrawn units are predicted using the classical and Bayesian methods, including the predictive values and the prediction intervals. The mean values and mean square errors of the estimators are calculated by Monte-Carlo simulation, and the mean square errors between them are compared, and the results show that all Bayesian estimates are better than the corresponding maximum likelihood estimates. Using a real data set, we compute the Bayesian estimates of the unknown parameters and reliability, and predict the observations of the censored units.</p> </abstract>

Bayesian estimation of parameters in viral dynamics models with antiviral effect of interferons in a cell culture.

The goal of this work is to estimate the efficacy of interferon therapy in the inhibition of infection by the human immunodeficiency virus type 1 (HIV-1) in a cell culture. For this purpose, three viral dynamics models with the antiviral effect of interferons are presented; the dynamics of cell growth differ among the models, and a variant with Gompertz-type cell dynamics is proposed. A Bayesian statistics approach is used to estimate the cell dynamics parameters, viral dynamics and interferon efficacy. The models are fitted to sets of experimental data on cell growth, HIV-1 infection without interferon therapy and HIV-1 infection with interferon therapy, respectively. The Watanabe-Akaike information criterion (WAIC) is used to determine the model that best fits the experimental data. In addition to the estimated model parameters, the average lifespan of the infected cells and the basic reproductive number are calculated.

Approximate Bayesian Estimation of Suspension Parameters of In-service High-speed Trains Based on Kriging Surrogate Model

Approximate Bayesian Estimation of Suspension Parameters of In-service High-speed Trains Based on Kriging Surrogate Model

Analysis of information measures using generalized type-Ⅰ hybrid censored data

<abstract><p>An entropy measure of uncertainty has a complementary dual function called extropy. In the last six years, this measure of randomness has gotten a lot of attention. It cannot, however, be applied to systems that have survived for some time. As a result, the idea of residual extropy was created. To estimate the extropy and residual extropy, Bayesian and non-Bayesian estimators of unknown parameters of the exponentiated gamma distribution are generated. Bayesian estimators are regarded using balanced loss functions like the balanced squared error, balanced linear exponential and balanced general entropy. We use the Lindley method to get the extropy and residual extropy estimates for the exponentiated gamma distribution based on generalized type-Ⅰ hybrid censored data. To test the effectiveness of the proposed methodologies, a simulation experiment was carried out, and the actual data set was studied for illustrative purposes. In summary, the mean squared error values decrease as the number of failures increases, according to the results obtained. The Bayesian estimates of residual extropy under the balanced linear exponential loss function perform well compared to the other estimates. Alternatively, the Bayesian estimates of the extropy perform well under a balanced general entropy loss function in the majority of situations.</p></abstract>

Window function convolution with deep neural network models

Traditional estimators of the galaxy power spectrum and bispectrum are sensitive to the survey geometry. They yield spectra that differ from the true underlying signal since they are convolved with the window function of the survey. For the current and future generations of experiments, this bias is statistically significant on large scales. It is thus imperative that the effect of the window function on the summary statistics of the galaxy distribution is accurately modelled. Moreover, this operation must be computationally efficient in order to allow sampling posterior probabilities while performing Bayesian estimation of the cosmological parameters. In order to satisfy these requirements, we built a deep neural network model that emulates the convolution with the window function, and we show that it provides fast and accurate predictions. We trained (tested) the network using a suite of 2000 (200) cosmological models within the cold dark matter scenario, and demonstrate that its performance is agnostic to the precise values of the cosmological parameters. In all cases, the deep neural network provides models for the power spectra and the bispectrum that are accurate to better than 0.1% on a timescale of 10 μs.

A Class of Bayesian Lower Bounds for Parameter Estimation Via Arbitrary Test-Point Transformation

