Computational Statistics最新文献

Bayesian multidimensional scaling (BMDS) is a probabilistic dimension reduction tool that allows one to model and visualize data consisting of dissimilarities between pairs of objects. Although BMDS has proven useful within, e.g., Bayesian phylogenetic inference, its likelihood and gradient calculations require burdensome [Formula: see text] floating-point operations, where N is the number of data points. Thus, BMDS becomes impractical as N grows large. We propose and compare two sparse versions of BMDS (sBMDS) that apply log-likelihood and gradient computations to subsets of the observed dissimilarity matrix data. Landmark sBMDS (L-sBMDS) extracts columns, while banded sBMDS (B-sBMDS) extracts diagonals of the data. These sparse variants let one specify a time complexity between [Formula: see text] and N. Under simplified settings, we prove posterior consistency for subsampled distance matrices. Through simulations, we examine the accuracy and computational efficiency across all models using both the Metropolis-Hastings and Hamiltonian Monte Carlo algorithms. We observe approximately 3-fold, 10-fold and 40-fold speedups with negligible loss of accuracy, when applying the sBMDS likelihoods and gradients to 500, 1000 and 5,000 data points with 50 bands (landmarks); these speedups only increase with the size of data considered. Finally, we apply the sBMDS variants to: (1) the phylogeographic modeling of multiple influenza subtypes to better understand how these strains spread through global air transportation networks and (2) the clustering of ArXiv manuscripts based on low-dimensional representations of article abstracts. In the first application, sBMDS contributes to holistic uncertainty quantification within a larger Bayesian hierarchical model. In the second, sBMDS approximates uncertainty quantification for a downstream modeling task.

This study aims to optimize the [Formula: see text]-nearest neighbors search (kNN search) by reducing the computational burden of the well-known Brute-force method while providing the same solution. While there exist rule-based approaches for reducing the computational burden of the kNN search, methods that use the stochastic patterns inherent to the data are lacking. Our method leverages data structures and probabilistic assumptions to enhance the scalability of the search. By focusing on the Training set where our neighbors reside, we define a sample space that limits the [Formula: see text]-nearest neighbors search to a smaller space. For each observation in the Query set (e.g., the set of observations for which a classification is desired), a fixed radius search is employed, with the radius stochastically linked to the desired number of neighbors. This approach allows us to find the [Formula: see text]-nearest neighbors using only a fraction of the entire Training set in contrast to the Brute-force method, which requires distances to be calculated between each observation in the Training set and each observation in the Query set. Through simulations and a theoretical computational complexity analysis, we demonstrate that our method outperforms the Brute-force approach, particularly when the Training and Query set sample sizes are large. In addition, a benchmarked comparison of our approach and the Brute-force method on an Alzheimer's disease data set further demonstrated this, showing a 27.57-fold improvement in total elapsed time. Overall, our stochastic approach significantly reduces the computational load of kNN search while maintaining accuracy, making it a viable alternative to traditional methods for large datasets.

Survey data using categorical item variables are widely used in applied research such as psychology, education, and behavioral studies. Unfortunately, survey data are highly susceptible to nonignorable missing values that may threaten the validity of statistical inference if naively ignored or inappropriately treated. This paper proposes a novel latent pattern mixture model for nonignorable missing values in multivariate categorical outcomes. The proposed model posits the existence of two categorical latent variables; one latent variable represents a nonresponse pattern, and the other represents a response pattern conditioning on the nonresponse pattern. We propose two parameter estimation strategies: the maximum-likelihood (ML) estimation using the expectation-maximization (EM) algorithm and Bayesian estimation using the Markov-Chain Monte Carlo (MCMC) algorithm. Simulation studies revealed that the ML estimation is preferred to the Bayesian estimation with noninformative priors in terms of standardized biases given the large sample size, whereas the Bayesian estimation can be preferred when the sample size is small. Finally, our real data example analyzed a data set with parental substance use disorder and revealed six latent classes of participants that are distinguished in response and missingness patterns.

In this article we explore parameter inference in a novel hybrid discrete-continuum model describing the movement of a population of cells in response to a self-generated chemotactic gradient. The model employs a drift-diffusion stochastic process, rendering likelihood-based inference methods impractical. Consequently, we consider approximate Bayesian computation (ABC) methods, which have gained popularity for models with intractable or computationally expensive likelihoods. ABC involves simulating from the generative model, using parameters from generated observations that are "close enough" to the true data to approximate the posterior distribution. Given the plethora of existing ABC methods, selecting the most suitable one for a specific problem can be challenging. To address this, we employ a simple drift-diffusion stochastic differential equation (SDE) as a benchmark problem. This allows us to assess the accuracy of popular ABC algorithms under known configurations. We also evaluate the bias between ABC-posteriors and the exact posterior for the basic SDE model, where the posterior distribution is tractable. The top-performing ABC algorithms are subsequently applied to the proposed cell movement model to infer its key parameters. This study not only contributes to understanding cell movement but also sheds light on the comparative efficiency of different ABC algorithms in a well-defined context.

