Credible sets in nonparametric regression

A common problem in Bayesian statistics is to determine whether a quantity obtained from a Bayesian posterior distribution is also meaningful in a frequentist context. In this thesis, we try to answer this question for credible sets in the so-called fixed design model. Taking a specific prior distribution, we study whether credible sets based on this prior can also be used as confidence intervals. In particular, our aim is to construct a credible set for a parameter function. Under certain assumptions on the smoothness of the function, it turns out that we can obtain meaningful results about both the frequentist coverage and the width of the credible set. We consider several different classes of functions in this thesis, each with a different set of assumptions. In the first chapter, we assume that we know rather a lot about the structure of the function, and use this to obtain a useful method. In chapter 2, we extend this to a method that adapts to the structure of the function. Finally, in the last chapter, we extend this to so-called credible bands, that describe the behaviour of the entire function, rather than at a specific point.UBL - phd migration 201

Genome-wide association analysis of insomnia complaints identifies risk genes and genetic overlap with psychiatric and metabolic traits.

To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked FilesPersistent insomnia is among the most frequent complaints in general practice. To identify genetic factors for insomnia complaints, we performed a genome-wide association study (GWAS) and a genome-wide gene-based association study (GWGAS) in 113,006 individuals. We identify three loci and seven genes associated with insomnia complaints, with the associations for one locus and five genes supported by joint analysis with an independent sample (n = 7,565). Our top association (MEIS1, P < 5 × 10-8) has previously been implicated in restless legs syndrome (RLS). Additional analyses favor the hypothesis that MEIS1 exhibits pleiotropy for insomnia and RLS and show that the observed association with insomnia complaints cannot be explained only by the presence of an RLS subgroup within the cases. Sex-specific analyses suggest that there are different genetic architectures between the sexes in addition to shared genetic factors. We show substantial positive genetic correlation of insomnia complaints with internalizing personality traits and metabolic traits and negative correlation with subjective well-being and educational attainment. These findings provide new insight into the genetic architecture of insomnia.Netherlands Organization for Scientific Research NWO Brain & Cognition 433-09-228 European Research Council ERC-ADG-2014-671084 INSOMNIA Netherlands Scientific Organization (NWO) VU University (Amsterdam, the Netherlands) Dutch Brain Foundation Helmholtz Zentrum Munchen - German Federal Ministry of Education and Research state of Bavaria German Migraine & Headache Society (DMKG) Almirall AstraZeneca Berlin Chemie Boehringer Boots Health Care GlaxoSmithKline Janssen Cilag McNeil Pharma MSD Sharp Dohme Pfizer Institute of Epidemiology and Social Medicine at the University of Munster German Ministry of Education and Research (BMBF) German Restless Legs Patient Organisation (RLS Deutsche Restless Legs Vereinigung) Swiss RLS Patient Association (Schweizerische Restless Legs Selbsthilfegruppe

Genome-wide association meta-analysis of 78,308 individuals identifies new loci and genes influencing human intelligence

Intelligence is associated with important economic and health-related life outcomes1. Despite intelligence having substantial heritability2 (0.54) and a confirmed polygenic nature, initial genetic studies were mostly underpowered3,4,5. Here we report a meta-analysis for intelligence of 78,308 individuals. We identify 336 associated SNPs (METAL P < 5 × 10−8) in 18 genomic loci, of which 15 are new. Around half of the SNPs are located inside a gene, implicating 22 genes, of which 11 are new findings. Gene-based analyses identified an additional 30 genes (MAGMA P < 2.73 × 10−6), of which all but one had not been implicated previously. We show that the identified genes are predominantly expressed in brain tissue, and pathway analysis indicates the involvement of genes regulating cell development (MAGMA competitive P = 3.5 × 10−6). Despite the well-known difference in twin-based heritability2 for intelligence in childhood (0.45) and adulthood (0.80), we show substantial genetic correlation (rg = 0.89, LD score regression P = 5.4 × 10−29). These findings provide new insight into the genetic architecture of intelligence

Adaptive Bayesian credible sets in regression with a Gaussian process prior

We investigate two empirical Bayes methods and a hierarchical Bayes method for adapting the scale of a Gaussian process prior in a nonparametric regression model. We show that all methods lead to a posterior contraction rate that adapts to the smoothness of the true regression function. Furthermore, we show that the corresponding credible sets cover the true regression function whenever this function satisfies a certain extrapolation condition. This condition depends on the specific method, but is implied by a condition of self-similarity. The latter condition is shown to be satisfied with probability one under the prior distribution

Genome-wide association meta-analysis of 78,308 individuals identifies new loci and genes influencing human intelligence

Intelligence is associated with important economic and health-related life outcomes. Despite intelligence having substantial heritability (0.54) and a confirmed polygenic nature, initial genetic studies were mostly underpowered. Here we report a meta-analysis for intelligence of 78,308 individuals. We identify 336 associated SNPs (METAL P < 5 × 10-8) in 18 genomic loci, of which 15 are new. Around half of the SNPs are located inside a gene, implicating 22 genes, of which 11 are new findings. Gene-based analyses identified an additional 30 genes (MAGMA P < 2.73 × 10-6), of which all but one had not been implicated previously. We show that the identified genes are predominantly expressed in brain tissue, and pathway analysis indicates the involvement of genes regulating cell development (MAGMA competitive P = 3.5 × 10-6). Despite the well-known difference in twin-based heritability for intelligence in childhood (0.45) and adulthood (0.80), we show substantial genetic correlation (rg = 0.89, LD score regression P = 5.4 × 10-29). These findings provide new insight into the genetic architecture of intelligence