In this paper, a new class of global mean-squared-error (MSE) lower bound for Bayesian parameter estimation is derived. First, it is shown that under the non-Bayesian framework, the Hammersley-Chapman-Robbins (HCR) for the problem of single-source parameter estimation, is related to the corresponding ambiguity function. This result is achieved by judicious choice of signal test-point. This result implies that optimal shift test-points may be parameter-dependent, but this approach cannot be imitated in test-point based Bayesian bounds, where the test-points should be independent of the random parameters. Based on this observation, a new class Bayesian MSE lower bound is derived. In the proposed class, the shift test-points in the Cauchy-Schwarz based bounds are substituted with arbitrary transformations. The proposed class generalizes the Weiss-Weinstein bound (WWB) to arbitrary transformations. For the problem of single source parameter estimation, a scaling transformation for the signal test-point is proposed based on the structure of the optimal test-point in the HCR bound in the non-Bayesian framework. The test-point scale parameters are analytically optimized and a closed-form expression for the bound, which depends on the ambiguity function, is derived. For the problem of direction-of-arrival (DOA) estimation using a linear array, a nonlinear transformation for the parameter of interest is proposed. In the problems of frequency estimation and DOA estimation, the proposed bound accurately predicts the threshold phenomenon of the maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a-posteriori</i> probability estimator, and is much tighter than the WWB in both the threshold prediction and the asymptotic performance. In addition, an asymptotic version of the bound was derived and it is analytically shown to be tighter than the Bayesian Cramér-Rao bound.

Bayesian estimation of nonlinear models parameters in the description of growth coffee fruits

Coffee is one of the main products of Brazilian agriculture and the country is currently the largest producer and exporter in the world. The coffee fruit has a double sigmoidal growth pattern, however, as well as in other fruits that also show such a growth pattern, the authors generally do not estimate parameters of regression models to describe such curve. In the study of fruit growth curves, the sample size is generally small, so the estimation of the parameters should preferably be done by the Bayesian methodology, since a priori information is incorporated, reducing the effects of having few observations. The Markov Chain Monte Carlo algorithms are the most used computational tool in Bayesian statistics. However, these generate dependent samples, can be complicated to implement and, mainly, to teach. There are also other alternatives to the MCMC algorithms to obtain approximations of integrals of interest in Bayesian inference, the main ones are based on the importance resampling techniques. The objective of this work is to use Bayesian inference with the weighted importance resampling technique in the estimation of parameters of double sigmoidal nonlinear regression models to the description of coffee fruit growth. The double nonlinear logistic model was used in the description of the accumulation of fresh weight in coffee fruits. All prioris used have Beta distribution and were obtained by the called prior of specialist technique. Bayesian methodology was efficient, since it provided parameters with practical interpretation to coffee fruit growth, consistent with the reality. Thus, Bayesian inference by weighted importance resampling was a good alternative for the parameters estimation of nonlinear double sigmoid regression models. The logistic model showed that the growth of coffee fruits is more intense in the first sigmoid (until 162 DAF)of the growth curve and stabilizes in its final weight after 262 daf.

The Kumaraswamy Distribution: Statistical Properties and Application

Modeling and analyzing lifetime data is an important aspect of statistical work in various scientific and technological fields such as medicine, engineering, insurance, and finance. The modeling and analysis of lifetimes is an important aspect of statistical work in various scientific and technological fields. In recent years, inverted Kumaraswamy distribution has been used quite effectively to model many lifetime data. The most broadly applied statistical distribution is Kumaraswamy distribution in hydrological problems and many natural phenomena. The Kumaraswamy distribution (KD) is widely applied for modeling data in practical domains, such as medicine, engineering, economics, and physics. The present work proposes the Bayesian estimators of KD parameters through the use of type-II censoring data in this research the problem to estimate the unknown parameters of Kumaraswamy distribution with two parameters θ and λ, these estimates are a maximum likelihood of ordered observation and the Bayesian for the parameter of the Kumaraswamy distribution (KUD) depended on ranked set sampling (RSS) techniques. Both the simulated are inserted into real-life data sets and are considered to make a comparison between the estimation based on Maximum Likelihood estimators and Bayesian Estimation methods based on (RSS) techniques. For comparison purposes, we employed (100) mean square error and the criteria like AICC (Akaike information corrected criterion). Finally, the importance and flexibility of the new model of real data set are proved empirically.

