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Humans can learn complex functional relationships between variables from small amounts of data. In doing so, they draw on prior expectations about the form of these relationships. In three experiments, we show that people learn to adjust these expectations through experience, learning about the likely forms of the functions they will encounter. Previous work has used Gaussian processes--a statistical framework that extends Bayesian nonparametric approaches to regression--to model human function learning. We build on this work, modeling the process of learning to learn functions as a form of hierarchical Bayesian inference about the Gaussian process hyperparameters.

Background Systematic reviews of randomised controlled trials (RCTs) have suggested that maternal vitamin D (25[OH]D) and calcium supplementation increase birth weight. However, limitations of many trials were highlighted in the reviews. Our aim was to combine genetic and RCT data to estimate causal effects of these two maternal traits on offspring birth weight. Methods and findings We performed two-sample mendelian randomisation (MR) using genetic instrumental variables associated with 25(OH)D and calcium that had been identified in genome-wide association studies (GWAS; sample 1; N = 122,123 for 25[OH]D and N = 61,275 for calcium). Associations between these maternal genetic variants and offspring birth weight were calculated in the UK Biobank (UKB) (sample 2; N = 190,406). We used data on mother-child pairs from two United Kingdom birth cohorts (combined N = 5,223) in sensitivity analyses to check whether results were influenced by fetal genotype, which is correlated with the maternal genotype (r [almost equal to] 0.5). Further sensitivity analyses to test the reliability of the results included MR-Egger, weighted-median estimator, 'leave-one-out', and multivariable MR analyses. We triangulated MR results with those from RCTs, in which we used randomisation to supplementation with vitamin D (24 RCTs, combined N = 5,276) and calcium (6 RCTs, combined N = 543) as an instrumental variable to determine the effects of 25(OH)D and calcium on birth weight. In the main MR analysis, there was no strong evidence of an effect of maternal 25(OH)D on birth weight (difference in mean birth weight -0.03 g [95% CI -2.48 to 2.42 g, p = 0.981] per 10% higher maternal 25[OH]D). The effect estimate was consistent across our MR sensitivity analyses. Instrumental variable analyses applied to RCTs suggested a weak positive causal effect (5.94 g [95% CI 2.15-9.73, p = 0.002] per 10% higher maternal 25[OH]D), but this result may be exaggerated because of risk of bias in the included RCTs. The main MR analysis for maternal calcium also suggested no strong evidence of an effect on birth weight (-20 g [95% CI -44 to 5 g, p = 0.116] per 1 SD higher maternal calcium level). Some sensitivity analyses suggested that the genetic instrument for calcium was associated with birth weight via exposures that are independent of calcium levels (horizontal pleiotropy). Application of instrumental variable analyses to RCTs suggested that calcium has a substantial effect on birth weight (178 g [95% CI 121-236 g, p = 1.43 x 10.sup.-9 ] per 1 SD higher maternal calcium level) that was not consistent with any of the MR results. However, the RCT instrumental variable estimate may have been exaggerated because of risk of bias in the included RCTs. Other study limitations include the low response rate of UK Biobank, which may bias MR estimates, and the lack of suitable data to test whether the effects of genetic instruments on maternal calcium levels during pregnancy were the same as those outside of pregnancy. Conclusions Our results suggest that maternal circulating 25(OH)D does not influence birth weight in otherwise healthy newborns. However, the effect of maternal circulating calcium on birth weight is unclear and requires further exploration with more research including RCT and/or MR analyses with more valid instruments., Author(s): William D. Thompson 1,2, Jessica Tyrrell 1, Maria-Carolina Borges 2,3, Robin N. Beaumont 1, Bridget A. Knight 1, Andrew R. Wood 1, Susan M. Ring 2,3,4, Andrew T. Hattersley [...]

Background: Depression is more common in obese than non-obese individuals, especially in women, but the causal relationship between obesity and depression is complex and uncertain. Previous studies have used genetic variants associated with BMI to provide evidence that higher body mass index (BMI) causes depression, but have not tested whether this relationship is driven by the metabolic consequences of BMI nor for differences between men and women.Methods: We performed a Mendelian randomization study using 48 791 individuals with depression and 291 995 controls in the UK Biobank, to test for causal effects of higher BMI on depression (defined using self-report and Hospital Episode data). We used two genetic instruments, both representing higher BMI, but one with and one without its adverse metabolic consequences, in an attempt to 'uncouple' the psychological component of obesity from the metabolic consequences. We further tested causal relationships in men and women separately, and using subsets of BMI variants from known physiological pathways.Results: Higher BMI was strongly associated with higher odds of depression, especially in women. Mendelian randomization provided evidence that higher BMI partly causes depression. Using a 73-variant BMI genetic risk score, a genetically determined one standard deviation (1 SD) higher BMI (4.9 kg/m2) was associated with higher odds of depression in all individuals [odds ratio (OR): 1.18, 95% confidence interval (CI): 1.09, 1.28, P = 0.00007) and women only (OR: 1.24, 95% CI: 1.11, 1.39, P = 0.0001). Meta-analysis with 45 591 depression cases and 97 647 controls from the Psychiatric Genomics Consortium (PGC) strengthened the statistical confidence of the findings in all individuals. Similar effect size estimates were obtained using different Mendelian randomization methods, although not all reached P < 0.05. Using a metabolically favourable adiposity genetic risk score, and meta-analysing data from the UK biobank and PGC, a genetically determined 1 SD higher BMI (4.9 kg/m2) was associated with higher odds of depression in all individuals (OR: 1.26, 95% CI: 1.06, 1.50], P = 0.010), but with weaker statistical confidence.Conclusions: Higher BMI, with and without its adverse metabolic consequences, is likely to have a causal role in determining the likelihood of an individual developing depression. [ABSTRACT FROM AUTHOR]

Presents a bibliography related to education of speech skills to clergy published in the August 1, 1964 issue of 'Speech Monographs.'