This paper considers listing all possible samples of size n with unequal probabilities without replacement in order to find the sample distribution. The main application of that is to estimate the Horvitz-Thompson (HT) estimator and possibly to know the shape of its sample distribution to construct confidence intervals. The algorithm computes all possible samples of the population, in contrast ...

A nite-state machine is called a Thompson machine if it can be constructed from a regular expression using Thompson's construction. We call the underlying digraph of a Thompson machine a Thompson di-graph. We establish and prove a characterization of Thompson digraphs. As one application of the characterization, we give an algorithm that generates an equivalent regular expression from a Thompso...

In the past decade or so the term postmodernism has captured the attention of a generation of artists, intellectuals, authors, and professionals to such a degree that the term has even crept into the comparatively sober psychoanalytic literature, the last place one would have expected to find it. Yet any marriage between the psychoanalytic treatment perspective with its painstaking, laborious p...

To follow the dynamicity of the user’s content, researchers have recently started to model interactions between users and the ContextAware Recommender Systems (CARS) as a bandit problem where the system needs to deal with exploration and exploitation dilemma. In this sense, we propose to study the freshness of the user’s content in CARS through the bandit problem. We introduce in this paper an ...

nature which gave to Thompson's work a value of its own. But not less necessary for this work, upon which Thompson and the Society were alike engaged, was his ability to consider his subject from every view-point; to state in exact proportion the evidence which told in favour of, or against, a hypothesis that had to be examined. There has passed into the hands of the Societ}' an unfinished piec...

The problem of converting a regular expression to NFA is a fundamental problem that has been well studied. However, the two basic construction algorithms: (1) Thompson, (2) McNaughton-Yamada and Glushkov, both have disadvantages. In this paper: First, a “smart” parsing algorithm is developed which constructs a parse tree with at most (3l − 1) nodes form a regular expression with l literals; Sec...

A Examples of TS distributions Example 1: Uniform distribution ⌘ ⇠ UBd(0,d). The uniform distribution satisfies the concentration property with constants c = 1 and c0 = e d by definition. Since the set {⌘|uT⌘ 1}\Bd(0, p d) is an hyper-spherical cap for any direction u of Rd, the the anti-concentration property is satisfied provided that the ratio between the volume of an hyper-spherical cap of ...

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...

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...