Density approximant based on noise multiplied data

Using noise multiplied data to protect confidential data has recently drawn some attention. Understanding the probability property of the underlying confidential data based on their masked data is of interest in confidential data analysis. This paper proposes the approach of sample-moment-based density approximant based on noise multiplied data and provides a new manner for approximating the density function of the underlying confidential data without accessing the original data. The approach of sample-moment-based density approximant is an extension of the approach of moment-based density approximant, which is mathematically equivalent to traditional orthogonal polynomials ap- proaches to the probability density function (Provost, 2005). This paper shows that, regardless of a negligible probability, a moment-based density approximant can be well approximated by its sample-moment-based approximant if the size of the sample used in the evaluation is reasonable large. Consequently, a density function can be reasonably approximated by its sample-moment-based density approximant. This paper focuses on the properties and the performance of the approach of the sample-moment-based density approximant based on noise multiplied data. Due to the restriction on the number of pages, some technical issues on implementing the approach proposed in practice will be discussed in another paper

On the Ratio of Fréchet Random Variables

Fréchet distribution, ratio of random variables,

Laplace random variables with application to price indices

Computer programs, Consumer price index, Economics, Estimation, Laplace distribution, Ratio of random variables,

Enhancing discovery of genetic variants for posttraumatic stress disorder through integration of quantitative phenotypes and trauma exposure information

BACKGROUND: Posttraumatic stress disorder (PTSD) is heritable and a potential consequence of exposure to traumatic stress. Evidence suggests that a quantitative approach to PTSD phenotype measurement and incorporation of lifetime trauma exposure (LTE) information could enhance the discovery power of PTSD genome-wide association studies (GWASs). METHODS: A GWAS on PTSD symptoms was performed in 51 cohorts followed by a fixed-effects meta-analysis (N = 182,199 European ancestry participants). A GWAS of LTE burden was performed in the UK Biobank cohort (N = 132,988). Genetic correlations were evaluated with linkage disequilibrium score regression. Multivariate analysis was performed using Multi-Trait Analysis of GWAS. Functional mapping and annotation of leading loci was performed with FUMA. Replication was evaluated using the Million Veteran Program GWAS of PTSD total symptoms. RESULTS: GWASs of PTSD symptoms and LTE burden identified 5 and 6 independent genome-wide significant loci, respectively. There was a 72% genetic correlation between PTSD and LTE. PTSD and LTE showed largely similar patterns of genetic correlation with other traits, albeit with some distinctions. Adjusting PTSD for LTE reduced PTSD heritability by 31%. Multivariate analysis of PTSD and LTE increased the effective sample size of the PTSD GWAS by 20% and identified 4 additional loci. Four of these 9 PTSD loci were independently replicated in the Million Veteran Program. CONCLUSIONS: Through using a quantitative trait measure of PTSD, we identified novel risk loci not previously identified using prior case-control analyses. PTSD and LTE have a high genetic overlap that can be leveraged to increase discovery power through multivariate methods.</p

RNA Interference: Its Use as Antiviral Therapy

RNA interference (RNAi) is a sequence-specific gene-silencing mechanism that has been proposed to function as a defence mechanism of eukaryotic cells against viruses and transposons. RNAi was first observed in plants in the form of a mysterious immune response to viral pathogens. But RNAi is more than just a response to exogenous genetic material. Small RNAs termed microRNA (miRNA) regulate cellular gene expression programs to control diverse steps in cell development and physiology. The discovery that exogenously delivered short interfering RNA (siRNA) can trigger RNAi in mammalian cells has made it into a powerful technique for generating genetic knock-outs. It also raises the possibility to use RNAi technology as a therapeutic tool against pathogenic viruses. Indeed, inhibition of virus replication has been reported for several human pathogens including human immunodeficiency virus, the hepatitis B and C viruses and influenza virus. We reviewed the field of antiviral RNAi research in 2003 (Haasnoot et al. 2003), but many new studies have recently been published. In this review, we present a complete listing of all antiviral strategies published up to and including December 2004. The latest developments in the RNAi field and their antiviral application are describe