1449. Therapeutic Drug Monitoring of Isoniazid and Rifampicin and Clinical Outcomes in Adults with Tuberculosis.

Abstract Background Directly Observed Treatment Short Course for Tuberculosis (TB) (DOTS) treatment currently produces a cure rate of 80%. Rifampicin (RMP) and isoniazid (INH) are the main bactericides; both show wide inter-individual pharmacokinetics and narrow therapeutic range. Therapeutic drug monitoring (TDM) of antiTB drugs is a strategy to improve the response to treatment. The aim of this work was to optimize and individualize antiTB treatment based on plasma concentrations of RMP and INH, NAT2 genotyping and the Bayesian estimation of PK parameters. Methods A prospective and analytical study including TB patients under DOTS scheme was performed. Venous blood samples were drawn 2 and 4 hours after last dose; INH and RMP were quantified by liquid chromatography coupled to tandem mass spectrometry. Anthropometric and clinical information was retrieved from medical records. Acetylator phenotype was determined based on NAT2 genotyping by real-time PCR. Bayesian estimation of the PK parameters was performed using NONMEM and dosing scheme was proposed to achieve therapeutic concentrations of RIF and INH. Results A total 62 patients were included from 18 to 80 years and 35 to 117 kg of total body weight. The most frequent was pulmonary infection (40%), 25% of patients had type 2 diabetes mellitus and 58.5% were slow acetylators for the NAT2 gene. Lower INH and RMP plasma concentrations were related to adverse clinical outcome, compared to those patients classified with early clinical success [1.9 vs 3.7 mg/L and 16.9 vs 10.0 mg/L (p&amp;lt; 0.05)]. Results indicate the need to adjust anti-TB drugs dose to more than 50% of the patients who show plasma concentrations outside the range for both drugs. Bayesian dosing performed was validated after individualization by quantification and interpretation of INH and RMP plasma concentrations followed by a narrow medical follow up. Conclusion Even with standard anti-TB treatment, great proportion of patients show subtherapeutic concentrations of RMP and INH which is associated with overall therapeutic failure. TDM is a useful tool to individualize antimicrobials dose and improve clinical outcomes at early stages of active TB. Disclosures All Authors: No reported disclosures.

Frhodo: A program for simulating chemical kinetic measurements and optimizing kinetic mechanisms

Chemical kinetic simulations are frequently used to extract kinetic and mechanistic information from experimental data by fitting simulations to the data. For simple systems of consecutive single channel reactions this is a relatively straightforward task. However, as the complexity of the system increases and particularly for systems involving competitive multi-channel reactions manually optimizing a mechanism to obtain the best fits to a range of experimental data quickly becomes a time-intensive and challenging process, especially when rate coefficients have pressure and temperature dependencies. There is considerable potential for exploiting automated optimization methods to rapidly screen reaction mechanisms and optimize the fit by adjusting rate coefficients within well-defined constraints. A new chemical kinetics simulation program, Frhodo, has been developed for this purpose. The program allows either manual simulation of individual experiments or fully automated optimization against a range of experimental data by adjusting user selected reactions within user defined constraints. Frhodo incorporates machine learning-based optimization routines that work by either minimizing standardized residuals or through Bayesian parameter estimation. Frhodo's optimization capabilities are demonstrated by reexamining two previously studied systems of relevance to combustion. Dissociation of diacetyl followed by recombination of methyl radicals is an example of a sequence of single channel, consecutive reactions. Pyrolysis of 2-methyl furan exemplifies multi-channel, unimolecular reactions that are often encountered and have temperature and pressure dependencies in the rate coefficients of the channels and branching ratios between them. For both systems the optimization routines resulted in solutions similar to the original studies. Comments are made on the strengths and limitations of the approach.

A unified numerical model for two-phase porous, mush and suspension flow dynamics in magmatic systems

SUMMARYMagmatic systems in the Earth’s mantle and crust contain multiple phases including solid crystals, liquid melt and low viscosity fluids. Depending on depth, tectonic setting and chemical composition, magmatic systems can range from partially molten rock at low melt fraction to magma mushes at intermediate melt fraction to magmatic suspensions at high melt fraction. However, the theories underpinning most process-based models of magmatic systems describe magma as a single-phase fluid, or as a two-phase mixture either in the porous flow regime at low melt fractions or in the suspension flow regime at high melt fractions. Connections between the two-phase end-member theories are poorly established and hinder investigations into the dynamics of mush flows at intermediate phase fractions, leaving a significant gap in bridging trans-crustal magma processing from source to surface. To address this knowledge gap and unify two-phase magma flow models, we develop a 2-D system-scale numerical model of the fluid mechanics of an n-phase system at all phase proportions, based on a recent theoretical model for multiphase flows in igneous systems. We apply the model to two-phase, solid-liquid mixtures by calibrating transport coefficients to theory and experiments on mixtures with olivine-rich rock and basaltic melt using a Bayesian parameter estimation approach. We verify the model using the method of manufactured solutions and test the scalability for high resolution modelling. We then demonstrate 1-D and 2-D numerical experiments across the porous, mush and suspension flow regimes. The experiments replicate known phenomena from end-member regimes, including rank-ordered porosity wave trains in 1-D and porosity wave breakup in 2-D in the porous flow regime, as well as particle concentration waves in 1-D and mixture convection in 2-D in the suspension flow regime. By extending self-consistently into the mush regime, the numerical experiments show that the weakening solid matrix facilitates liquid localization into liquid-rich shear bands with their orientation controlled by the solid stress distribution. Although the present model can already be used to investigate three-phase mixtures using conceptually derived transport coefficients, more rigorous calibration to experiments and end-member theories is needed to ensure accurate timescales and mechanics. With a self-consistent way to examine multiphase mixtures at any phase proportion, this new model transcends theoretical limitations of existing multiphase numerical models to enable new investigations into two-phase or higher magma mush dynamics.

