Parameters Of Statistical Model Research Articles

Exploring the Effects of Additional Vibration on the Perceived Quality of an Electric Cello

Haptic feedback holds the potential to enhance the engagement and expressivity of future digital and electric musical instruments. This study investigates the impact of artificial vibration on the perceived quality of a silent electric cello. We developed a haptic cello prototype capable of rendering vibration signals of varying degree of congruence with the produced sound. Experienced cellists participated in an experiment comparing setups with and without vibrotactile feedback, rating them on preference, perceived power, liveliness, and feel. Results show nuanced effects, with added vibrations moderately enhancing feel and liveliness, and significantly increasing perceived power when using vibrations obtained from the pickup at the cello’s bridge. High uncertainty in our statistical model parameters underscores substantial individual differences in the participants responses, as commonly found in qualitative assessments, and highlights the importance of consistent feedback in the vibrotactile and auditory channels. Our findings contribute valuable insights to the intersection of haptics and music technology, paving the way for creating richer and more engaging experiences with future musical instruments.

Recurrence and transience of a Markov chain on + and evaluation of prior distributions for a Poisson mean

Abstract Eaton (1992) considered a general parametric statistical model paired with an improper prior distribution for the parameter and proved that if a certain Markov chain, constructed using the model and the prior, is recurrent, then the improper prior is strongly admissible, which (roughly speaking) means that the generalized Bayes estimators derived from the corresponding posterior distribution are admissible. Hobert and Robert (1999) proved that Eaton’s Markov chain is recurrent if and only if its so-called conjugate Markov chain is recurrent. The focus of this paper is a family of Markov chains that contains all of the conjugate chains that arise in the context of a Poisson model paired with an arbitrary improper prior for the mean parameter. Sufficient conditions for recurrence and transience are developed and these are used to establish new results concerning the strong admissibility of non-conjugate improper priors for the Poisson mean.

Identification of Hardening Parameters of Two-Level Statistical Model of Polycrystal Inelastic Deformation

Identification of Hardening Parameters of Two-Level Statistical Model of Polycrystal Inelastic Deformation

A Comparative Evaluation of the Outlier Detection Methods

In data mining, in order to calculate descriptive statistics and other statistical model parameters correctly, outliers should be identified and excluded from the data set before starting data analysis. This paper studied and compared the performance of model-based, density-based, clustering-based, angle-based, and isolation-based outlier detection methods used in data mining. ROC and AUC curves were used to compare the performances of outlier detection methods. A data set with a standard normal distribution and fit a logistic regression was simulated. To compare the methods, the data was modified by randomly adding 30 outliers to the data set. The iForest algorithm was found to have higher predictive power than Mahalanobis, LOF, k-means, and ABOD. In addition, outliers were found in a real data set with the iForest algorithm and deleted from the data set. Then, the data sets with outliers and without outliers were compared. The results showed that the model without outliers has a higher predictive ability.

New Generalized Weibull Inverse Gompertz Distribution: Properties and Applications

In parametric statistical modeling, it is essential to create generalizations of current statistical distributions that are more flexible when modeling actual data sets. Therefore, this study introduces a new generalized lifetime model named the odd Weibull Inverse Gompertz distribution (OWIG). The OWIG is derived by combining the odd Weibull family of distributions with the inverse Gompertz distribution. Essential statistical properties are discussed, including reliability functions, moments, Rényi entropy, and order statistics. The proposed OWIG is particularly significant as its hazard rate functions exhibit various monotonic and nonmonotonic shapes. This enables OWIG to model different hazard behaviors more commonly observed in natural phenomena. OWIG’s parameters are estimated and its flexibility in predicting unique symmetric and asymmetric patterns is shown by analyzing real-world applications from psychology, environmental, and medical sciences. The results demonstrate that the proposed OWIG is an excellent candidate as it provides the most accurate fits to the data compared with some competing models.

