Log-Regularly Varying Scale Mixture of Normals for Robust Regression

Linear regression with the classical normality assumption for the error distribution may lead to an undesirable posterior inference of regression coefficients due to the potential outliers. This paper considers the finite mixture of two components with thin and heavy tails as the error distribution, which has been routinely employed in applied statistics. For the heavily-tailed component, we introduce the novel class of distributions; their densities are log-regularly varying and have heavier tails than those of Cauchy distribution, yet they are expressed as a scale mixture of normal distributions and enable the efficient posterior inference by Gibbs sampler. We prove the robustness to outliers of the posterior distributions under the proposed models with a minimal set of assumptions, which justifies the use of shrinkage priors with unbounded densities for the coefficient vector in the presence of outliers. The extensive comparison with the existing methods via simulation study shows the improved performance of our model in point and interval estimation, as well as its computational efficiency. Further, we confirm the posterior robustness of our method in the empirical study with the shrinkage priors for regression coefficients.Comment: 62 page

〈論文〉レンブラント・ファン・レイン作《マルハレータ・デ・ヘール》の白絵具（鉛白）に使用されたメディウムについて : リンシードオイルの加工法を中心に

レンブラント・ファン・レイン（Rembrandt van Rijn、1606-1669年）の油彩画において、メディウムは、魅力的な画肌を形成する重要な要素である。1900年代中頃までの研究者たちは、実見調査に基づき、レンブラント作品に使用されたメディウムを、樹脂の割合が多いものと推察した。しかし、1900年代後半にヨーロッパの美術館で実施した、メディウムの科学分析の結果では、レンブラント作品から、樹脂の検出はなく、分析した作品の大部分は乾性油単体であることが判明した。そこで本研究では、レンブラント作品のメディウム分析に関する情報をもとに、絵具の再現実験を行ない、レンブラントが使用したであろうメディウムを検証した。検証で得た結果から、油彩画のメディウム作品の画肌の形成にどのような影響を与えているか考察した。ロンドン・ナショナルギャラリーの分析では、《マルハレータ・デ・ヘール》の白襟部分のメディウムは、被熱のあるリンシードオイルであることが推定されている。筆者は、この作品の実見調査を行ない、使用された白絵具の特性に関する情報を収集したところ、可塑性、粘性、流動性の3つの特性を合わせ持つ絵具であると推察した。これに加え、乾燥速度と光沢性を考慮し、リンシードオイルの加工法に着目した実験を行なった。その結果、サンシックンドリンシードオイルに鉛を添加して加熱処理したメディウムを使用することで、レンブラント作品の絵具の特性に近いものが再現できることがわかった。また、鉛を添加して加熱処理することで、絵具の乾燥速度と光沢性が向上することを明らかにした。Based on examinations conducted by researchers in the middle of the 1900s, the binding medium used by Rembrandt van Rijn (1606-1669) was thought to contain a lot of resin.The late 1900s, however, scientific analysis of the binding medium carried out at European museums has not detected resin, and in the majority of the works analyzed, what has been detected is simple drying oil. In this research, from the production of paint based on information about the analysis of the binding medium in Rembrandt\u27s works, I investigated the binding medium that Rembrandt would have used, and I examined what kind of influence the binding medium in oil painting has on the formation of the surface layer of the painting. From scientific analysis of samples taken from the white ruff of "Portrait of Margaretha de Geer", it is presumed that it was subjected to heat. Upon conducting an examination of this work and collecting data on the white paint used, the author found that it exhibited a combination of three characteristics: plasticity, viscosity and fluidity. Based on this fact, I focused on the processing method of the binding medium and conducted experiments. It was found that, sun thickened linseed oil with added lead and subjected to heat treatment enabled replication of something with properties close to those of the paint in Rembrandt\u27s work. In addition, it was revealed that a binding medium with added lead and heat treated increases the glossiness of the paint