Bayesian variable selection and estimation in multivariate skew-normal generalized partial linear mixed models for longitudinal data

This paper proposes a novel generalized partial linear mixed models (GPLMMs) with the random effects distribution distributed as a multivariate skew-normal distribution for discrete longitudinal data over time. Under the Bayesian framework, we extended the Bayesian version of adaptive lasso (least absolute shrinkage and selection operator) for linear regression to the Bayesian adaptive lasso with the least squares approximation (LSA) method for generalized partial linear mixed models. A hybrid algorithm combining the Gibbs sampler and the Metropolis-Hastings algorithm in conjunction with the Bayesian adaptive lasso with LSA is used to simultaneously obtain the Bayesian estimates of unknown parameters, smoothing function and random effects, as well as select important covariates in GPLMMs. Several simulation studies and a real example are presented to illustrate the proposed methodologies.

Smartphone-Based Pedestrian NLOS Positioning Based on Acoustics and IMU Parameter Estimation

This paper proposes an integrated positioning algorithm for mobile devices and achieves long-term and high-accuracy indoor pedestrian tracking under severe non-Line-of-Sight (NLOS) scenarios. The traditional fusion method for hand-held devices lacks zero-speed correction and cannot clear the accumulated error of the Pedestrian Dead Reckoning (PDR). Secondly, the PDR algorithm also requires user privacy data for high positioning accuracy. Hence, we propose a customized model with acoustic and PDR through self-updating parameters with two novel fusing strategies: Kalman Filter with Least-Square (KFLS) and Kalman Filter with Bayesian Parameter Estimation (KFBPE), which utilize numerical feedback and Bayesian distribution, respectively. Experiments with Huawei Mate 9 show that both methods above can effectively eliminate the outlier resulting from severe signal loss, regardless of hand-holding gestures, with no individual privacy data required. Extensive experimental results demonstrate that the proposed methods are more efficient for NLOS and perform much better than the baselines of traditional fusion frameworks like the standard Kalman Filter. KFBPE has a relatively smoother tracking result, which guarantees an average positioning accuracy of up to 25 cm under the circumstance of nearly thirty percent acoustic signal loss (or NLOS) at the same time.

The Radius of PSR J0740+6620 from NICER with NICER Background Estimates

We report a revised analysis for the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, studied previously with joint fits to NICER and XMM-Newton data by Riley et al. (2021) and Miller et al. (2021). We perform a similar Bayesian estimation for the pulse-profile model parameters, except that instead of fitting simultaneously the XMM-Newton data, we use the best available NICER background estimates to constrain the number of photons detected from the source. This approach eliminates any potential issues in the cross-calibration between these two instruments, providing thus an independent check of the robustness of the analysis. The obtained neutron star parameter constraints are compatible with the already published results, with a slight dependence on how conservative the imposed background limits are. A tighter lower limit causes the inferred radius to increase, and a tighter upper limit causes it to decrease. We also extend the study of the inferred emission geometry to examine the degree of deviation from antipodality of the hot regions. We show that there is a significant offset to an antipodal spot configuration, mainly due to the non-half-cycle azimuthal separation of the two emitting spots. The offset angle from the antipode is inferred to be above 25° with 84% probability. This seems to exclude a centered-dipolar magnetic field in PSR J0740+6620.

