Error Structure Research Articles

Структура клинической рефракции глаз у детей подросткового возраста

Purpose. To analyze the frequency of myopia in the structure of clinical eye refraction in adolescent children. Material and methods. Analysis of the results of an ophthalmological examination of 690 schoolchildren aged 11, 13, 15 years using the continuous sampling method. Results. In the structure of totality of the examined children, refractive errors were noted in 405 people (58.7 %), in the structure of myopia refractive error amounted to 339 people (83.7 %). 65.5 % of schoolchildren had mild myopia, 37.5 % had moderate myopia, and 1.8 % had high myopia. In 32 schoolchildren habitually excessive tension of accommodation was revealed. The progressive course of myopia was noted in 45 children (13 %), of which in half of the cases it was at the age of 11 years. According to the picture of fundus, the chorioretinal form of myopia predominated. In the structure of refractive errors, corneal astigmatism was detected in 118 children (29 %), of which in 55 % of children it was myopic, in 22 % it was mixed. 201 schoolchildren had incomplete vision correction due to refractive amblyopia, in 90 % of cases it was of a weak degree. Conclusion. In the structure of clinical refraction of the examined children, 285 (41.3 %) schoolchildren had emmetropia, 405 (58.7 %) schoolchildren had refractive errors. Of the entire set of refractive errors, myopia occurred in 339 people (83.7 %). Mild myopia occurred in almost half of the total population of pupils (62.5 %) of age from 11 to 15 years. There is a tendency to increase myopic refraction from 11 to 15 years of age. Keywords: refraction, myopia, childhood, morbidity

Analytical modelling of adaptive optics systems: Role of the influence function

Context. Adaptive optics (AO) is now a tool commonly deployed in astronomy. The real time correction of the atmospheric turbulence that AO enables allows telescopes to perform close to the diffraction limit at the core of their point spread function (PSF). Among other factors, AO-corrected PSFs depend on the ability of the wavefront corrector (WFC), generally a deformable mirror, to fit the incident wavefront corrugations. Aims. In this work, we focus on this error introduced by the WFC, the so-called fitting error. To date, analytical models only depend on the WFC cut-off frequency, and Monte Carlo simulations are the only solution for studying the impact of the WFC influence function shape on the AO-corrected PSF. We aim to develop an analytical model accounting for the influence function shape. Methods. We first obtain a general analytical model of the fitting error structure function. With additional hypotheses, we then derive an analytical model of the AO-corrected power spectral density. These two analytical solutions are compared with Monte Carlo simulations on different ideal profiles (piston, pyramid, Gaussian) as well as with real hardware (DM192 from ALPAO). Results. Our analytical predictions show a very good agreement with the Monte Carlo simulations. We show that in the image plane, the depth of the correction as well as the transition profile between the AO-corrected area and the remaining turbulent halo depend on the influence functions of the WFC. We also show that the generally assumed hypothesis of stationarity of the AO correction is actually not met. Conclusions. As the fitting error is the intrinsic optimal limit of an AO system, our analytical model allows for the assessment of the theoretical limits of extreme AO systems limited by the WFC in high-contrast imaging through a context where other errors become comparable.

Nowcasting from cross‐sectionally dependent panels

SummaryThis paper builds a mixed‐frequency panel data model for nowcasting economic variables across many countries. The model extends the mixed‐frequency panel vector autoregression (MF‐PVAR) to allow for heterogeneous coefficients and a multifactor error structure to model cross‐sectional dependence. We propose a modified common correlated effects (CCE) estimation technique which performs well in simulations. The model is applied in two distinct settings: nowcasting gross domestic product (GDP) growth for a pool of advanced and emerging economies and nowcasting inflation across many European countries. Our method is capable of beating standard benchmark models and can produce updated nowcasts whenever data releases occur in any country in the panel.

A Mixed-Effects Model in Which the Parameters of the Autocorrelated Error Structure Can Differ between Individuals

Research in psychology has seen a rapid increase in the usage of experience sampling methods and daily diary methods. The data that result from using these methods are typically analyzed with a mixed-effects or a multilevel model because it allows testing hypotheses about the time course of the longitudinally assessed variable or the influence of time-varying predictors in a simple way. Here, we describe an extension of this model that does not only allow to include random effects for the mean structure but also for the residual variance, for the parameter of an autoregressive process of order 1 and/or the parameter of a moving average process of order 1. After we have introduced this extension, we show how to estimate the parameters with maximum likelihood. Because the likelihood function contains complex integrals, we suggest using adaptive Gauss-Hermite quadrature and Quasi-Monte Carlo integration to approximate it. We illustrate the models using a real data example and also report the results of a small simulation study in which the two integral approximation methods are compared.

