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Related Concept Videos

Sampling Plans01:23

Sampling Plans

Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
Sampling Methods: Overview01:06

Sampling Methods: Overview

A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of sampling...
Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
Random Sampling Method01:09

Random Sampling Method

Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

Sampling materials are classified into three main types: solid, liquid, and gas.
Solid samples include a variety of substances, such as sediments from water bodies, soil, metals, and biological tissues. Two standard methods for extracting sediments from water bodies are grab sampling and piston coring. Grab sampling involves using a device to collect a discrete sediment sample from the bottom of a water body with minimal disturbance. Grab samples do not always represent the entire area due to...

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The Penalized Profile Sampler.

Guang Cheng1, Michael R Kosorok

  • 1Department of Statistical Science, Duke University, 214 Old Chemistry Building, Durham, NC 27708, USA.

Journal of Multivariate Analysis
|May 1, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a penalized profile sampler for semiparametric inference, offering an approximately Bayesian approach. The method adjusts accuracy via a smoothing parameter, avoiding complex priors for nuisance components.

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Area of Science:

  • Statistics
  • Statistical Inference

Background:

  • Semiparametric models involve both parametric and non-parametric components.
  • Nuisance parameters in these models often pose challenges for inference.
  • Existing methods may require specifying priors for infinite-dimensional components.

Purpose of the Study:

  • To introduce and evaluate a penalized profile sampler for semiparametric inference.
  • To develop an approximately Bayesian method that avoids priors on nuisance parameters.
  • To assess the frequentist performance and accuracy of the proposed sampler.

Main Methods:

  • Extending the profile sampler by profiling a penalized log-likelihood.
  • Applying profiling and penalization to nuisance parameters.
  • Using a prior only on the parametric component, not the full likelihood.

Main Results:

  • The penalized profile sampler demonstrates adjustable accuracy through the smoothing parameter.
  • First and second-order frequentist performance was investigated.
  • Theoretical validity was shown for partly linear and logistic regression models.

Conclusions:

  • The penalized profile sampler offers a flexible and accurate approach to semiparametric inference.
  • It effectively bypasses the need for priors on nuisance components.
  • Simulation studies confirm the theoretical findings and practical utility.