Inferences from Multinomial Data: Learning About a Bag of Marbles

Conceptualisation of Uncertainty in Decision Neuroscience Research: Do We Really Know What Types of Uncertainties The Measured Neural Correlates Relate To?

In the article "What are neural correlates neural correlates of?" published in the journal BioSocieties, Gabriel Abend points out that neuroscientists cannot avoid philosophical questions concerning the conceptualization and operationalization of social-psychological phenomena they deal with at the physiological level. In this article, we build on Abend's thesis and, through a systematic literature review of decision neuroscience studies, test it with the example of the social-psychological phenomenon of uncertainty in decision making. In this paper, we provide an overview of studies that appropriately attempt to conceptualise uncertainty, and then use these studies to analyse papers looking for neural correlates of uncertainty. Based on a systematic review of studies, we investigate what types of uncertainty authors in the field of decision neuroscience address and define, what criteria they use to distinguish between these types, what problems are associated with their conceptualization, and whether the neural correlates of different types of uncertainty can be accurately identified. The paper concludes that, particularly in the economic context, a collaboration between the natural and social sciences works well, and neuroscience studies use economic conceptualizations of uncertainty that are further developed by sophisticated decision tasks. However, the paper also highlights problematic aspects that obscure the understanding of the phenomena under study. These include the lack of criteria for distinguishing between different types of phenomena, the unclear use of the general concept of uncertainty, and the confusion of phenomena or their erroneous synonymous use.

Novel Credal Decision Tree-Based Ensemble Approaches for Predicting the Landslide Susceptibility

Landslides are natural and often quasi-normal threats that destroy natural resources and may lead to a persistent loss of human life. Therefore, the preparation of landslide susceptibility maps is necessary in order to mitigate harmful effects. The key objective of this research is to develop landslide susceptibility maps for the Taleghan basin of Alborz province, Iran, using hybrid Machine Learning (ML) algorithms, i.e., k-fold cross validation and ML techniques of credal decision tree (CDT), Alternative Decision Tree (ADTree), and their ensemble method (CDT-ADTree), which have been state-of-the-art soft computing techniques rarely used in the case of landslide susceptibility assessments. In this study, 22 key landslide causative factors (LCFs) were considered to explore their spatial relationship to landslides, based on local geomorphological and geo-environmental influences. The Random Forest (RF) algorithm was used for the identification of variables importance of different LCFs that are more prone to landslide susceptibility. A receiver operation characteristics (ROC) curve with area under the curve (AUC), accuracy, precision, and robustness index was used to evaluate and compare landslide susceptibility models. The output of the model performance shows that the CDT-ADTree model is the more robust model for the landslide susceptibility where the AUC, accuracy, and precision are 0.981, 0.837, and 0.867, respectively, than the standalone model of CDT and ADTree model. Therefore, it is concluded that the CDT-ADTree ensemble model can be applied as a new promising technique for spatial prediction of the landslide in further studies.

On the Use of m-Probability-Estimation and Imprecise Probabilities in the Naïve Bayes Classifier

Within the field of supervised classification, the naïve Bayes (NB) classifier is a very simple and fast classification method that obtains good results, being even comparable with much more complex models. It has been proved that the NB model is strongly dependent on the estimation of conditional probabilities. In the literature, it had been shown that the classical and Laplace estimations of probabilities have some drawbacks and it was proposed a NB model that takes into account the a priori probabilities in order to estimate the conditional probabilities, which was called m-probability-estimation. With a very scarce experimentation, this approximation based on m-probability-estimation demonstrated to provide better results than NB with classical and Laplace estimations of probabilities. In this research, a new naïve Bayes variation is proposed, which is based on the m-probability-estimation version and takes into account imprecise probabilities in order to calculate the a priori probabilities. An exhaustive experimental research is carried out, with a large number of data sets and different levels of class noise. From this experimentation, we can conclude that the proposed NB model and the m-probability-estimation approach provide better results than NB with classical and Laplace estimation of probabilities. It will be also shown that the proposed NB implies an improvement over the m-probability-estimation model, especially when there is some class noise.