A New Corpus of Lexical Substitution and Word Blend Errors: Probing the Semantic Structure of Lemma Access Failures.

Models of lemma access in language production predict occasional mis-selection of lemmas linked to highly similar concepts (synonyms) and concepts standing in a set-superset relation (subsumatives). It is unclear, however, if such errors occur in spontaneous speech, and if they do, whether humans can detect them given their minimal impact on sentence meaning. This data report examines a large corpus of English spontaneous speech errors and documents a low but non-negligible occurrence of these categories. The existence of synonym and subsumative errors is documented in a larger open access data set that supports a range of new investigations of the semantic structure of lexical substitution and word blend speech errors.

Identifiability of enzyme kinetic parameters in substrate competition: a case study of CD39/NTPDase1.

CD39 (NTPDase1-nucleoside triphosphate diphosphohydrolase 1) is a membrane-tethered ectonucleotidase that hydrolyzes extracellular ATP to ADP and ADP to AMP. This enzyme is expressed in a variety of cell types and tissues and has broadly been recognized within vascular tissue to have a protective role in converting "danger" ligands (ATP) into neutral ligands (AMP). In this study, we investigate the enzyme kinetics of CD39 using a Michaelis-Menten modeling framework. We show how the unique situation of having a reaction product also serving as a substrate (ADP) complicates the determination of the governing kinetic parameters. Model simulations using values for the kinetic parameters reported in the literature do not align with corresponding time-series data. This dissonance is explained by CD39 kinetic parameters previously being determined by graphical/linearization methods, which have been shown to distort the underlying error structure and lead to inaccurate parameter estimates. Modern methods of estimating these kinetic parameters using nonlinear least squares are still challenging due to unidentifiable parameter interactions. We propose a workflow to accurately determine these parameters by isolating the ADPase and ATPase reactions and estimating the respective ADPase parameters and ATPase parameters with independent data sets. Theoretically, this ensures all kinetic parameters are identifiable and reliable for future prospective model simulations involving CD39. These kinds of mathematical models can be used to understand how circulating purinergic nucleotides affect disease etiology and potentially inform the development of corresponding therapies.

An ORP-EIS approach to distinguish the contribution of the buried interface to the electrochemical behaviour of coated aluminium

In this work, the influence of the buried coating/metal oxide interface as a crucial parameter in hybrid systems’ durability was investigated. To evaluate these hybrid interfaces in situ and in realistic conditions/environments, an integrated approach based on the use of odd random phase electrochemical impedance spectroscopy (ORP-EIS) is employed. In this approach proposed previously by our group, in addition to the effectively shortened measurement time, supplementary information about the stochastic noise, non-linearities and non-stationarities is provided. This information allows the rapid analysis of the error structures on the experimental data as well as providing a statistical evaluation for the proposed electrochemical equivalent circuit (EEC). To elaborate on the interfacial influences, aluminium substrates received two different surface pre-treatments (tartaric sulfuric acid (TSA) anodizing and acidic pickling) and were coated with a pigmented polyurethane based and a pigmented epoxy-amine based coating. The ORP-EIS data was fitted to an appropriate EEC and the output parameters were used to distinguish between the diffusion of water and ions. It was shown that prior to the arrival of ions at the buried interface, the coating response is dominating. With further diffusion of ions and their arrival at the interface, the onset of the contribution of different surface pre-treatments was captured and quantified.

Novel specification tests for synchronous additive concurrent model formulation based on martingale difference divergence

This paper presents new specification tests for a general synchronous additive concurrent model formulation. As a novelty, our proposal does not require a preliminary model or error structure estimation. No tuning parameters are involved either. We develop a suitable test statistic using the martingale difference divergence coefficient. As a result, this statistic measures the departure from the conditional mean independence in the concurrent model framework, considering the information of all observed time instants. In particular, global as well as partial dependence tests are introduced. Then, we allow one to quantify the effect of a group of covariates or to apply covariates selection one by one. We obtain its asymptotic distribution under the null and propose a bootstrap algorithm to compute the p-values in practice. Through simulations, we illustrate our method, and its performance is compared to existing competitors. In addition, we use this in the analysis of three real datasets related to gait data, flu activity, and casual bike rentals.

