Australian and New Zealand Journal of Statistics

Summary Model selection is a ubiquitous problem that arises in the application of many statistical and machine learning methods. In the likelihood and related settings, it is typical to use the method of information criteria (ICs) to choose the most parsimonious among competing models by penalizing the likelihood‐based objective function. Theorems guaranteeing the consistency of ICs can often be difficult to verify and are often specific and bespoke. We present a set of results that guarantee consistency for a class of ICs, which we call PanIC (from the Greek root ‘ pan ’, meaning ‘ of everything ’), with easily verifiable regularity conditions. PanICs are applicable in any loss‐based learning problem and are not exclusive to likelihood problems. We illustrate the verification of regularity conditions for model selection problems regarding finite mixture models, least absolute deviation and support vector regression and principal component analysis, and demonstrate the effectiveness of PanICs for such problems via numerical simulations. Furthermore, we present new sufficient conditions for the consistency of BIC‐like estimators and provide comparisons of the BIC with PanIC.

Hien Duy Nguyen

Australian & New Zealand Journal of Statistics

PanIC: Consistent information criteria for general model selection problems

PanIC：一般模型选择问题的相合信息准则

Summary In modern data analysis, it is common to use machine learning methods to predict outcomes on unlabelled datasets and then use these pseudo‐outcomes in subsequent statistical inference. Inference in this setting is often called post‐prediction inference. We propose a novel assumption‐lean framework for statistical inference under post‐prediction setting, called prediction de‐correlated inference (PDC). Our approach is safe, in the sense that PDC can automatically adapt to any black‐box machine‐learning model and consistently outperform the supervised counterparts. The PDC framework also offers easy extensibility for accommodating multiple predictive models. Both numerical results and real‐world data analysis demonstrate the superiority of PDC over the state‐of‐the‐art methods.

Feng Gan

Wanfeng Liang

Changliang Zou

Prediction de‐correlated inference: A safe approach for post‐prediction inference

预测去相关推理：一种安全的后预测推理方法

Summary A new method for estimating the proportion of null effects is proposed for solving large‐scale multiple comparison problems. It utilises maximum likelihood estimation of nonparametric mixtures, which also provides a density estimate of the test statistics. It overcomes the problem of the usual nonparametric maximum likelihood estimator that cannot produce a positive probability at the location of null effects in the process of estimating nonparametrically a mixing distribution. The profile likelihood is further used to help produce a range of null proportion values, corresponding to which the density estimates are all consistent. With a proper choice of a threshold function on the profile likelihood ratio, the upper endpoint of this range can be shown to be a consistent estimator of the null proportion. Numerical studies show that the proposed method has an apparently convergent trend in all cases studied and performs favourably when compared with existing methods in the literature.

Xiangjie Xue

Yong Wang

A nonparametric mixture approach to density and null proportion estimation in large‐scale multiple comparison problems

大规模多重比较问题中密度和零比例估计的非参数混合方法

Summary We discuss the use of the following greedy algorithms in the prediction of multivariate time series: Matching Pursuit Algorithm (MPA), Orthogonal Matching Pursuit (OMP), Relaxed Matching Pursuit (RMP), Frank–Wolfe Algorithm (FWA) and Constrained Matching Pursuit (CMP). The last two are known to be solvers for the lasso problem. Some of the algorithms are well‐known (e.g. OMP), while others are less popular (e.g. RMP). We provide a unified presentation of all the algorithms, and evaluate their computational complexity for the high‐dimensional case and for the big data case. We show how 12 information theoretic (IT) criteria can be used jointly with the greedy algorithms. As part of this effort, we derive new theoretical results that allow modification of the IT criteria such that to be compatible with RMP. The prediction capabilities are tested in experiments with two data sets. The first one involves air pollution data measured in Auckland (New Zealand) and the second one concerns the House Price Index in England (the United Kingdom).

Fangyao Li

Christopher M. Triggs

Ciprian Doru Giurcăneanu

On the selection of predictors by using greedy algorithms and information theoretic criteria

基于贪婪算法和信息论准则的预测因子选择研究

Summary Frequentist and Bayesian methods differ in many aspects but share some basic optimal properties. In real‐life prediction problems, situations exist in which a model based on one of the above paradigms is preferable depending on some subjective criteria. Nonparametric classification and regression techniques, such as decision trees and neural networks, have both frequentist (classification and regression trees (CARTs) and artificial neural networks) as well as Bayesian counterparts (Bayesian CART and Bayesian neural networks) to learning from data. In this paper, we present two hybrid models combining the Bayesian and frequentist versions of CART and neural networks, which we call the Bayesian neural tree (BNT) models. BNT models can simultaneously perform feature selection and prediction, are highly flexible, and generalise well in settings with limited training observations. We study the statistical consistency of the proposed approaches and derive the optimal value of a vital model parameter. The excellent performance of the newly proposed BNT models is shown using simulation studies. We also provide some illustrative examples using a wide variety of standard regression datasets from a public available machine learning repository to show the superiority of the proposed models in comparison to popularly used Bayesian CART and Bayesian neural network models.