Penalized regression methods that shrink model coefficients are popular approaches to improve prediction and for variable selection in high-dimensional settings. We present a penalized (or regularized) regression approach for multinomial logistic models for categorical outcomes with a novel adaptive L1-type penalty term, that incorporates weights based on intra- and inter-outcome category distances of each predictor. A predictor that has large between- and small within-outcome category distances is penalized less and has a higher likelihood to be selected for the final model. We propose and study three measures for weight calculation: an analysis of variance (ANOVA)-based measure and two indices used in clustering approaches. Our novel approach, that we term the discriminative power lasso (DP-lasso), thus combines elements of marginal screening with regularized regression methods. We studied the performance of DP-lasso and other published methods in simulations with varying numbers of outcome categories, numbers of predictors, strengths of associations and predictor correlation structures. For correlated predictors, the DP-lasso approach with ANOVA based weights (DPan) resulted in much sparser models than other regularization approaches, especially in high-dimensional settings. When the number p of (correlated) predictors was much larger than the available sample size N, DPan had the highest true positive rate while maintaining low false positive rates for all simulation settings. Similarly, when $p<N$ , DPan had high true positive rates and the lowest false positive rates of all methods studied. Thus we recommend DPan for analysing categorical outcomes in relation to high-dimensional predictors. We further illustrate all approaches in ultra high-dimensional settings, using several single-cell RNA-sequencing datasets.

Supplementary information: The online version contains supplementary material available at 10.1007/s00180-025-01635-0.

Likelihood-free inference for simulator-based statistical models has developed rapidly from its infancy to a useful tool for practitioners. However, models with more than a handful of parameters still generally remain a challenge for the Approximate Bayesian Computation (ABC) based inference. To advance the possibilities for performing likelihood-free inference in higher dimensional parameter spaces, we introduce an extension of the popular Bayesian optimisation based approach to approximate discrepancy functions in a probabilistic manner which lends itself to an efficient exploration of the parameter space. Our approach achieves computational scalability for higher dimensional parameter spaces by using separate acquisition functions, discrepancies, and associated summary statistics for distinct subsets of the parameters. The efficient additive acquisition structure is combined with exponentiated loss-likelihood to provide a misspecification-robust characterisation of posterior distributions for subsets of model parameters. The method successfully performs computationally efficient inference in a moderately sized parameter space and compares favourably to existing modularised ABC methods. We further illustrate the potential of this approach by fitting a bacterial transmission dynamics model to a real data set, which provides biologically coherent results on strain competition in a 30-dimensional parameter space.

We consider two inverse Gaussian populations with a common mean but different scale-like parameters, where all parameters are unknown. We construct noninformative priors for the ratio of the scale-like parameters to derive matching priors of different orders. Reference priors are proposed for different groups of parameters. The Bayes estimators of the common mean and ratio of the scale-like parameters are also derived. We propose confidence intervals of the conditional error rate in classifying an observation into inverse Gaussian distributions. A generalized variable-based confidence interval and the highest posterior density credible intervals for the error rate are computed. We estimate parameters of the mixture of these inverse Gaussian distributions and obtain estimates of the expected probability of correct classification. An intensive simulation study has been carried out to compare the estimators and expected probability of correct classification. Real data-based examples are given to show the practicality and effectiveness of the estimators.

Compared to other European competitions, participation in the Uefa Champions League is a real “bargain” for football clubs due to the hefty bonuses awarded based on performance during the group qualification phase. To perform successfully in football depends on several multidimensional factors, and analyzing the main ones remains challenging. In the performance study, little attention has been paid to teams’ behavior when playing at home and away. Our study combines statistical techniques to develop a procedure to examine teams’ performance. Several considerations make the 2022–2023 Serie A league season particularly interesting to analyze with our approach. Except for Napoli, all the teams showed different home-and-away behaviors concerning the results obtained at the season’s end. Ball possession and corners have positively influenced scored points in both home and away games with a different impact. The precision indicator was not an essential variable. The procedure highlighted the negative roles played by offside, as well as yellow and red cards.

This paper deals with the challenging themes of the way sporting teams and athletes are ranked in sports competitions. Starting from the paradigmatic case of soccer, we advance a new method for ranking teams in the official national championships through computational statistics methods based on Kendall correlations and radar charts. In detail, we consider the goals for and against the teams in the individual matches as a further source of score assignment beyond the usual win-tie-lose trichotomy. Our approach overcomes some biases in the scoring rules that are currently employed. The methodological proposal is tested over the relevant case of the Italian “Serie A” championships played during 1930–2023.

In this paper, we develop a fully Bayesian adaptive lasso quantile regression model to analyze data with non-ignorable missing responses, which frequently occur in various fields of study. Specifically, we employ a logistic regression model to deal with missing data of non-ignorable mechanism. By using the asymmetric Laplace working likelihood for the data and specifying Laplace priors for the regression coefficients, our proposed method extends the Bayesian lasso framework by imposing specific penalization parameters on each regression coefficient, enhancing our estimation and variable selection capability. Furthermore, we embrace the normal-exponential mixture representation of the asymmetric Laplace distribution and the Student-t approximation of the logistic regression model to develop a simple and efficient Gibbs sampling algorithm for generating posterior samples and making statistical inferences. The finite-sample performance of the proposed algorithm is investigated through various simulation studies and a real-data example.