Bernoulli race particle filters

When the weights in a particle filter are not available analytically, standard resampling methods cannot be employed. To circumvent this problem state-of-the-art algorithms replace the true weights with non-negative unbiased estimates. This algorithm is still valid but at the cost of higher variance of the resulting filtering estimates in comparison to a particle filter using the true weights. We propose here a novel algorithm that allows for resampling according to the true intractable weights when only an unbiased estimator of the weights is available. We demonstrate our algorithm on several examples

Bernoulli race particle filters

When the weights in a particle filter are not available analytically, standard resampling methods cannot be employed. To circumvent this problem state-of-the-art algorithms replace the true weights with non-negative unbiased estimates. This algorithm is still valid but at the cost of higher variance of the resulting filtering estimates in comparison to a particle filter using the true weights. We propose here a novel algorithm that allows for resampling according to the true intractable weights when only an unbiased estimator of the weights is available. We demonstrate our algorithm on several examples

Large sample asymptotics of the pseudo-marginal method

The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density. Practically, one has to trade-off the computational resources used to obtain this estimator against the asymptotic variances of the ergodic averages obtained by the pseudo-marginal algorithm. Recent works optimizing this trade-off rely on some strong assumptions which can cast doubts over their practical relevance. In particular, they all assume that the distribution of the difference between the log-density and its estimate is independent of the parameter value at which it is evaluated. Under regularity conditions we show here that, as the number of data points tends to infinity, a space-rescaled version of the pseudo-marginal chain converges weakly towards another pseudo-marginal chain for which this assumption indeed holds. A study of this limiting chain allows us to provide parameter dimension-dependent guidelines on how to optimally scale a normal random walk proposal and the number of Monte Carlo samples for the pseudo-marginal method in the large-sample regime. This complements and validates currently available results

Journal of the American Veterinary Medical Association 209 10 1733 1736 UNITED STATES

Double-phase parathyroid gland scintigraphy, using technetium Tc 99m sestamibi, correctly identified the existence and location of a parathyroid adenoma in a dog with primary hyperparathyroidism. The parathyroid adenoma was removed surgically 2 days after scintigraphy. An area of focal radionuclide uptake persisted in the region corresponding to the left external parathyroid gland in the delayed-phase image. Delayed-phase images from 3 healthy dogs and a dog with hypercalcemia of malignancy caused by lymphoma did not reveal an area of persistent radiotracer uptake. Double-phase parathyroid gland scintigraphy, using 99mTc-sestamibi, is a simple, rapid, noninvasive test, which can be used for detection and localization of parathyroid adenomas in hypercalcemic dogs. It also can help to differentiate these dogs from dogs with hypercalcemia of malignancy