The marginal likelihood plays an important role in many areas of Bayesian statistics such as parameter estimation, model comparison, and model averaging. In most applications, however, the marginal likelihood is not analytically tractable and must be approximated using numerical methods. Here we provide a tutorial on bridge sampling (Bennett, 1976; Meng & Wong, 1996), a reliable and relatively straightforward sampling method that allows researchers to obtain the marginal likelihood for models of varying complexity. First, we introduce bridge sampling and three related sampling methods using the beta-binomial model as a running example. We then apply bridge sampling to estimate the marginal likelihood for the Expectancy Valence (EV) model—a popular model for reinforcement learning. Our results indicate that bridge sampling provides accurate estimates for both a single participant and a hierarchical version of the EV model. We conclude that bridge sampling is an attractive method for mathematical psychologists who typically aim to approximate the marginal likelihood for a limited set of possibly high-dimensional models.

Both microbial products and T cell factors influence dendritic cell (DC) maturation. However, it is not known which T cells are capable of interacting with DCs at the initiation of adaptive immunity, when foreign antigen-specific T cells are rare. We show here that self-reactive CD1-restricted T cells can promote DC maturation by recognizing CD1 in the absence of foreign antigens. T cell recognition of all four CD1 isoforms can trigger DC maturation, but their distinct mechanisms of costimulation lead to profound differences in concomitant interleukin 12 p70 production. Distinct CD1-reactive T cells may thus differentially direct DC development early in the immune response, thereby controlling subsequent polarization of acquired immunity.

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Immature myeloid dendritic cells (DCs) express only low levels of major histocompatibility complex (MHC) class II but express high levels of CD1 a, b, and c antigen-presenting molecules at the cell surface. As Vδ1+ γ/δ T cells are the main tissue subset of γ/δ T cells and they are known to recognize CD1c in the absence of specific foreign antigen recognition, we examined the possible interaction of these T cells with immature DCs. We show that CD1-restricted γ/δ T cells can mediate the maturation of DCs. DC maturation required cell–cell contact and could be blocked by antibodies against CD1c. The maturation process was partially mediated by tumor necrosis factor α. Importantly, immature DCs matured in the presence of lipopolysaccharide and CD1-restricted γ/δ T cells produced bioactive interleukin-12p70. In addition, these DCs were able to efficiently present peptide antigens to naive CD4+ T cells. CD1-restricted γ/δ T cell recognition of immature DCs provides the human immune system with the capacity to rapidly generate a pool of mature DCs early during microbial invasion. This may be an important source of critical host signals for T helper type 1 polarization of antigen-specific naive T cells and the subsequent adaptive immune response.