〈論文〉リンシードの加工法が鉛白の絵具特性や塗膜形成に及ぼす影響 : 重合油を用いたブラックオイルを中心に

本研究では、乾燥性に優れたリンシードオイルの加工法に焦点を当て、リンシードオイルに一酸化鉛を添加し、加熱する方法にて検証を行なった。この加工法で製作したオイルは一般に‘ブラックオイル’と呼ばれる。先行研究において、生のリンシードオイルをブラックオイルに加工する研究は数多く行われてきているが、重合したリンシードオイルをブラックオイルに加工する研究はほとんどみられない。そこで、生のリンシードオイルと重合したリンシードオイルそれぞれをブラックオイルに加工することで、絵具特性、塗膜形成がどのように変化するか、古くから用いられてきた鉛白で絵具を製作し、比較検証を行なった。比較の観点は、①乾燥性、②光沢度、③粘度、④筆の動かしやすさ、粘り気、⑤絵具の色彩に与える影響、⑥形成性の6つから成り、測定機器を用いることが可能なものに関しては数値化を試みた。実験の結果から、生のリンシードオイルと重合したリンシードオイルそれぞれをブラックオイルに加工する場合の絵具特性、塗膜形成に及ぼす影響の違いについて考察した。In this study, I focus on the processing method of linseed oil, which has excellent drying properties. Consideration is given to the method of adding the litharge to linseed oil and heating it. The oil produced by this processing method is generally called \u27black oil\u27. In previous studies, a lot of research has been done on processing raw linseed oil into black oil, but there are very few cases of processing polymerized linseed oil into black oil. Therefore, by processing both raw linseed oil and polymerized linseed oil into black oil, paint was made with old lead white and a comparative verification of how the paint properties and film formation change was carried out. The comparative viewpoints consisted of six points: ① drying properties, ② glossiness, ③ viscosity, ④ the brush\u27s ease of movement and stickiness, ⑤ effect on the color of the paint, and ⑥ plasticity. I attempted to quantify those things to which measuring equipment could be applied. The results of these experiments show the different effect on paint properties and film formation in the case of processing black oil from raw linseed oil and polymerized linseed oil, and demonstrate an example of the superiority of black oil made with stand oil

Posterior Robustness with Milder Conditions: Contamination Models Revisited

Robust Bayesian linear regression is a classical but essential statistical tool. Although novel robustness properties of posterior distributions have been proved recently under a certain class of error distributions, their sufficient conditions are restrictive and exclude several important situations. In this work, we revisit a classical two-component mixture model for response variables, also known as contamination model, where one component is a light-tailed regression model and the other component is heavy-tailed. The latter component is independent of the regression parameters, which is crucial in proving the posterior robustness. We obtain new sufficient conditions for posterior (non-)robustness and reveal non-trivial robustness results by using those conditions. In particular, we find that even the Student-$t$ error distribution can achieve the posterior robustness in our framework. A numerical study is performed to check the Kullback-Leibler divergence between the posterior distribution based on full data and that based on data obtained by removing outliers.Comment: 19 pages, 1 figur

On Data Augmentation for Models Involving Reciprocal Gamma Functions

In this paper, we introduce a new and efficient data augmentation approach to the posterior inference of the models with shape parameters when the reciprocal gamma function appears in full conditional densities. Our approach is to approximate full conditional densities of shape parameters by using Gauss’s multiplication formula and Stirling’s formula for the gamma function, where the approximation error can be made arbitrarily small. We use the techniques to construct efficient Gibbs and Metropolis-Hastings algorithms for a variety of models that involve the gamma distribution, Student’s t-distribution, the Dirichlet distribution, the negative binomial distribution, and the Wishart distribution. The proposed sampling method is numerically demonstrated through simulation studies

Stimulation of DNA Glycosylase Activities by XPC Protein Complex: Roles of Protein-Protein Interactions

We showed that XPC complex, which is a DNA damage detector for nucleotide excision repair, stimulates activity of thymine DNA glycosylase (TDG) that initiates base excision repair. XPC appeared to facilitate the enzymatic turnover of TDG by promoting displacement from its own product abasic site, although the precise mechanism underlying this stimulation has not been clarified. Here we show that XPC has only marginal effects on the activity of E. coli TDG homolog (EcMUG), which remains bound to the abasic site like human TDG but does not significantly interacts with XPC. On the contrary, XPC significantly stimulates the activities of sumoylated TDG and SMUG1, both of which exhibit quite different enzymatic kinetics from unmodified TDG but interact with XPC. These results point to importance of physical interactions for stimulation of DNA glycosylases by XPC and have implications in the molecular mechanisms underlying mutagenesis and carcinogenesis in XP-C patients

DNA-binding polarity of human replication protein A positions nucleases in nucleotide excision repair

The human single-stranded DNA-binding replication A protein (RPA) is involved in various DNA-processing events. By comparing the affinity of hRPA for artificial DNA hairpin structures with 3'- or 5'-protruding single-stranded arms, we found that hRPA binds ssDNA with a defined polarity; a strong ssDNA interaction domain of hRPA is positioned at the 5' side of its binding region, a weak ssDNA-binding domain resides at the 3' side. Polarity appears crucial for positioning o