For estimating a lower bounded location or mean parameter for a symmetric and logconcave density, we investigate the frequentist performance of the 100(1 − α)% Bayesian HPD credible set associated with priors which are truncations of flat priors onto the restricted parameter space. Various new properties are obtained. Namely, we identify precisely where the minimum coverage is obtained and we show that this minimum coverage is bounded between 1 − 3α 2 and 1 − 3α 2 + α 2 1+α ; with the lower bound 1 − 3α 2 improving (for α ≤ 1/3) on the previously established ([9]; [8]) lower bound 1−α 1+α . Several illustrative examples are given.AMS 2000 subject classifications: 62F10, 62F30, 62C10, 62C15, 35Q15, 45B05, 42A99.

Adjustment techniques to mitigate selection bias in nonprobability samples often involve modelling the propensity to participate in the nonprobability sample along with inverse propensity weighting. It is well known that procedures for estimating weights are effective if the covariates selected in the propensity model are related to both the variable of interest and the participation indicator. In most surveys, there are many variables of interest, making weight adjustments difficult to determine as a suitable weight for one variable may be unsuitable for other variables. The standard compromise is to include a large number of covariates in the propensity model but this may increase the variability of the estimates, especially when some covariates are weakly related to the variables of interest. Weight smoothing, developed for probability surveys, could be helpful in these situations. It aims to remove the variability caused by overfit propensity models by replacing the inverse propensity weights with predicted weights obtained using a smoothing model. In this article, we study weight smoothing in the nonprobability survey context, both theoretically and empirically, to understand its effectiveness at improving the efficiency of estimates.