Computational Statistics最新文献

Regression modelling often presents a trade-off between predictiveness and interpretability. Highly predictive and popular tree-based algorithms such as Random Forest and boosted trees predict very well the outcome of new observations, but the effect of the predictors on the result is hard to interpret. Highly interpretable algorithms like linear effect-based boosting and MARS, on the other hand, are typically less predictive. Here we propose a novel regression algorithm, automatic piecewise linear regression (APLR), that combines the predictiveness of a boosting algorithm with the interpretability of a MARS model. In addition, as a boosting algorithm, it automatically handles variable selection, and, as a MARS-based approach, it takes into account non-linear relationships and possible interaction terms. We show on simulated and real data examples how APLR’s performance is comparable to that of the top-performing approaches in terms of prediction, while offering an easy way to interpret the results. APLR has been implemented in C++ and wrapped in a Python package as a Scikit-learn compatible estimator.

This work presents a new scalable automatic Bayesian Lasso methodology with variational inference for non-parametric splines regression that can capture the non-linear relationship between a response variable and predictor variables. Note that under non-parametric point of view the regression curve is assumed to lie in a infinite dimension space. Regression splines use a finite approximation of this infinite space, representing the regression function by a linear combination of basis functions. The crucial point of the approach is determining the appropriate number of bases or equivalently number of knots, avoiding over-fitting/under-fitting. A decision-theoretic approach was devised for knot selection. Comprehensive simulation studies were conducted in challenging scenarios to compare alternative criteria for knot selection, thereby ensuring the efficacy of the proposed algorithms. Additionally, the performance of the proposed method was assessed using real-world datasets. The novel procedure demonstrated good performance in capturing the underlying data structure by selecting the appropriate number of knots/basis.

In this article, we propose a Poisson-Lindley distribution as a stochastic abundance model in which the sample is according to the independent Poisson process. Jeffery’s and Bernardo’s reference priors have been obtaining and proposed the Bayes estimators of the number of species for this model. The proposed Bayes estimators have been compared with the corresponding profile and conditional maximum likelihood estimators for their square root of the risks under squared error loss function (SELF). Jeffery’s and Bernardo’s reference priors have been considered and compared with the Bayesian approach based on biological data.

Normally distributed random numbers are commonly used in scientific computing in various fields. It is important to generate a set of random numbers as close to a normal distribution as possible for reducing initial fluctuations. Two types of samples from a uniform distribution are examined as source samples for inverse transform sampling methods. Three types of inverse transform sampling methods with new approximations of inverse cumulative distribution functions are also discussed for converting uniformly distributed source samples to normally distributed samples.

This article presents the gretl package BayTool which integrates the software functionalities, mostly concerned with frequentist approaches, with Bayesian estimation methods of commonly used econometric models. Computational efficiency is achieved by pairing an extensive use of Gibbs sampling for posterior simulation with the possibility of splitting single-threaded experiments into multiple cores or machines by means of parallelization. From the user’s perspective, the package requires only basic knowledge of gretl scripting to fully access its functionality, while providing a point-and-click solution in the form of a graphical interface for a less experienced audience. These features, in particular, make BayTool stand out as an excellent teaching device without sacrificing more advanced or complex applications.

Designing vaccine efficacy (VE) trials often requires recruiting large numbers of participants when the diseases of interest have a low incidence. When developing novel vaccines, such as for COVID-19 disease, the plausible range of VE is quite large at the design stage. Thus, the number of events needed to demonstrate efficacy above a pre-defined regulatory threshold can be difficult to predict and the time needed to accrue the necessary events can often be long. Therefore, it is advantageous to evaluate the efficacy at earlier interim analysis in the trial to potentially allow the trials to stop early for overwhelming VE or futility. In such cases, incorporating interim analyses through the use of the sequential probability ratio test (SPRT) can be helpful to allow for multiple analyses while controlling for both type-I and type-II errors. In this article, we propose a Bayesian SPRT for designing a vaccine trial for comparing a test vaccine with a control assuming two Poisson incidence rates. We provide guidance on how to choose the prior distribution and how to optimize the number of events for interim analyses to maximize the efficiency of the design. Through simulations, we demonstrate how the proposed Bayesian SPRT performs better when compared with the corresponding frequentist SPRT. An R repository to implement the proposed method is placed at: https://github.com/Merck/bayesiansprt.

Network-based Semi-Supervised Clustering (NeSSC) is a semi-supervised approach for clustering in the presence of an outcome variable. It uses a classification or regression model on resampled versions of the original data to produce a proximity matrix that indicates the magnitude of the similarity between pairs of observations measured with respect to the outcome. This matrix is transformed into a complex network on which a community detection algorithm is applied to search for underlying community structures which is a partition of the instances into highly homogeneous clusters to be evaluated in terms of the outcome. In this paper, we focus on the case the outcome variable to be used in NeSSC is numeric and propose an alternative selection criterion of the optimal partition based on a measure of overlapping between density curves as well as a penalization criterion which takes accounts for the number of clusters in a candidate partition. Next, we consider the performance of the proposed method for some artificial datasets and for 20 different real datasets and compare NeSSC with the other three popular methods of semi-supervised clustering with a numeric outcome. Results show that NeSSC with the overlapping criterion works particularly well when a reduced number of clusters are scattered localized.

This paper discusses the first exit and Dirichlet problems of the nonisotropic tempered (alpha)-stable process (X_t). The upper bounds of all moments of the first exit position (left| X_{tau _D}right|) and the first exit time (tau _D) are explicitly obtained. It is found that the probability density function of (left| X_{tau _D}right|) or (tau _D) exponentially decays with the increase of (left| X_{tau _D}right|) or (tau _D), and (mathrm{E}left[ tau _Dright] sim mathrm{E}left[ left| X_{tau _D}-mathrm{E}left[ X_{tau _D}right] right| ^2right]), (mathrm{E}left[ tau _Dright] sim left| mathrm{E}left[ X_{tau _D}right] right|). Next, we obtain the Feynman–Kac representation of the Dirichlet problem by employing the semigroup theory. Furthermore, averaging the generated trajectories of the stochastic process leads to the solution of the Dirichlet problem, which is also verified by numerical experiments.

The Benford law is used world-wide for detecting non-conformance or data fraud of numerical data. It says that the significand of a data set from the universe is not uniformly, but logarithmically distributed. Especially, the first non-zero digit is One with an approximate probability of 0.3. There are several tests available for testing Benford, the best known are Pearson’s (chi ^2)-test, the Kolmogorov–Smirnov test and a modified version of the MAD-test. In the present paper we propose some tests, three of the four invariant sum tests are new and they are motivated by the sum invariance property of the Benford law. Two distance measures are investigated, Euclidean and Mahalanobis distance of the standardized sums to the orign. We use the significands corresponding to the first significant digit as well as the second significant digit, respectively. Moreover, we suggest inproved versions of the MAD-test and obtain critical values that are independent of the sample sizes. For illustration the tests are applied to specifically selected data sets where prior knowledge is available about being or not being Benford. Furthermore we discuss the role of truncation of distributions.

Let ({X_{i},1le ile n}) be a sequence of linear process based on dependent random variables with random coefficients, which has a mean shift at an unknown location. The cumulative sum (CUSUM, for short) estimator of the change point is studied. The strong convergence, (L_{r}) convergence, complete convergence and the rate of strong convergence are established for the CUSUM estimator under some mild conditions. These results improve and extend the corresponding ones in the literature. Simulation studies and two real data examples are also provided to support the theoretical results.