Exploring local explanations of nonlinear models using animated linear projections

AbstractThe increased predictive power of machine learning models comes at the cost of increased complexity and loss of interpretability, particularly in comparison to parametric statistical models. This trade-off has led to the emergence of eXplainable AI (XAI) which provides methods, such as local explanations (LEs) and local variable attributions (LVAs), to shed light on how a model use predictors to arrive at a prediction. These provide a point estimate of the linear variable importance in the vicinity of a single observation. However, LVAs tend not to effectively handle association between predictors. To understand how the interaction between predictors affects the variable importance estimate, we can convert LVAs into linear projections and use the radial tour. This is also useful for learning how a model has made a mistake, or the effect of outliers, or the clustering of observations. The approach is illustrated with examples from categorical (penguin species, chocolate types) and quantitative (soccer/football salaries, house prices) response models. The methods are implemented in the R package cheem, available on CRAN.

A new Topp-Leone Kumaraswamy Marshall-Olkin generated family of distributions with applications

We aim in this paper to propose a novel class of distributions that was created by merging the Topp-Leone distribution and the Generated families of Kumaraswamy and Marshall-Olkin. Its cumulative distribution function characterizes it and includes rational and polynomial functions. In particular, the following desirable properties of the new family are presented: Shannon entropy, order statistics, the quantile power series, and several associated measures and functions. Then, using a specific family member identified before, we create a parametric statistical model with the basic distribution being the inverse exponential distribution. Finally, a thorough investigation has been made to implement this new distribution with three data sets: the glass fibers data set, the glass Alumina data set and the hailing times data set. In comparison to six prominent competitors, the new model performs favorably on all statistical tests and criteria that were examined.

QSAR ANALYSIS USING SEMI-EMPIRICAL AM1 METHOD, MOLECULAR DOCKING, AND ADMET STUDIES OF CHALCONE DERIVATIVES AS ANTIMALARIAL COMPOUNDS

Malaria is a serious caused by protozoan parasites such as Plasmodium groups and has fatal consequences for human health. The increase in the resistance of the Plasmodium parasites toward existing antimalarial drugs prompts the exploration of novel compounds. In this study, quantitative structure-activity relationship (QSAR) analysis using the semi-empirical AM1 method was conducted to identify the optimal model that relates physicochemical properties and biological activity of chalcone derivatives. In addition, ADMET prediction and molecular docking were also carried out. Multilinear regression calculations for statistical parameters of QSAR models revealed that Model 4, with 11 independent variables, provided the best predictions and exhibited a robust correlation with antimalarial activity represented by inhibitory concentration (IC50). ADMET predictions indicated favorable absorption, distribution, metabolism, excretion, and toxicity properties, particularly for B2D, showing promising antimalarial attributes. Molecular docking studies targeting 5 mutated PfDHODH proteins revealed B2D’s potential to reach therapeutic targets efficiently. It has low docking scores for mutations I (-10.5 kcal/mol), II (-8.6 kcal/mol), and V (-10.5 kcal/mol) with RMSD < 2Å, in carrying out its role for antimalarial activity. This research successfully identifies B2D as an efficient inhibitor of PfDHODH receptors. Thus, it is a highly promising novel antimalarial drug.

SpTe2M: An R package for nonparametric modeling and monitoring of spatiotemporal data

Spatiotemporal data are common in practice. Such data often have complicated structures that are difficult to describe by parametric statistical models. Thus, it is often challenging to analyze spatiotemporal data effectively since most existing statistical methods and software packages in the literature are based on parametric modeling and cannot handle certain applications properly. This paper introduces the new package SpTe2M, which was developed for implementing some recent nonparametric methods for modeling and monitoring spatiotemporal data. This package provides analytic tools for modeling spatiotemporal data nonparametrically and for monitoring dynamic spatial processes sequentially over time. It can be used for different applications, including disease surveillance and environmental monitoring. The use of the package is demonstrated using the Florida influenza-like illness data observed during 2012–2014 and the PM2.5 concentration data in China collected during 2014–2016.