Tanujit Chakraborty

Gauri Kamat

Ashis Kumar Chakraborty

Bayesian neural tree models for nonparametric regression

非参数回归的贝叶斯神经树模型

Emi Tanaka

Telling Stories with Data: With Application in R. By RohanAlexander. CRC Press. 2023. 622 pages. AU$129.60 (hardback). ISBN: 978‐1‐0321‐3477‐2.

用数据讲故事：R语言应用。作者：Rohan Alexander。CRC出版社。2023年。622页。澳元129.60（精装本）。ISBN: 978‐1‐0321‐3477‐2。

Summary Seasonal autoregressive (SAR) time series models have been extended to fit time series exhibiting multiple seasonalities. However, hardly any research in Bayesian literature has been done on modelling multiple seasonalities. In this article, we propose a full Bayesian analysis of triple SAR (TSAR) models for time series with triple seasonality, considering identification, estimation and prediction for these TSAR models. In this Bayesian analysis of TSAR models, we assume the model errors to be normally distributed and the model order to be a random variable with a known maximum value, and we employ the g prior for the model coefficients and variance. Accordingly, we first derive the posterior mass function of the TSAR order in closed form, which then enables us to identify the best order of TSAR model as the order value with the highest posterior probability. In addition, we derive the conditional posteriors to be a multivariate normal for the TSAR coefficients and to be an inverse gamma for the TSAR variance; also, we derive the conditional predictive distribution to be a multivariate normal for future observations. Since these derived conditional distributions are in closed forms, we introduce the Gibbs sampler to present the Bayesian analysis of TSAR models and to easily produce multiple‐step‐ahead predictions. Using Julia programming language, we conduct an extensive simulation study, aiming to evaluate the accuracy of our proposed full Bayesian analysis for TSAR models. In addition, we apply our work on time series to hourly electricity load in some European countries.

Ayman A. Amin

Full Bayesian analysis of triple seasonal autoregressive models

三重季节性自回归模型的全贝叶斯分析

Summary This paper first describes the difficulties in providing the required sample sizes for clinical trials that guarantee type 1 and type 2 error control. The required sample sizes obviously depend on the test employed, and in this study we use the so‐called E ‐test, which is known to have extremely favourable size properties and higher power than alternatives. To compute exact powers for this test in real time is not currently feasible, so a corpus of pre‐computed exact powers (and sizes) was created, covering sample sizes up to 500. When there are no solutions within the corpus, a novel extrapolation technique is used. Exact size can be computed after the sample sizes have been extracted; however, for the E ‐test the exact size is virtually always very close to the nominal target. All the code has been converted into an R‐package , which is available on CRAN and illustrated.

Chris J. Lloyd

Exact samples sizes for clinical trials subject to size and power constraints

受样本量和功效约束的临床试验的精确样本量

短名	Aust. N. Z. J. Stat.
Journal Impact	0.98
国际分区	STATISTICS & PROBABILITY(Q3)
期刊索引	SCI Q3中科院 4 区

ISSN	1369-1473, 1467-842X
h-index	46
国内分区	数学(4区)数学统计学与概率论(3区)

涉及主题	数学统计计算机科学经济计量经济学机器学习人工智能物理医学应用数学估计员
出版信息	出版商: Wiley-Blackwell Publishing Ltd，出版周期: Quarterly，期刊类型: journal，开源期刊: 否
基本数据	创刊年份: 1998，原创研究文献占比: 100.00%，自引率:0.00%， Gold OA占比: 14.10%
平均审稿周期	网友分享经验：>12周，或约稿
平均录用比例	网友分享经验：容易

Australian and New Zealand Journal of Statistics

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PanIC: Consistent information criteria for general model selection problems

Prediction de‐correlated inference: A safe approach for post‐prediction inference

A nonparametric mixture approach to density and null proportion estimation in large‐scale multiple comparison problems

On the selection of predictors by using greedy algorithms and information theoretic criteria

Bayesian neural tree models for nonparametric regression

PanIC: Consistent information criteria for general model selection problems

Prediction de‐correlated inference: A safe approach for post‐prediction inference

Telling Stories with Data: With Application in R. By RohanAlexander. CRC Press. 2023. 622 pages. AU$129.60 (hardback). ISBN: 978‐1‐0321‐3477‐2.

Full Bayesian analysis of triple seasonal autoregressive models

Exact samples sizes for clinical trials subject to size and power constraints