A DISTRIBUTION LAW OF THE RESULTS OF MEASUREMENT OF COMPOSITION AND PROPERTIES OF PETROLEUM PRODUCTS

Идентификацию закона распределения результатов измерений состава и свойств нефтепродуктов проводили путем проверки сложной гипотезы с использованием пяти критериев согласия: χ2-Пирсона, Колмогорова, Смирнова, ω2 Крамера-Мизеса-Смирнова; Ω2 Андерсона-Дарлинга. В качестве возможных функций распределения вероятностей рассматривали 12 симметричных одномодальных законов распределения, а также 66 смесей этих же законов распределения. Целью идентификации являлось нахождение универсального закона распределения (смеси законов распределений) справедливого для всех рассматриваемых величин. Проверка сложной гипотезы о соответствии какому-либо симметричному одномодальному закону распределения показала, что не существует универсального закона распределения справедливого для всех методик измерений состава и свойств нефтепродуктов, наиболее часто не отвергалась гипотеза о соответствии данных обобщенному логистическому распределению, распределению Лапласа и двустороннему экспоненциальному распределению. Проверка сложной гипотезы о соответствии какой-либо смеси симметричных одномодальных законов распределения показала, что эмпирическая функция распределения результатов измерений состава и свойств нефтепродуктов может быть представлена в виде смеси двух нормальных распределений с разными значениями параметров положения и масштаба. При этом для одной и той же выборки значения достигаемого уровня значимости гипотезы о соответствии смеси законов распределений в несколько раз выше среднего значения достигаемого уровня значимости гипотезы о соответствии одному закону распределения. На основе проведенного исследования обоснована вероятностная модель процесса испытаний нефтепродуктов, в рамках которой результат испытаний нефтепродуктов рассматривается как случайная величина с функцией распределения в виде смеси нормальных законов распределения: «основного» с дисперсией, не превышающей установленные требования (при статистически управляемом состоянии процесса испытаний), и «засоряющего» с дисперсией значительно превышающей установленные требования (при статистически неуправляемом состоянии процесса испытаний). The identification of a distribution law of the results of measurements of the composition and properties of petroleum products was carried out by testing a complex hypothesis using five goodness-of-fit tests: χ2-Pearson, Kolmogorov, Smirnov, ω2Cramer-Mises-Smirnov; Ω2 Anderson-Darling. Twelve symmetric unimodal distribution laws and 66 mixtures of the same distribution laws were considered as possible probability distribution functions. The purpose of the identification was to find a universal distribution law (a mixture of distribution laws) that is valid for all considered quantities. Testing the complex hypothesis of compliance with any symmetric unimodal distribution law showed that there is no universal distribution law that is valid for all measurement techniques of the composition and properties of petroleum products; most often the hypothesis of the correspondence the data to the generalized logistic distribution, the Laplace distribution and the two-sided exponential distribution was not rejected. Testing a complex hypothesis about the correspondence of any mixture of symmetric unimodal distribution laws showed that the empirical distribution function of the results of measurements of the composition and properties of petroleum products can be represented as a mixture of two normal distributions with different values ​​of the position and scale parameters. At the same time, for the same sample, the values ​​of the achieved significance level of the hypothesis about the correspondence to the mixture of distribution laws is several times higher than the average value of the achieved significance level of the hypothesis about the correspondence to one distribution law. Based on this study, a chance model of the process of testing petroleum products was substantiated, within which the result of testing petroleum products is considered as a random variable with a distribution function in the form of a mixture of normal distribution laws: "basic" with a variance not exceeding the established requirements (with a statistically controlled state of the test process), and "fouling" with a variance significantly exceeding the established requirements (with a statistically uncontrolled state of the test process).

Hierarchical Bayes Conjoint Choice Models - Model Framework, Bayesian Inference, Model Selection, and Interpretation of Estimation Results

Choice-based conjoint (CBC) is nowadays the most widely used variant of conjoint analysis, a class of methods for measuring consumer preferences. The primary reason for the increasing dominance of the CBC approach over the last 35 years is that it closely mimics real choice behavior of consumers by asking respondents repeatedly to choose their preferred alternative from a set of several offered alternatives (choice sets). Within the framework of CBC analysis, the multinomial logit (MNL) model is the most frequently used discrete choice model due to the existence of closed form solutions for conditional choice probabilities. The popularity of CBC and the MNL model has grown even more since the introduction of hierarchical Bayesian (HB) estimation techniques that accommodate individual consumer heterogeneity in choice data, and which have now become state-of-the-art in marketing theory and practice. Still, researchers and practitioners have to make further decisions under this framework (CBC, MNL, HB estimation), such as how to represent preference heterogeneity. Here, using a normal distribution (and therefore a unimodal distribution) has become the standard approach in the marketing literature. However, the thin tails of the normal distribution suggest that the standard HB-MNL model should not be the “go-to” approach to approximate multimodal preference distributions, because individual preference patterns lying at the tails of the normal distribution (i.e., that do not fit well with the assumption of a unimodal distribution) tend to be shrunk to the population mean. This shrinkage, especially in multimodal data settings, could mask important information (e.g., new or different structures in the data). A mixture of normal distributions avoids this limited flexibility of the most simple continuous approach of assuming a unimodal prior heterogeneity distribution. There are currently two prominent HB-CBC modeling approaches embedding the mixture-of-normals (MoN) approach: the more widespread MoN-HB-MNL model, and the Dirichlet process mixture (DPM)-HB-MNL model. In this article, we review the prominent HB-MNL model (with its normal prior), the MoN-HB-MNL model, and the DPM-HB-MNL model and apply them to an empirical multi-country CBC data set. We compare the statistical performance of the three models in terms of goodness-of-fit and predictive accuracy, show how to include consumer background characteristics in the upper level of these models, and illustrate how to interpret the estimation results (with a special focus on cross-county heterogeneity). In sum, our article serves as a kind of user guide to the estimation and interpretation of Hierarchical Bayes Conjoint Choice Models. For our data, we observed that all three choice models (both with and without consumer background characteristics) resulted in a one-component solution. The DPM-HB-MNL model nevertheless yielded a higher cross-validated hit rate compared to the MoN-HB-MNL and the HB-MNL models due to its even more flexible prior assumptions. The two latter models tended to slightly overfit our empirical data, which was reflected by higher goodness-of-fit statistics but a lower predictive accuracy compared to the DPM-HB-MNL model. We showed that this result could be attributed to the weaker extent of Bayesian shrinkage of these two models. The DPM-HB-MNL model showed a stronger shrinkage effect and seems therefore somewhat more robust against overfitting. Including consumer background characteristics in terms of country of origin information for the respondents did not improve the statistical model performance (especially not the predictive performance). Still, using the country of origin information for respondents in a post-hoc segmentation analysis helped us to explain some differences in brand preferences between the five countries.