Topp-Leone Cauchy Family of Distributions with Applications in Industrial Engineering

The goal of this research is to create a new general family of Topp-Leone distributions called the Topp-Leone Cauchy Family (TLC), which is exceedingly versatile and results from a careful merging of the Topp-Leone and Cauchy distribution families. Some of the new family’s theoretical properties are investigated using specific results on stochastic functions, quantile functions and associated measures, generic moments, probability weighted moments, and Shannon entropy. A parametric statistical model is built from a specific member of the family. The maximum likelihood technique is used to estimate the model’s unknown parameters. Furthermore, to emphasize the new family’s practical potential, we applied our model to two real-world data sets and compared it to existing rival models.

Unified topological inference for brain networks in temporal lobe epilepsy using the Wasserstein distance

Persistent homology offers a powerful tool for extracting hidden topological signals from brain networks. It captures the evolution of topological structures across multiple scales, known as filtrations, thereby revealing topological features that persist over these scales. These features are summarized in persistence diagrams, and their dissimilarity is quantified using the Wasserstein distance. However, the Wasserstein distance does not follow a known distribution, posing challenges for the application of existing parametric statistical models. To tackle this issue, we introduce a unified topological inference framework centered on the Wasserstein distance. Our approach has no explicit model and distributional assumptions. The inference is performed in a completely data driven fashion. We apply this method to resting-state functional magnetic resonance images (rs-fMRI) of temporal lobe epilepsy patients collected from two different sites: the University of Wisconsin-Madison and the Medical College of Wisconsin. Importantly, our topological method is robust to variations due to sex and image acquisition, obviating the need to account for these variables as nuisance covariates. We successfully localize the brain regions that contribute the most to topological differences. A MATLAB package used for all analyses in this study is available at https://github.com/laplcebeltrami/PH-STAT.

Time-integrated radiation risk metrics and interpopulation variability of survival

Task Group 115 of the International Commission on Radiological Protection is focusing on mission-related exposures to space radiation and concomitant health risks for space crew members including, among others, risk of cancer development. Uncertainties in cumulative radiation risk estimates come from the stochastic nature of the considered health outcome (i.e., cancer), uncertainties of statistical inference and model parameters, unknown secular trends used for projections of population statistics and unknown variability of survival properties between individuals or population groups. The variability of survival is usually ignored when dealing with large groups, which can be assumed well represented by the statistical data for the contemporary general population, either in a specific country or world averaged. Space crew members differ in many aspects from individuals represented by the general population, including, for example, their lifestyle and health status, nutrition, medical care, training and education. The individuality of response to radiation and lifespan is explored in this modelling study. Task Group 115 is currently evaluating applicability and robustness of various risk metrics for quantification of radiation-attributed risks of cancer for space crew members. This paper demonstrates the impact of interpopulation variability of survival curves on values and uncertainty of the estimates of the time-integrated radiation risk of cancer.

CGAN-EB: A non-parametric empirical Bayes method for crash frequency modeling using conditional generative adversarial networks as safety performance functions

In this paper, a new non-parametric empirical Bayes approach called CGAN-EB is proposed for approximating empirical Bayes (EB) estimates in traffic locations (e.g., road segments) which benefits from the modeling advantages of deep neural networks, and its performance is compared in a simulation study with the traditional approach based on negative binomial model (NB-EB). The NB-EB uses negative binomial model in order to model the crash data and is the most common approach in practice. To model the crash data in the proposed CGAN-EB, conditional generative adversarial network is used, which is a powerful deep neural network based method that can model any types of distributions. A number of simulation experiments are designed and conducted to evaluate the CGAN-EB performance in different conditions and compare it with the NB-EB. The results show that CGAN-EB performs as well as NB-EB when conditions favor the NB-EB model (i.e. data conform to the assumptions of the NB model) and outperforms NB-EB in experiments reflecting conditions frequently encountered in practice, specifically low sample means, and when crash frequency does not follow a log-linear relationship with covariates.