GIS Based Hybrid Computational Approaches for Flash Flood Susceptibility Assessment

Flash floods are one of the most devastating natural hazards; they occur within a catchment (region) where the response time of the drainage basin is short. Identification of probable flash flood locations and development of accurate flash flood susceptibility maps are important for proper flash flood management of a region. With this objective, we proposed and compared several novel hybrid computational approaches of machine learning methods for flash flood susceptibility mapping, namely AdaBoostM1 based Credal Decision Tree (ABM-CDT); Bagging based Credal Decision Tree (Bag-CDT); Dagging based Credal Decision Tree (Dag-CDT); MultiBoostAB based Credal Decision Tree (MBAB-CDT), and single Credal Decision Tree (CDT). These models were applied at a catchment of Markazi state in Iran. About 320 past flash flood events and nine flash flood influencing factors, namely distance from rivers, aspect, elevation, slope, rainfall, distance from faults, soil, land use, and lithology were considered and analyzed for the development of flash flood susceptibility maps. Correlation based feature selection method was used to validate and select the important factors for modeling of flash floods. Based on this feature selection analysis, only eight factors (distance from rivers, aspect, elevation, slope, rainfall, soil, land use, and lithology) were selected for the modeling, where distance to rivers is the most important factor for modeling of flash flood in this area. Performance of the models was validated and compared by using several robust metrics such as statistical measures and Area Under the Receiver Operating Characteristic (AUC) curve. The results of this study suggested that ABM-CDT (AUC = 0.957) has the best predictive capability in terms of accuracy, followed by Dag-CDT (AUC = 0.947), MBAB-CDT (AUC = 0.933), Bag-CDT (AUC = 0.932), and CDT (0.900), respectively. The proposed methods presented in this study would help in the development of accurate flash flood susceptible maps of watershed areas not only in Iran but also other parts of the world.

Novel Entropy and Rotation Forest-Based Credal Decision Tree Classifier for Landslide Susceptibility Modeling

Landslides are a major geological hazard worldwide. Landslide susceptibility assessments are useful to mitigate human casualties, loss of property, and damage to natural resources, ecosystems, and infrastructures. This study aims to evaluate landslide susceptibility using a novel hybrid intelligence approach with the rotation forest-based credal decision tree (RF-CDT) classifier. First, 152 landslide locations and 15 landslide conditioning factors were collected from the study area. Then, these conditioning factors were assigned values using an entropy method and subsequently optimized using correlation attribute evaluation (CAE). Finally, the performance of the proposed hybrid model was validated using the receiver operating characteristic (ROC) curve and compared with two well-known ensemble models, bagging (bag-CDT) and MultiBoostAB (MB-CDT). Results show that the proposed RF-CDT model had better performance than the single CDT model and hybrid bag-CDT and MB-CDT models. The findings in the present study overall confirm that a combination of the meta model with a decision tree classifier could enhance the prediction power of the single landslide model. The resulting susceptibility maps could be effective for enforcement of land management regulations to reduce landslide hazards in the study area and other similar areas in the world.

Bayesian-multiplicative treatment of count zeros in compositional data sets

Compositional count data are discrete vectors representing the numbers of outcomes falling into any of several mutually exclusive categories. Compositional techniques based on the log-ratio methodology are appropriate in those cases where the total sum of the vector elements is not of interest. Such compositional count data sets can contain zero values which are often the result of insufficiently large samples. That is, they refer to unobserved positive values that may have been observed with a larger number of trials or with a different sampling design. Because the log-ratio transformations require data with positive values, any statistical analysis of count compositions must be preceded by a proper replacement of the zeros. A Bayesian-multiplicative treatment has been proposed for addressing this count zero problem in several case studies. This treatment involves the Dirichlet prior distribution as the conjugate distribution of the multinomial distribution and a multiplicative modification of the non-zero values. Different parameterizations of the prior distribution provide different zero replacement results, whose coherence with the vector space structure of the simplex is stated. Their performance is evaluated from both the theoretical and the computational point of view.

A multinomial-dirichlet model for analysis of competing hypotheses

Analysis of competing hypothesis, a method for evaluating explanations of observed evidence, is used in numerous fields, including counterterrorism, psychology, and intelligence analysis. We propose a Bayesian extension of the methodology, posing the problem in terms of a multinomial-Dirichlet hierarchical model. The yet-to-be observed true hypothesis is regarded as a multinomial random variable and the evaluation of the evidence is treated as a structured elicitation of a prior distribution on the probabilities of the hypotheses. This model provides the user with measures of uncertainty for the probabilities of the hypotheses. We discuss inference, such as point and interval estimates of hypothesis probabilities, ratios of hypothesis probabilities, and Bayes factors. A simple example involving the stadium relocation of the San Diego Chargers is used to illustrate the method. We also present several extensions of the model that enable it to handle special types of evidence, including evidence that is irrelevant to one or more hypotheses, evidence against hypotheses, and evidence that is subject to deception.