Decreasing weight prior distributions for mixture models play an important role in nonparametric Bayesian inference. Various random probability measures with decreasing weights have been previously explored and it has shown that they provide efficient alternative to the more traditional Dirichlet process model. This ordering of implicitly alleviates so-called label switching problem, as larger ...

We obtain new local Calderón--Zygmund estimates for elliptic equations with matrix-valued weights linear as well nonlinear equations. introduce a novel log-BMO condition on the weight $\mathbb M$. In particular, we assume smallness of logarithm in BMO. This allows us to include degenerate, discontinuous weights. The assumption parameter is sharp and terms integrability exponent gradient. novelt...

Abstract Survey weighting allows researchers to account for bias in survey samples, due unit nonresponse or convenience sampling, using measured demographic covariates. Unfortunately, practice, it is impossible know whether the estimated weights are sufficient alleviate concerns about unobserved confounders incorrect functional forms used weighting. In following paper, we propose two sensitivit...