Mitochondrial dysfunction was highlighted as a crucial vulnerability factor for the development of depression. However, systemic studies assessing stress-induced changes in mitochondria-associated... Show moreMitochondrial dysfunction was highlighted as a crucial vulnerability factor for the development of depression. However, systemic studies assessing stress-induced changes in mitochondria-associated genes in brain regions relevant to depression symptomatology remain scarce. Here, we performed a genome-wide transcriptomic study to examine mitochondrial gene expression in the prefrontal cortex (PFC) and nucleus accumbens (NAc) of mice exposed to multimodal chronic restraint stress. We identified mitochondria-associated gene pathways as most prominently affected in the PFC and with lesser significance in the NAc. A more detailed mitochondrial gene expression analysis revealed that in particular mitochondrial DNA-encoded subunits of the oxidative phosphorylation complexes were altered in the PFC. The comparison of our data with a reanalyzed transcriptome data set of chronic variable stress mice and major depression disorder subjects showed that the changes in mitochondrial DNA-encoded genes are a feature generalizing to other chronic stress-protocols as well and might have translational relevance. Finally, we provide evidence for changes in mitochondrial outputs in the PFC following chronic stress that are indicative of mitochondrial dysfunction. Collectively, our work reinforces the idea that changes in mitochondrial gene expression are key players in the prefrontal adaptations observed in individuals with high behavioral susceptibility and resilience to chronic stress. Show less
We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor product B-splines and endowing the... Show moreWe study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor product B-splines and endowing the coefficients with Gaussian priors. In the usual fixed-in-advanced sampling plan, we establish posterior contraction rates for mode and maximum and show that they coincide with the minimax rates for this problem. To quantify estimation uncertainty, we construct credible sets for these two quantities that have high coverage probabilities with optimal sizes. If one is allowed to collect data sequentially, we further propose a Bayesian two-stage estimation procedure, where a second stage posterior is built based on samples collected within a credible set arising from a first stage posterior. Under appropriate conditions on the radius of this credible set, we can accelerate optimal contraction rates in the fixed-in-advanced setting to the minimax sequential rates. A simulation experiment shows that our Bayesian two-stage procedure outperforms single-stage procedure and also slightly improves upon a non-Bayesian two-stage procedure, due to shrinkage effect of our Bayesian estimators. Show less
In the setting of nonparametric multivariate regression with unknown error variance, we study asymptotic properties of a Bayesian method for estimating a regression function f and its mixed partial... Show moreIn the setting of nonparametric multivariate regression with unknown error variance, we study asymptotic properties of a Bayesian method for estimating a regression function f and its mixed partial derivatives. We use a random series of tensor product of B-splines with normal basis coefficients as a prior for f, and the error variance is either estimated using the empirical Bayes approach or is endowed with a suitable prior in a hierarchical Bayes approach. We establish pointwise, L2 and supremum norm posterior contraction rates for f and its mixed partial derivatives, and show that they coincide with the minimax rates. Our results cover even the anisotropic situation, where the true regression function may have different smoothness in different directions. Using the convergence bounds, we show that pointwise, L2 and supremum norm credible sets for f and its mixed partial derivatives have guaranteed frequentist coverage with optimal size. New results on tensor products of B-splines are also obtained in the course. Show less