Computer analysis of abnormal proliferation and transformation cells in gastric mucosa and its clinical significance

ABSTRACT To investigate the image computer analysis of abnormally proliferating transformed cells of gastric mucosa and its clinical significance. The pathological pictures of gastric adenomatous polyp cells, abnormally proliferating altered cells, and tubular adenocarcinoma cells in the stomach mucosa were assessed by image computer method on a total of 96 gastroscopic biopsy and ESD resection specimens. The data of cytoplasmic area, nuclear area, nuclear-cytoplasmic ratio, nuclear factor and N-heterotypic index of gastric adenomatous polyps, abnormal proliferative transformation and gastric intramucosal tubular adenocarcinoma were collected, and the mean, standard deviation and variance were calculated respectively. Standard Error, Maximum, Minimum Parameters and Statistical Structure. There were substantial discrepancies between gastric mucosal gastric adenomatous polyp cells and gastric mucosal abnormally proliferating transformed cells, according to the five data in the abnormal cells in the stomach mucosal proliferation area (p < 0.01); There was no significant difference between cells (p > 0.05). Computer analysis of cell images can provide quantitative values for the pathological diagnosis of gastric adenomatous polyp cells, abnormally proliferating transformed cells and tubular adenocarcinoma cells in the gastric mucosa, especially the degree of atypical proliferation. The monitoring of abnormally proliferated and transformed cells in gastric mucosa is of great significance for clinicians to accurately treat and track cell transformation, and to control the occurrence and development of gastric adenocarcinoma.

Maximum likelihood factor analysis for resolution of noisy smartphone based diffuse reflectance data from CdS pigments

This study aims to use multivariate chemometric methods such as principal component analysis (PCA), maximum likelihood common factor analysis (MLFA), and multivariate curve resolution alternating least squares (MCR-ALS) to analyze a designed data set and obtain an estimation of measurement error structure in the absence of replicates. For this purpose, we developed a smartphone-based diffuse reflectance spectrophotometer (smartDRS) with the advantage of being rapid, simple, and cost-effective in acquiring spectral information from the produced pigment samples based on a designed experiment. In our experimental design, the effects of different factors on the color of synthesized cadmium sulfide (CdS) pigment are investigated. DR spectral data from synthesized CdS samples were rapidly and successfully measured using the homemade device. The contribution of three forms (two crystalline and one amorphous) of CdS with three different spectra in each of the 16 synthesized pigment samples was illustrated and confirmed by using MLFA-MCR-ALS. Based on RGB values obtained from spectral information, the concentration profile of the brightest form of CdS was considered as a quantitative criterion of the whiteness of CdS samples and the response in the experimental design. The experimental design results showed pH, use of the furnace, and time for CdS drying as the main factors, in addition to a two-factor (Cd/S molar ratio × drying time) and a three-factor (pH × furnace × drying time) interactions are statistically significant on experimental design response. MLFA results also showed that independent noise in the measured diffuse reflectance data is heteroscedastic but not simply proportional to the signal intensities. This study shows the success of maximum likelihood-based multivariate analysis of diffuse reflectance spectral data from smartDRS for quantitatively investigating affecting factors on synthesized CdS color. Results from the application of PCA before MCR-ALS were considerably different from what was obtained from MLFA and MCR-ALS and were not in accordance with the previous reports.

Confronting population models with experimental microcosm data: from trajectory matching to state‐space models

