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Sampling Plans01:23

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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...
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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.
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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...
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Cluster Sampling Method01:20

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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.
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Sampling Methods: Overview01:06

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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. 
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Random Sampling Method01:09

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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...
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    Approximate dynamic programming (ADP) effectively solves Markovian decision problems by improving state-space sampling. This study introduces a novel hybrid approach for infinite-horizon problems, balancing system-driven and uniform sampling for better value function approximation.

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    Area of Science:

    • Operations Research
    • Artificial Intelligence
    • Control Theory

    Background:

    • Approximate dynamic programming (ADP) is crucial for solving Markovian decision problems.
    • The curse of dimensionality necessitates efficient state-space sampling for value function approximation.
    • Existing sampling methods include uniform covering and system trajectory-driven approaches.

    Purpose of the Study:

    • To extend the F-discrepancy framework for efficient ADP sampling to infinite-horizon discounted problems.
    • To develop a constructive algorithm for generating system-behavior-driven sampling points.
    • To refine the algorithm into a hybrid approach balancing system-driven and uniform sampling.

    Main Methods:

    • Extension of the F-discrepancy concept to infinite-horizon discounted Markovian decision problems.
    • Development of a constructive algorithm for generating sampling points based on system behavior.
    • Refinement of the algorithm to create a hybrid sampling strategy.
    • Theoretical analysis using a novel F-discrepancy notion and simulation tests.

    Main Results:

    • A constructive algorithm for generating efficient sampling points for infinite-horizon ADP.
    • A refined hybrid sampling method that balances system-driven and uniform designs.
    • Theoretical validation of the proposed F-discrepancy and sampling properties.
    • Demonstration of the sampling method's effectiveness through simulations.

    Conclusions:

    • The proposed hybrid sampling method enhances ADP efficiency for infinite-horizon problems.
    • The novel F-discrepancy framework provides theoretical underpinnings for improved sampling.
    • This approach offers a more balanced and effective state-space exploration for ADP.