京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19111号 / 情博第557号 / 新制||情||98(附属図書館) / 32062 / 京都大学大学院情報学研究科知能情報学専攻 / (主査)教授 松山 隆司, 教授 美濃 導彦, 准教授 梁 雪峰 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Multiple testing literature contains ample research on controlling false discoveries for hypotheses classified according to one criterion, which we refer to as `one-way classified hypotheses'. However, one often encounters the scenario of `two-way classified hypotheses' where hypotheses can be partitioned into two sets of groups via two different criteria. Associated multiple testing procedures that incorporate such structural information are potentially more effective than their one-way classified or non-classified counterparts. To the best of our knowledge, very little research has been pursued in this direction. This dissertation proposes two types of multiple testing procedures for two-way classified hypotheses. In the first part, we propose a general methodology for controlling the false discovery rate (FDR) using the Benjamini-Hochberg (BH) procedure based on weighted p-values. The weights can be appropriately chosen to reflect one- or two-way classified structure of hypotheses, producing novel multiple testing procedures for two-way classified hypotheses. Newer results for one-way classified hypotheses have been obtained in this process. Our proposed procedures control the false discovery rate (FDR) non-asymptotically in their oracle forms under positive regression dependence on subset of null p-values (PRDS) and in their data-adaptive forms for independent p-values. Simulation studies demonstrate that our proposed procedures can be considerably more powerful than some contemporary methods in many instances and that our data-adaptive procedures can non-asymptotically control the FDR under certain dependent scenarios. The proposed two-way adaptive procedure is applied to a data set from microbial abundance study, for which it makes more discoveries than an existing method. In the second part, we propose a Local false discovery rate (Lfdr) based multiple testing procedure for two-way classified hypotheses. The procedure has been developed in its oracle form under a model based framework that isolates the effects due to two-way grouping from the significance of an individual hypothesis. Simulation studies show that our proposed procedure successfully controls the average proportion of false discoveries, and is more powerful than existing methods. / Statistics

Recent Next Generation Sequencing methods provide a count of RNA molecules in the form of short reads, yielding discrete, often highly non-normally distributed gene expression measurements. Due to this feature of RNA sequencing (RNA-seq) data, appropriate statistical inference methods are required. Although Negative Binomial (NB) regression has been generally accepted in the analysis of RNA-seq data, its appropriateness in the application to genetic studies has not been exhaustively evaluated. Additionally, adjusting for covariates that have an unknown relationship with expression of a gene has not been extensively evaluated in RNA-seq studies using the NB framework. Finally, the dependent structures in RNA-Seq data may violate the assumptions of some multiple testing correction methods. In this dissertation, we suggest an alternative regression method, evaluate the effect of covariates, and compare various multiple testing correction methods. We conduct simulation studies and apply these methods to a real data set. First, we suggest Firth’s logistic regression for detecting differentially expressed genes in RNA-seq data. We also recommend the data adaptive method that estimates a recalibrated distribution of test statistics. Firth’ logistic regression exhibits an appropriately controlled Type-I error rate using the data adaptive method and shows comparable power to NB regression in simulation studies. Next, we evaluate the effect of disease-associated covariates where the relationship between the covariate and gene expression is unknown. Although the power of NB and Firth’s logistic regression is decreased as disease-associated covariates are added in a model, Type-I error rates are well controlled in Firth’ logistic regression if the relationship between a covariate and disease is not strong. Finally, we compare multiple testing correction methods that control family-wise error rates and impose false discovery rates. The evaluation reveals that an understanding of study designs, RNA-seq data, and the consequences of applying specific regression and multiple testing correction methods are very important factors to control family-wise error rates or false discovery rates. We believe our statistical investigations will enrich gene expression studies and influence related statistical methods.

A regular paving (RP) is a finite succession of bisections that partitions a multidimensional box into sub-boxes using a binary tree-based data structure, with the restriction that an existing sub-box in the partition may only be bisected on its first widest side. Mapping a real value to each element of the partition gives a real-mapped regular paving (RMRP) that can be used to represent a piecewise-constant function density estimate on a multidimensional domain. The RP structure allows real arithmetic to be extended to density estimates represented as RMRPs. Other operations such as computing marginal and conditional functions can also be carried out very efficiently by exploiting these arithmetical properties and the binary tree structure. The purpose of this thesis is to explore the potential for density estimation using RPs. The thesis is structured in three parts. The first part formalises the operational properties of RP-structured density estimates. The next part considers methods for creating a suitable RP partition for an RMRP-structured density estimate. The advantages and disadvantages of a Markov chain Monte Carlo algorithm, already developed, are investigated and this is extended to include a semi-automatic method for heuristic diagnosis of convergence of the chain. An alternative method is also proposed that uses an RMRP to approximate a kernel density estimate. RMRP density estimates are not differentiable and have slower convergence rates than good multivariate kernel density estimators. The advantages of an RMRP density estimate relate to its operational properties. The final part of this thesis describes a new approach to Bayesian inference for complex models with intractable likelihood functions that exploits these operational properties.

Incomplete data represents a major challenge for a successful prediction and subsequent removal of multiples. In this paper, a new method will be represented that tackles this challenge in a two-step approach. During the first step, the recenly developed curvelet-based recovery by sparsity-promoting inversion (CRSI) is applied to the data, followed by a prediction of the primaries. During the second high-resolution step, the estimated primaries are used to improve the frequency content of the recovered data by combining the focal transform, defined in terms of the estimated primaries, with the curvelet transform. This focused curvelet transform leads to an improved recovery, which can subsequently be used as input for a second stage of multiple prediction and primary-multiple separation.