AbstractPopulation and community ecology traditionally has a very strong theoretical foundation with well‐known dynamical models, such as the logistic and its variations, and many modifications of the classical Lotka–Volterra predator–prey and interspecific competition models. More and more, these classical models are being confronted with data via fitting to empirical time series for purposes of projections or for estimating model parameters of interest. However, using statistical models to fit theoretical models to data is far from trivial, especially for time series data where subsequent measurements are not independent. This raises the question of whether statistical inferences using pure observation error models, such as simple (non‐)linear regressions, are biased, and whether more elaborate process error models or state‐space models have to be used to address this complexity. In order to help empiricists, especially researchers working with experimental laboratory populations in micro‐ and mesocosms, make informed decisions about the statistical formalism to use, we here compare different error structures one could use when fitting classical deterministic ordinary differential equation (ODE) models to empirical data. We consider a large range of biological scenarios and theoretical models, from single species to community dynamics and trophic interactions. In order to compare the performance of different error structure models, we use both realistically simulated data and empirical data from microcosms in a Bayesian framework. We find that many model parameters can be estimated precisely with an appropriate choice of error structure using pure observation error or state‐space models, if observation errors are not too high. However, Allee effect models are typically hard to identify and state‐space models should be preferred when model complexity increases. Our work shows that, at least in the context of low environmental stochasticity and high quality observations, deterministic models can be used to describe stochastic population dynamics that include process variability and observation error. We discuss when more complex state‐space model formulations may be required for obtaining accurate parameter estimates. Finally, we provide a comprehensive tutorial for fitting these models in R.

Yield Adjustment Using GPR-Derived Spatial Covariance Structure in Cassava Field: A Preliminary Investigation

Many processes concerning below-ground plant performance are not fully understood, such as spatial and temporal dynamics and their relation to environmental factors. Accounting for these spatial patterns is very important as they may be used to adjust for the estimation of cassava fresh root yield masked by field heterogeneity. The yield of cassava is an important characteristic that every breeder seeks to maintain in their germplasm. Ground-Penetrating Radar (GPR) has proven to be an effective tool for studying the below-ground characteristics of developing plants, but it has not yet been explored with respect to its utility in normalizing spatial heterogeneity in agricultural field experiments. In this study, the use of GPR for this purpose was evaluated in a cassava field trial conducted in Momil, Colombia. Using the signal amplitude of the GPR radargram from each field plot, we constructed a spatial plot error structure using the variance of the signal amplitude and developed GPR-based autoregressive (AR) models for fresh root yield adjustment. The comparison of the models was based on the average standard error (SE) of the Best Linear Unbiased Estimator (BLUE) and through majority voting (MV) with respect to the SE of the genotype across the models. Our results show that the GPR-based AR model outperformed the other models, yielding an SE of 9.57 and an MV score of 88.33%, while the AR1 × AR1 and IID models had SEs of 10.15 and 10.56% and MV scores of 17.37 and 0.00%, respectively. Our results suggest that GPR can serve a dual purpose in non-destructive yield estimation and field spatial heterogeneity normalization in global root and tuber crop programs, presenting a great potential for adoption in many applications.

Estimation of Heritability under Correlated Errors Using the Full-Sib Model

In plant and animal breeding, sometimes observations are not independently distributed. There may exist a correlated relationship between the observations. In the presence of highly correlated observations, the classical premise of independence between observations is violated. Plant and animal breeders are particularly interested to study the genetic components for different important traits. In general, for estimating heritability, a random component in the model must adhere to specific assumptions, such as random components, including errors, having a normal distribution, and being identically independently distributed. However, in many real-world situations, all of the assumptions are not fulfilled. In this study, correlated error structures are considered errors that are associated to estimate heritability for the full-sib model. The number of immediately preceding observations in an autoregressive series that are used to predict the value at the current observation is defined as the order of the autoregressive models. First-order and second-order autoregressive models i.e., AR(1) and AR(2) error structures, have been considered. In the case of the full-sib model, theoretical derivation of Expected Mean sum square (EMS) considering AR(1) structure has been obtained. A numerical explanation is provided for the derived EMS considering AR(1) structure. The predicted mean squares error (MSE) is obtained after including the AR(1) error structures in the model, and heritability is estimated using the resulting equations. It is noticed that correlated errors have a major influence on heritability estimation. Different correlation patterns, such as AR(1) and AR(2), can be inferred to change heritability estimates and MSE values. To attain better results, several combinations are offered for various scenarios.

Estimation of Ordinary Differential Equation Models for Gene Regulatory Networks Through Data Cloning.

Ordinary differential equations (ODEs) are widely used for elucidating dynamic processes in various fields. One of the applications of ODEs is to describe dynamics of gene regulatory networks (GRNs), which is a critical step in understanding disease mechanisms. However, estimation of ODE models for GRNs is challenging because of inflexibility of the model and noisy data with complex error structures such as heteroscedasticity, correlations between genes, and time dependency. In addition, either a likelihood or Bayesian approach is commonly used for estimation of ODE models, but both approaches have benefits and drawbacks in their own right. Data cloning is a maximum likelihood (ML) estimation method through the Bayesian framework. Since it works in the Bayesian framework, it is free from local optimum problems that are common drawbacks of ML methods. Also, its inference is invariant for the selection of prior distributions, which is a major issue in Bayesian methods. This study proposes an estimation method of ODE models for GRNs through data cloning. The proposed method is demonstrated through simulation and it is applied to real gene expression time-course data.