A modified uncertain maximum likelihood estimation with applications in uncertain statistics

In uncertain statistics, the uncertain maximum likelihood estimation is a method of estimating the values of unknown parameters of an uncertain statistical model that make the observed data most likely. However, the observed data obtained in practice usually contain outliers. In order to eliminate the influence of outliers when estimating unknown parameters, this article modifies the uncertain maximum likelihood estimation. Following that, the modified uncertain maximum likelihood estimation is applied to uncertain regression analysis, uncertain time series analysis, and uncertain differential equation. Finally, some real-world examples are provided to illustrate the modified uncertain maximum likelihood estimation.

A Bayesian approach to (online) transfer learning: Theory and algorithms

Transfer learning is a machine learning paradigm where knowledge from one problem is utilized to solve a new but related problem. While conceivable that knowledge from one task could help solve a related task, if not executed properly, transfer learning algorithms can impair the learning performance instead of improving it – commonly known as negative transfer. In this paper, we use a parametric statistical model to study transfer learning from a Bayesian perspective. Specifically, we study three variants of transfer learning problems, instantaneous, online, and time-variant transfer learning. We define an appropriate objective function for each problem and provide either exact expressions or upper bounds on the learning performance using information-theoretic quantities, which allow simple and explicit characterizations when the sample size becomes large. Furthermore, examples show that the derived bounds are accurate even for small sample sizes. The obtained bounds give valuable insights into the effect of prior knowledge on transfer learning, at least with respect to our Bayesian formulation of the transfer learning problem. In particular, we formally characterize the conditions under which negative transfer occurs. Lastly, we devise several (online) transfer learning algorithms that are amenable to practical implementations, some of which do not require the parametric assumption. We demonstrate the effectiveness of our algorithms with real data sets, focusing primarily on when the source and target data have strong similarities.

Hubble constant by natural selection: Evolution chips in the Hubble tension

The Approximate Bayesian Computation (ABC) algorithm considers natural selection in biology as a guiding principle for statistical model selection and parameter estimation. We take this ABC approach to cosmology and use it to infer which ΛCDM model anchored on a choice of a Hubble constant prior would be preferred by the data. We find in all of our runs that the Planck Hubble constant (H0=67.4±0.5 km s−1Mpc−1) always emerges naturally selected by the ABC over the SH0ES estimate (H0=73.30±1.04 km s−1Mpc−1). The result holds regardless of how we mix our data sets, including supernovae, cosmic chronometers, baryon acoustic oscillations, and growth data. Compared with the traditional MCMC, we find that the ABC always results with narrower cosmological constraints, but remain consistent inside the corresponding MCMC posteriors.

Analysis of the performance of predictive models during Covid-19 and the Russian-Ukrainian war

In our paper, we investigate how effectively artificial intelligence can be used to predict stock market trends in the world’s leading equity markets over the period 01/01/2010 to 09/16/2022. Covid-19 and the Russian-Ukrainian war have had a strong impact on the capital markets and therefore the study was conducted in a highly volatile environment. The analysis was performed on three time intervals, using two machine learning algorithms of different complexity (decision tree, LSTM) and a parametric statistical model (linear regression). The evaluation of the results obtained was based on mean absolute percentage error (MAPE). In our study, we show that predictive models can perform better than linear regression in the period of high volatility. Another important finding is that the predictive models performed better in the post-Russian-Ukrainian war period than after the outbreak of Covid-19. Stock market price forecasting can play an important role in fundamental and technical analysis, can be incorporated into the decision criteria of algorithmic trading, or can be used on its own to automate trading.

