We provide a review of prior distributions for objective Bayesian analysis. We start by examining some foundational issues and then organize our exposition into priors for: i) estimation or prediction; ii) model selection; iii) high-dimensional models. With regard to i), we present some basic notions, and then move to more recent contributions on discrete parameter space, hierarchical models, nonparametric models, and penalizing complexity priors. Point ii) is the focus of this paper: it discusses principles for objective Bayesian model comparison, and singles out some major concepts for building priors, which are subsequently illustrated in some detail for the classic problem of variable selection in normal linear models. We also present some recent contributions in the area of objective priors on model space. With regard to point iii) we only provide a short summary of some default priors for high-dimensional models, a rapidly growing area of research.

Background: Impaired intellectual performance is associated with an increased risk of schizophrenia.Aims: To investigate whether this association is due to the influence of prenatal and early childhood exposures on both intellectual development and the risk of schizophrenia.Method: Cohort of 197 613 Swedish male conscripts with linked birth, census and hospital admission data together with five measures of verbal and non-verbal intellectual performance recorded at conscription.Results109 643 subjects had complete data; over a mean 5-year follow-up, 60 developed schizophrenia and 92 developed other non-affective psychoses. Poor scores for each of the five tests were associated with 3-to 14-fold increased risk of psychosis, particularly schizophrenia. Controlling for birth-related exposures, including birth weight, and parental education did not attenuate these associations.Results: 109 643 subjects had complete data; over amean 5-year follow-up,60 developed schizophrenia and 92 developed other non-affective psychoses. Poor scores for each of the five testswere associatedwith 3-to 14-foldincreasedrisk of psychosis, particularly schizophrenia. Controlling for birth-related exposures, including birthweight, and parental education didnot attenuate these associations.Conclusions: Poor intellectual performance at 18 years of age is associated with early-onset psychotic disorder. Associations do not appear to be confounded by prenatal adversity or childhood circumstances, as indexed by parental education.

Factors influencing fetal and childhood growth may affect a person’s risk of developing schizophrenia. Associations of size at birth and body size in young adulthood with schizophrenia and other nonaffective psychoses were assessed in a cohort of 334,577 Swedish male conscripts born in 1973–1980 for whom linked birth, census, hospital admission, and adult height and weight data were available. Complete data on all study variables were available for 246,655 subjects. Over a mean 3.4-year follow-up beginning at age 18 years, 80 subjects developed schizophrenia and 124 developed other nonaffective psychoses. A reverse J-shaped association was found between gestation-adjusted birth weight and schizophrenia. The hazard ratios were 7.03 (95% confidence interval: 1.59, 31.10) for males of low birth weight (4.0 kg). Birth weight was not strongly related to other nonaffective psychoses. Taller males had a reduced risk of psychosis. The lowest risks were seen for low birth weight males who became tall adults. The associations with birth weight indicate that fetal exposures, including possible effects of gestational diabetes, are important in the etiology of psychosis. The role of childhood exposures, as indexed by adult height and body mass index, appears to be less strong.

Background. Although urban place of birth has been identified as a risk factor for schizophrenia, the extent to which this association is mediated by socially patterned risk factors such as obstetric complications and childhood socio-economic position is unclear. The diagnostic specificity of the association within the clinical psychotic syndromes is also unclear.Method. A population cohort of 696025 males and females, born in Sweden between 1973 and 1980 and with linked birth and socio-economic data was followed up from age 16 for up to 9·8 years. Hospitalized cases of schizophrenia and other non-affective psychosis were identified from the Swedish Inpatient Discharge Register. We examined associations of these disorders with a three-level measure of urbanicity of birthplace before and after controlling for measures of foetal nutrition, obstetric complications and level of maternal education.Results. Urban compared to rural birthplace was associated both with increased risk of adult onset schizophrenia (hazard ratio 1·34, CI 0·91–1·96) and other non-affective psychoses (hazard ratio 1·63, CI 1·18–2·26). None of these associations was greatly affected by adjustment for obstetric complications or maternal educational level. In the group of other non-affective psychoses urban–rural differences in disease risk were strongest among those born in the winter months.Conclusion. Urbanization of birthplace is associated with increased risk of non-affective psychosis but this is not confined to narrowly defined cases. The magnitude of the association in Sweden is lower than that reported in other studies. Causal factors underlying this association appear to operate independently of risks associated with obstetric complications and parental educational status.