Variance-based sensitivity of Bayesian inverse problems to the prior distribution

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of the hyperparameters defining the prior on the posterior statistics of the quantities of interest. Our approach relies on global sensitivity analysis (GSA) of Bayesian inverse problems with respect to the hyperparameters defining the prior. This, however, is a challenging problem--a naive double loop sampling approach would require running a prohibitive number of Markov chain Monte Carlo (MCMC) sampling procedures. The present work takes a foundational step in making such a sensitivity analysis practical through (i) a judicious combination of efficient surrogate models and (ii) a tailored importance sampling method. In particular, we can perform accurate GSA of posterior prediction statistics with respect to prior hyperparameters without having to repeat MCMC runs. We demonstrate the effectiveness of the approach on a simple Bayesian linear inverse problem and a nonlinear inverse problem governed by an epidemiological model

Intrathecal heparan-N-sulfatase in patients with Sanfilippo syndrome type A: A phase IIb randomized trial.

Abstract Background Sanfilippo syndrome type A (mucopolysaccharidosis type IIIA) is a lysosomal disorder wherein deficient heparan-N-sulfatase (HNS) activity results in the accumulation of heparan sulfate in the central nervous system and is associated with progressive neurodegeneration in early childhood. We report on the efficacy, pharmacokinetics, safety, and tolerability of intrathecal (IT) administration of recombinant human HNS (rhHNS) from a phase IIb randomized open-label trial. Methods Twenty-one patients, randomized 1:1:1 to rhHNS IT 45 mg administered every 2 weeks (Q2W), every 4 weeks (Q4W), or no treatment, were assessed for amelioration in neurocognitive decline as determined by the Bayley Scales of Infant and Toddler Development®, Third Edition. The primary efficacy goal was defined as ≤10-point decline (responder) in at least three patients in a dosing cohort after 48 weeks. Other efficacy assessments included adaptive behavioral function, assessments of cortical gray matter volume, and glycosaminoglycan (GAG) levels in urine. Results A clinical response to rhHNS IT was observed in three treated patients (two in the Q2W group, one in the Q4W group). Cerebrospinal fluid heparan sulfate and urine GAG levels were reduced in all treated patients. However, most secondary efficacy assessments were similar between treated patients (n = 14; age, 17.8–47.8 months) and untreated controls (n = 7; age, 12.6–45.0 months). Treatment-emergent adverse events that occurred with rhHNS IT were mostly mild, none led to study discontinuation, and there were no deaths. Conclusion rhHNS IT treatment reduced heparan sulfate and GAG levels in treated patients. Though the primary neurocognitive endpoint was not met, important lessons in the design and endpoints for evaluation of cognitive and behavioral diseases resulted. Trial registration ClinicalTrials.gov NCT02060526 ; EudraCT 2013-003450-24

Periodic Homogenization and Material Symmetry in Linear Elasticity

Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic material and the material symmetries of the effective, macroscopic elasticity tensor. Previous results of this type exist but here more general symmetries on the microscale are considered. Using an explicit example, we show that it is possible for a material to be fully anisotropic on the microscale and yet the symmetry group on the macroscale can contain elements other than plus or minus the identity. Another example demon- strates that not all material symmetries of the macroscopic elastic tensor are generated by symmetries of the periodic elastic structure.Comment: 18 pages, 5 figure