Time-Varying Uncertainty of the Federal Reserve's Output Gap Estimate

A factor stochastic volatility model estimates the common component to output gap estimates produced by the staff of the Federal Reserve, its time-varying volatility, and time-varying, horizon-specific forecast uncertainty. The output gap estimates are uncertain even well after the fact. Nevertheless, the common component is clearly procyclical, and positive innovations to the common component produce movements in macroeconomic variables consistent with an increase in aggregate demand. Heightened macroeconomic uncertainty, as measured by the common component's volatility, leads to persistently negative economic responses.

On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation

In this paper the nonlinear multi-species Boltzmann equation with random uncertainty coming from the initial data and collision kernel is studied. Well-posedness and long-time behavior – exponential decay to the global equilibrium – of the analytical solution, and spectral gap estimate for the corresponding linearized gPC-based stochastic Galerkin system are obtained, by using and extending the analytical tools provided in [M. Briant and E. S. Daus, Arch. Ration. Mech. Anal., 3, 1367–1443, 2016] for the deterministic problem in the perturbative regime, and in [E. S. Daus, S. Jin and L. Liu, Kinet. Relat. Models, 12, 909–922, 2019] for the single-species problem with uncertainty. The well-posedness result of the sensitivity system presented here has not been obtained so far even for the single-species case.

Brain Age in Early Stages of Bipolar Disorders or Schizophrenia

Background The greater presence of neurodevelopmental antecedants may differentiate schizophrenia from bipolar disorders (BD). Machine learning/pattern recognition allows us to estimate the biological age of the brain from structural magnetic resonance imaging scans (MRI). The discrepancy between brain and chronological age could contribute to early detection and differentiation of BD and schizophrenia. Methods We estimated brain age in 2 studies focusing on early stages of schizophrenia or BD. In the first study, we recruited 43 participants with first episode of schizophrenia-spectrum disorders (FES) and 43 controls. In the second study, we included 96 offspring of bipolar parents (48 unaffected, 48 affected) and 60 controls. We used relevance vector regression trained on an independent sample of 504 controls to estimate the brain age of study participants from structural MRI. We calculated the brain-age gap estimate (BrainAGE) score by subtracting the chronological age from the brain age. Results Participants with FES had higher BrainAGE scores than controls (F(1, 83) = 8.79, corrected P = .008, Cohen’s d = 0.64). Their brain age was on average 2.64 ± 4.15 years greater than their chronological age (matched t(42) = 4.36, P < .001). In contrast, participants at risk or in the early stages of BD showed comparable BrainAGE scores to controls (F(2,149) = 1.04, corrected P = .70, η2 = 0.01) and comparable brain and chronological age. Conclusions Early stages of schizophrenia, but not early stages of BD, were associated with advanced BrainAGE scores. Participants with FES showed neurostructural alterations, which made their brains appear 2.64 years older than their chronological age. BrainAGE scores could aid in early differential diagnosis between BD and schizophrenia.