Accounting for respondent’s preference uncertainty in choice experiments

ABSTRACT Preference uncertainty is an important aspect affecting respondents’ choices and attribute valuation. However, elicitation of preference uncertainty and its modelling is strongly restricted within choice experiments. This paper applies modelling techniques to account for the preference uncertainty data to evaluate road traffic noise. The paper argues that modelling the preference uncertainty data to examine the error structure can shed significant light on the potential causes of preference uncertainty. The results also reveal that accounting for preference uncertainty data within modelling can have important implications for the valuation exercise. It is found that the nested logit model can examine significant correlation between similar preference certainty levels arising from choice-set characteristics while the error components logit model can be used to examine the effect of inherent respondent uncertainty and stochastic factors on preference uncertainty. The paper therefore recommends treating and accounting for preference uncertainty within choice experiments and thereby examine its impact on any subsequent valuations.

Why do inverse models disagree? A case study with two European CO2 inversions

Abstract. We present an analysis of atmospheric transport impact on estimating CO2 fluxes using two atmospheric inversion systems (CarboScope-Regional (CSR) and Lund University Modular Inversion Algorithm (LUMIA)) over Europe in 2018. The main focus of this study is to quantify the dominant drivers of spread amid CO2 estimates derived from atmospheric tracer inversions. The Lagrangian transport models STILT (Stochastic Time-Inverted Lagrangian Transport) and FLEXPART (FLEXible PARTicle) were used to assess the impact of mesoscale transport. The impact of lateral boundary conditions for CO2 was assessed by using two different estimates from the global inversion systems CarboScope (TM3) and TM5-4DVAR. CO2 estimates calculated with an ensemble of eight inversions differing in the regional and global transport models, as well as the inversion systems, show a relatively large spread for the annual fluxes, ranging between −0.72 and 0.20 PgC yr−1, which is larger than the a priori uncertainty of 0.47 PgC yr−1. The discrepancies in annual budget are primarily caused by differences in the mesoscale transport model (0.51 PgC yr−1), in comparison with 0.23 and 0.10 PgC yr−1 that resulted from the far-field contributions and the inversion systems, respectively. Additionally, varying the mesoscale transport caused large discrepancies in spatial and temporal patterns, while changing the lateral boundary conditions led to more homogeneous spatial and temporal impact. We further investigated the origin of the discrepancies between transport models. The meteorological forcing parameters (forecasts versus reanalysis obtained from ECMWF data products) used to drive the transport models are responsible for a small part of the differences in CO2 estimates, but the largest impact seems to come from the transport model schemes. Although a good convergence in the differences between the inversion systems was achieved by applying a strict protocol of using identical prior fluxes and atmospheric datasets, there was a non-negligible impact arising from applying a different inversion system. Specifically, the choice of prior error structure accounted for a large part of system-to-system differences.

Modeling compatible taper and stem volume of pure Scots pine stands in Northeastern Turkey

Compatible taper and volume equations for pure and natural Scots pine stands in the northeastern part of Turkey (Ardahan Province) were developed using a nonlinear mixed-effects modeling approach. Experimental data were obtained from 137 felled sample trees in different diameter and height classes. The most successful model (Jiang et al. 2005) explained 98.3% of the variance in stem diameter estimation and the RMSE, ME, MAE, AIC and BIC value obtained using this model were 1.955 cm, 0.043 cm, 1.300 cm, 9783.8 and 9812.6, respectively. Considering the criterion values of AIC, BIC and -2LnL, the model with random-effects in two parameters (b1 and b3) was the most successful for Scots pine. While the mixed model including random parameters did not completely solved the problem of the autocorrelation of errors in this study, the use of the autoregressive error structure AR(1) eliminated the autocorrelation in the residuals. In addition, the best estimation results among 20 different calibration options were obtained using the option of measuring two tree diameters at d1.30 and d5.30 with validation data. The most successful model explained 99.18% of the total variance in stem volume estimation in Scots pine.