Probabilistic planning for ligament-balanced TKA—Identification of critical ligament properties

Total knee arthroplasty (TKA) failures are often attributed to unbalanced knee ligament loading. The current study aims to develop a probabilistic planning process to optimize implant component positioning that achieves a ligament-balanced TKA. This planning process accounts for both subject-specific uncertainty, in terms of ligament material properties and attachment sites, and surgical precision related to the TKA process typically used in clinical practice. The consequent uncertainty in the implant position parameters is quantified by means of a surrogate model in combination with a Monte Carlo simulation. The samples for the Monte Carlo simulation are generated through Bayesian parameter estimation on the native knee model in such a way that each sample is physiologically relevant. In this way, a subject-specific uncertainty is accounted for. A sensitivity analysis, using the delta-moment-independent sensitivity measure, is performed to identify the most critical ligament parameters. The designed process is capable of estimating the precision with which the targeted ligament-balanced TKA can be realized and converting this into a success probability. This study shows that without additional subject-specific information (e.g., knee kinematic measurements), a global success probability of only 12% is estimated. Furthermore, accurate measurement of reference strains and attachment sites critically improves the success probability of the pre-operative planning process. To allow more precise planning, more accurate identification of these ligament properties is required. This study underlines the relevance of investigating in vivo or intraoperative measurement techniques to minimize uncertainty in ligament-balanced pre-operative planning results, particularly prioritizing the measurement of ligament reference strains and attachment sites.

Mathematical Models for Early Detection of Relapse in Multiple Myeloma Patients Treated with Bortezomib/Lenalidomide/Dexamethasone

Background: Multiple Myeloma (MM, an incurable bone marrow plasma cell malignancy, is the second most common hematological malignancy in the United States. The introduction of novel triplet-based induction therapy with bortezomib (Bor), lenalidomide (Len), and dexamethasone (Dex) has shown excellent results in several large, randomized phase III trials and is considered a standard of care for newly diagnosed MM (1-3). The question lies at which timing a clinician should move from VRd combination therapy to auto-HCT and sequential second-line therapy. Guidelines recommend waiting for International Myeloma Working Group Uniform Response Criteria (IMWG Criteria) to be met before proceeding to the next line of therapy. A tool to anticipate progression before IMWG Criteria may allow early switch to the next line therapy while the disease burden is relatively low (4). We aimed to evaluate predictive accuracy of a mathematical model to anticipate relapse 6 months before the IMWG Criteria are met. Methods: Four hundred seventy patients initially treated with a subset of VRd and with ≥ 3 serum M-protein values prior to auto-HCT, including one baseline value ≥ 0.5g/dL in the CoMMpass study (IA16) and were randomly split 2:1 into training and testing sets. A model of M-protein dynamics was developed using the training set. By fitting the model to each observation window in the testing set, distribution of future response trajectories was created for the whole population utilizing Bayesian parameter estimation, and by combining all the M-protein estimated trajectories, Receiver Operating Characteristics (ROC) curve was generated. As a comparator, we also tested most M-protein "velocity" through the two most recent time points as a predictor. Results: The two-population tumor growth inhibition model with additive drug effect and transit model for cell killing was identified to be the best model for both training and testing set. The model identified baseline R-ISS staging on M-protein baseline (M0), 1st response treatment outcome of first 2 cycles, which we will gain information before 3 months protein value data are gained, on frequency of resistant cell population (ϕ), and existence of t(4;14) mutation-positive cells on resistant cell function (dRes/dt) as the best predictor of serum M-protein kinetics. The ROC area under the curve (AUC) value of relapse prediction 180 days ahead of observed relapse by FPC was 0.829 with sensitivity and specificity both of 78% using an observation time of least 360 days, which was superior to the M-protein velocity ROC score of 0.713 under the same conditions (Fig 1B). ROC AUC continues to improve, and maintains its advantage over M-protein velocity, with each additional 90 days of observation time. Conclusion: The individualized model-based approach from data within the first 9 or more months of VRd treatment could provide prospective and reasonable predictions of future M-protein trajectories in individuals with MM. It allowed predictions for personalized "progression free" curve under various treatment scenarios. This model may enable a future study testing the difference in patient outcomes when treatment is switched when relapse is imminent versus already occurred. Reference: (1) Rosiñol, L. et al. Bortezomib, lenalidomide, and dexamethasone as induction therapy prior to autologous transplant in multiple myeloma. Blood134, 1337-45 (2019). (2) Durie, B.G.M. et al. Bortezomib with lenalidomide and dexamethasone versus lenalidomide and dexamethasone alone in patients with newly diagnosed myeloma without intent for immediate autologous stem-cell transplant (SWOG S0777): a randomised, open-label, phase 3 trial. Lancet389, 519-27 (2017). (3) Attal, M. et al. Lenalidomide, Bortezomib, and Dexamethasone with Transplantation for Myeloma. N Engl J Med376, 1311-20 (2017). (4) Jackson, G. et al. Response-adapted intensification with cyclophosphamide, bortezomib, and dexamethasone versus no intensification in patients with newly diagnosed multiple myeloma (Myeloma XI): a multicentre, open-label, randomised, phase 3 trial. Lancet Haematol.6, e616-29 (2019). Figure 1View largeDownload PPTFigure 1View largeDownload PPT Close modal