Adaptive Unimodal Cost Volume Filtering for Deep Stereo Matching

State-of-the-art deep learning based stereo matching approaches treat disparity estimation as a regression problem, where loss function is directly defined on true disparities and their estimated ones. However, disparity is just a byproduct of a matching process modeled by cost volume, while indirectly learning cost volume driven by disparity regression is prone to overfitting since the cost volume is under constrained. In this paper, we propose to directly add constraints to the cost volume by filtering cost volume with unimodal distribution peaked at true disparities. In addition, variances of the unimodal distributions for each pixel are estimated to explicitly model matching uncertainty under different contexts. The proposed architecture achieves state-of-the-art performance on Scene Flow and two KITTI stereo benchmarks. In particular, our method ranked the 1st place of KITTI 2012 evaluation and the 4th place of KITTI 2015 evaluation (recorded on 2019.8.20). The codes of AcfNet are available at: https://github.com/youmi-zym/AcfNet.

Unimodal head-width distribution of the European eel (Anguilla anguilla L.) from the Zeeschelde does not support disruptive selection

Since the early 20th century, European eels (Anguilla anguilla L.) have been dichotomously classified into ‘narrow’ and ‘broad’ heads. These morphs are mainly considered the result of a differential food choice, with narrow heads feeding primarily on small/soft prey and broad heads on large/hard prey. Yet, such a classification implies that head-width variation follows a bimodal distribution, leading to the assumption of disruptive selection. We investigated the head morphology of 272 eels, caught over three consecutive years (2015–2017) at a single location in the Zeeschelde (Belgium). Based on our results, BIC favored a unimodal distribution, while AIC provided equal support for a unimodal and a bimodal distribution. Notably, visualization of the distributions revealed a strong overlap between the two normal distributions under the bimodal model, likely explaining the ambiguity under AIC. Consequently, it is more likely that head-width variation followed a unimodal distribution, indicating there are no disruptive selection pressures for bimodality in the Zeeschelde. As such, eels could not be divided in two distinct head-width groups. Instead, their head widths showed a continuum of narrow to broad with a normal distribution. This pattern was consistent across all maturation stages studied here.

Beta, Sigma and Distributional Convergence in Human Development? Evidence from the Metropolitan Regions of Bolivia

Almost half of the population of Bolivia lives in the metropolitan regions of La Paz, Santa Cruz, and Cochabamba. Motivated by the development potential of these regions, this paper evaluates the process of regional convergence in human development through the lens of three frameworks: beta, sigma, and distributional convergence. The overall result highlights an increase in the speed of convergence that is driven by both relative forward mobility of the less developed regions and relative backward mobility of the more developed regions. Additionally, the distributional convergence framework indicates that the formation of multiple convergence clusters is a salient feature of inequality reduction. In the long-run, convergence appears to be characterized by the transformation of a trimodal distribution into a left–skewed unimodal distribution. This last result implies that the least developed regions are still relatively far from achieving complete convergence in human development.

Individual differences in schizophrenia

BackgroundWhether there are distinct subtypes of schizophrenia is an important issue to advance understanding and treatment of schizophrenia.AimsTo understand and treat individuals with schizophrenia, the aim was to advance understanding of differences between individuals, whether there are discrete subtypes, and how fist-episode patients (FEP) may differ from multiple episode patients (MEP).MethodThese issues were analysed in 687 FEP and 1880 MEP with schizophrenia using the Positive and Negative Syndrome Scale for (PANSS) schizophrenia before and after antipsychotic medication for 6 weeks.ResultsThe seven Negative Symptoms were correlated with each other and with P2 (conceptual disorganisation), G13 (disturbance of volition), and G7 (motor retardation). The main difference between individuals was in the cluster of seven negative symptoms, which had a continuous unimodal distribution. Medication decreased the PANSS scores for all the symptoms, which were similar in the FEP and MEP groups.ConclusionsThe negative symptoms are a major source of individual differences, and there are potential implications for treatment.