A Mixture Autoregressive Model Based on an Asymmetric Exponential Power Distribution

In nonlinear time series analysis, the mixture autoregressive model (MAR) is an effective statistical tool to capture the multimodality of data. However, the traditional methods usually need to assume that the error follows a specific distribution that is not adaptive to the dataset. This paper proposes a mixture autoregressive model via an asymmetric exponential power distribution, which includes normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. Therefore, the proposed method can be seen as a generalization of some existing model, which can adapt to unknown error structures to improve prediction accuracy, even in the case of fat tail and asymmetry. In addition, an expectation-maximization algorithm is applied to implement the proposed optimization problem. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze the daily return series of the Hong Kong Hang Seng Index. The results indicate that the proposed method is more robust and adaptive to the error distributions than other existing methods.

Machine learning algorithms for three-dimensional mean-curvature computation in the level-set method

We propose a data-driven mean-curvature solver for the level-set method. This work is the natural extension to R3 of our two-dimensional error-correcting strategy presented in Larios-Cárdenas and Gibou (October 2022) [1] and the hybrid inference system of Larios-Cárdenas and Gibou (August 2022) [2]. However, in contrast to [1,2], which built resolution-dependent dictionaries of curvature neural networks, here we develop a single pair of neural models in R3, regardless of the mesh size. The core of our system comprises two feedforward neural networks. These models ingest preprocessed level-set, gradient, and curvature information to fix numerical mean-curvature approximations for selected nodes along the interface. To reduce the problem's complexity, we have used the local Gaussian curvature κG to classify stencils and fit these networks separately to non-saddle (where κG⪆0) and saddle (where κG⪅0) input patterns. The Gaussian curvature is essential for enhancing generalization and simplifying neural network design. For example, non-saddle stencils are easier to handle because they exhibit a mean-curvature error distribution characterized by monotonicity and symmetry. While the latter has allowed us to train only on half the mean-curvature spectrum, the former has helped us blend the machine-learning-corrected output and the baseline estimation seamlessly around near-flat regions. On the other hand, the saddle-pattern error structure is less clear; thus, we have exploited no latent characteristics beyond what is known. Such a stencil distinction makes learning-tuple generation in R3 quite involving. In this regard, we have trained our models on not only spherical but also sinusoidal and hyperbolic paraboloidal patches at various configurations. Our approach to building their data sets is systematic but gleans samples randomly while ensuring well-balancedness. Furthermore, we have resorted to standardization and dimensionality reduction as a preprocessing step and integrated layer-wise regularization to minimize outlying effects. In addition, our strategy leverages mean-curvature rotation and reflection invariance to improve stability and precision at inference time. The synergy among all these features has led to a performant mean-curvature solver that works for any grid resolution. Experiments with several interfaces confirm that our proposed system can yield more accurate mean-curvature estimations in the L1 and L∞ norms than modern particle-based interface reconstruction and level-set schemes around under-resolved regions. Although there is ample room for improvement, this research already shows the potential of machine learning to remedy geometrical problems in well-established numerical methods. Our neural networks are available online at https://github.com/UCSB-CASL/Curvature_ECNet_3D.

Copolymerization Reactivity Ratio Inference: Determining Confidence Contours in Parameter Space via a Bayesian Hierarchical Approach

AbstractConfidence contours in parameter space are a helpful tool to compare and classify determined estimators. For more intricate parameter estimations of nonlinear nature or complex error structures, the procedure of determining confidence contours is a statistically complex task. For polymer chemists, such particular cases are encountered in determination of reactivity ratios in copolymerization. Hereby, determination of reactivity ratios in copolymerization requires nonlinear parameter estimation. Additionally, data may possess (possibly correlated) errors in both dependent and independent variables. A common approach for such nonlinear estimations is the error‐in‐variables model yielding statistically unbiased estimators. Regarding reactivity ratios, to date published procedures neglect the non‐Gaussian structure of the error estimates that is a consequence of the nonlinearity of the model. In this publication, this issue is addressed by employing a Bayesian hierarchical model, which correctly propagates the errors of all variables. The statistical procedure is discussed in chemist friendly language to encourage confident usage of the tool. The approach is based on a Python program requiring minimal installation effort. A detailed manual of the code is included in the appendix of this work, in an effort to make this procedure available to all interested polymer chemists.