A Bayesian approach for torque modelling of BeXRB pulsars with application to super-Eddington accretors

ABSTRACT In this study, we present a method to estimate posterior distributions for standard accretion torque model parameters and binary orbital parameters for X-ray binaries using a nested sampling algorithm for Bayesian parameter estimation. We study the spin evolution of two Be X-ray binary systems in the Magellanic Clouds, RX J0520.5−6932 and RX J0209−7427, during major outbursts, in which they surpassed the Eddington limit. Moreover, we apply our method to the recently discovered Swift J0243.6+6124, the only known Galactic pulsating ultra-luminous X-ray source. This is an excellent candidate for studying the disc evolution at super-Eddington accretion rates, because its luminosity spans several orders of magnitude during its outburst, with a maximum LX that exceeded the Eddington limit by a factor of ∼10. Our method, when applied to RX J0520.5−6932 and RX J0209−7427, is able to identify the more favourable torque model for each system, while yielding meaningful ranges for the NS and orbital parameters. Our analysis for Swift J0243.6+6124 illustrates that, contrary to the standard torque model predictions, the magnetospheric radius (Rm) and the Alfvén radius (RA) are not proportional to each other when surpassing the Eddington limit. Reported distance estimates of this source range between 5 and 7 kpc. Smaller distances require non-typical neutron star properties (i.e. mass and radius) and possibly lower radiative efficiency of the accretion column.

Nuclear physics uncertainties in light hypernuclei

The energy levels of light hypernuclei are experimentally accessible observables that contain valuable information about the interaction between hyperons and nucleons. In this work we study strangeness $S = -1$ systems $^{3,4}_\Lambda$H and $^{4,5}_\Lambda$He using the ab initio no-core shell model (NCSM) with realistic interactions obtained from chiral effective field theory ($\chi$EFT). In particular, we quantify the finite precision of theoretical predictions that can be attributed to nuclear physics uncertainties. We study both the convergence of the solution of the many-body problem (method uncertainty) and the regulator- and calibration data-dependence of the nuclear $\chi$EFT Hamiltonian (model uncertainty). For the former, we implement infrared correction formulas and extrapolate finite-space NCSM results to infinite model space. We then use Bayesian parameter estimation to quantify the resulting method uncertainties. For the latter, we employ a family of 42 realistic Hamiltonians and measure the standard deviation of predictions while keeping the leading-order hyperon-nucleon interaction fixed. Following this procedure we find that model uncertainties of ground-state $\Lambda$ separation energies amount to $\sim 20(100)$ keV in $^3_\Lambda$H($^4_\Lambda$H,He) and $\sim 400$ keV in $^5_\Lambda$He. Method uncertainties are comparable in magnitude for the $^4_\Lambda$H,He $1^+$ excited states and $^5_\Lambda$He, which are computed in limited model spaces, but otherwise much smaller. This knowledge of expected theoretical precision is crucial for the use of binding energies of light hypernuclei to infer the elusive hyperon-nucleon interaction.

Classical and Bayesian Uncertainty Intervals for the Reliability of Multidimensional Scales

The reliability of a multidimensional test instrument is commonly estimated using coefficients ωt (total) and ωh (hierarchical). However, point estimates for the coefficients are rarely accompanied by uncertainty estimates. In this study, we compare bootstrap and normal-theory confidence intervals. In addition, we develop Bayesian versions of coefficients ωt and ωh by sampling from a second-order factor model. Results from a comprehensive simulation study show that the studied confidence intervals performed well when the sample size was sufficiently large (). The Bayesian estimates performed well across most studied conditions. When the sample size was small and the reliability low, only the bias-corrected and accelerated bootstrap confidence interval approached a satisfactory coverage among all intervals. This study guides on ωt and ωh confidence intervals and introduces ωt and ωh credible intervals that are easy to use and come with the benefits of Bayesian parameter estimation.