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Related Concept Videos

Sampling Methods: Overview01:06

Sampling Methods: Overview

3.7K
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...
3.7K
Cluster Sampling Method01:20

Cluster Sampling Method

11.0K
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...
11.0K
Downsampling01:20

Downsampling

872
When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
872
Sampling Plans01:23

Sampling Plans

1.5K
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...
1.5K
Sampling Distribution01:12

Sampling Distribution

17.6K
Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
17.6K
Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

3.3K
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...
3.3K

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Related Experiment Videos

Learning with kernel smoothing models and low-discrepancy sampling.

Cristiano Cervellera, Danilo Macciò

    IEEE Transactions on Neural Networks and Learning Systems
    |May 9, 2014
    PubMed
    Summary

    This study shows kernel smoothing models perform well when training data is chosen using low-discrepancy sequences. This combination ensures accurate function estimation and error convergence for machine learning tasks.

    Related Experiment Videos

    Area of Science:

    • Machine Learning
    • Numerical Analysis
    • Statistical Modeling

    Background:

    • Kernel smoothing models are used for function estimation.
    • The selection of training data influences model performance.
    • Low-discrepancy sequences are efficient sampling methods.

    Purpose of the Study:

    • To analyze the performance of kernel smoothing models.
    • To investigate the impact of low-discrepancy sequences on training set selection.
    • To evaluate convergence rates of estimation and approximation errors.

    Main Methods:

    • Kernel smoothing model analysis.
    • Low-discrepancy sequence sampling.
    • Empirical risk minimization consistency proofs.
    • Convergence rate analysis.

    Main Results:

    • Consistency of empirical risk minimization is guaranteed.
    • Good convergence rates for estimation error.
    • Convergence of approximation error is achieved.
    • Simulations confirm theoretical properties.

    Conclusions:

    • Combining kernel smoothing with low-discrepancy sampling yields strong theoretical properties.
    • This approach is effective for estimating unknown target functions.
    • The method demonstrates practical utility in machine learning applications.