A Novel Odd Beta Prime-Logistic Distribution: Desirable Mathematical Properties and Applications to Engineering and Environmental Data

In parametric statistical modeling, it is important to construct new extensions of existing probability distributions (PDs) that can make modeling data more flexible and help stakeholders make better decisions. In the present study, a new family of probability distributions (FPDs) called the odd beta prime generalized (OBP-G) FPDs is proposed to improve the traditional PDs. A new PD called the odd beta prime-logistic (OBP-logistic) distribution has been developed based on the developed OBP-G FPDs. Some desirable mathematical properties of the proposed OBP-logistic distribution, including the moments, moment-generating function, information-generating function, quantile function, stress–strength, order statistics, and entropies, are studied and derived. The proposed OBP-logistic distribution’s parameters are determined by adopting the maximum likelihood estimation (MLE) method. The applicability of the new PD was demonstrated by employing three data sets and these were compared by the known extended logistic distributions, such as the gamma generalized logistic distribution, new modified exponential logistic distribution, gamma-logistic distribution, exponential modified Weibull logistic distribution, exponentiated Weibull logistic distribution, and transmuted Weibull logistic distribution. The findings reveal that the studied distribution provides better results than the competing PDs. The empirical results showed that the new OBP-logistic distribution performs better than the other PDs based on several statistical metrics. We hoped that the newly constructed OBP-logistic distribution would be an alternative to other well-known extended logistic distributions for the statistical modeling of symmetric and skewed data sets.

Long-term deformation safety evaluation method of concrete dams based on the time-varying stability of concrete material

A concrete dam is a kind of large-volume hydraulic structure made of concrete materials. The deformation of the concrete material of the dam body has an obvious time effect. The time-effect component of deformation comprehensively reflects the trend change of the dam deformation and its stability is an important index for evaluating the long-term safety state of concrete dams. Dam safety monitoring theory is generally applied to obtain the time-effect component based on statistical models. The regression parameters of traditional concrete dam deformation statistical models are fixed values, which cannot effectively reflect the dynamic changes in concrete dam deformation characteristics. The variable parameter statistical model is more applicable to practical deformation law of concrete dam based on time-varying parameter. This paper constructs a novel variable parameter statistical model based on the recursive least squares with forgetting factor (FFRLS) method to derive a more precisely concrete dam time-effect component. FFRLS method assigns different weights to the modeling historical data and enhances the impact of new data on the statistical model. To analyze the long-term stability of the time-effect component of concrete deformation, the stability evaluation criterion of the time-effect component is established by its long-term variation characteristics and cusp catastrophe theory. The engineering example shows that the prediction effect of the variable parameter statistical model is better than that of the fixed parameter statistical model and traditional variable parameter statistical model, the mean absolute percentage error of FFRLS model are decreased by 97.39% and 54.63% on average compared with least squares (LS) and recursive least squares (RLS) model. By fusing FFRLS variable parameter statistical model and cusp point mutation model, the safety state of concrete dam after long-term operation can be rapidly and effectively evaluated. The proposed evaluation method has significant engineering application value in concrete dam statistical modeling and safety evaluation.

Quantification and statistical modeling of droplet-based single-nucleus RNA-sequencing data.

In complex tissues containing cells that are difficult to dissociate, single-nucleus RNA-sequencing (snRNA-seq) has become the preferred experimental technology over single-cell RNA-sequencing (scRNA-seq) to measure gene expression. To accurately model these data in downstream analyses, previous work has shown that droplet-based scRNA-seq data are not zero-inflated, but whether droplet-based snRNA-seq data follow the same probability distributions has not been systematically evaluated. Using pseudonegative control data from nuclei in mouse cortex sequenced with the 10x Genomics Chromium system and mouse kidney sequenced with the DropSeq system, we found that droplet-based snRNA-seq data follow a negative binomial distribution, suggesting that parametric statistical models applied to scRNA-seq are transferable to snRNA-seq. Furthermore, we found that the quantification choices in adapting quantification mapping strategies from scRNA-seq to snRNA-seq can play a significant role in downstream analyses and biological interpretation. In particular, reference transcriptomes that do not include intronic regions result in significantly smaller library sizes and incongruous cell type classifications. We also confirmed the presence of a gene length bias in snRNA-seq data, which we show is present in both exonic and intronic reads, and investigate potential causes for the bias.