The Horvitz-Thompson estimator is a general estimator for a population total, which can be used for any probability sampling plan. This includes both sampling with and without replacement. • Let π i be the probability that the i th unit of the population is included in the sample (inclusion probability). • On each unit i, we measure a response y i , and typically seek to estimate: τ = N i=1 y i...

In my years at the U.S. Department of Health and Human Services, we have made tremendous progress in our efforts to improve the health, safety, and well-being of the American people. The Department's recent Steps to a HealthierUS initiative aims to help Americans live longer, better, and healthier lives by reducing the burden of diabetes, overweight, obesity, asthma, heart disease and stroke, a...

The daily life routine activities require a good range of knee motion, losing that after femur fracture is common problem can be triggered by extension contracture, flexion or combined contractures. This case report about 19-year-old male with unremarkable medical history who suffered from contracture no following wrongly applied plate for distal fracture, which was treated successfully surgica...

Thompson sampling provides a solution to bandit problems in which new observations are allocated to arms with the posterior probability that an arm is optimal. While sometimes easy to implement and asymptotically optimal, Thompson sampling can be computationally demanding in large scale bandit problems, and its performance is dependent on the model fit to the observed data. We introduce bootstr...

Let p be an odd prime and S a finite p-group. B. Oliver’s conjecture arises from an open problem in the theory of p-local finite groups. It is the claim that a certain characteristic subgroup X(S) of S always contains the Thompson subgroup. In previous work the first two authors and M. Lilienthal recast Oliver’s conjecture as a statement about the representation theory of the factor group S/X(S...

Thompson Sampling (TS) has surged a lot of interest due to its good empirical performance, in particular in the computational advertising. Though successful, the tools for its performance analysis appeared only recently. In this paper, we describe and analyze SpectralTS algorithm for a bandit problem, where the payoffs of the choices are smooth given an underlying graph. In this setting, each c...

We derive an alternative proof for the regret of Thompson sampling (TS) in the stochastic linear bandit setting. While we obtain a regret bound of order e O(d3/2 p T ) as in previous results, the proof sheds new light on the functioning of the TS. We leverage on the structure of the problem to show how the regret is related to the sensitivity (i.e., the gradient) of the objective function and h...

Three groups F ⊆ T ⊆ V , known as Thompson groups, have generated interest since R. J. Thompson introduced them in the late 1960s. Part of their initial interest was the fact that T and V supplied the first known examples of infinite, simple, finitely presented groups. Since then, other properties of the groups have been studied as well as their interaction with other areas of mathematics. The ...

283 Neural correlates of perceptual decisions have been identified in the visual cortex of monkeys observing weak or ambiguous stimuli1–4. Implicit in such studies is a behavioral report about a sensory event that allows an inference about the subject’s perceptual state. To examine the link between sensation and action, we have used a signal-detection protocol to investigate visual signals in a...