Sampling Algorithm

A Sampling Algorithm is a data processing algorithm that can solve a sampling task (select a random sample from a statistical population efficiently).

• AKA: Sampling Technique, Sample Selection Method.
• Context:
  • It can (typically) implement Core Sampling Elements, such as:
    • It can utilize randomization methods for unbiased selection.
    • It can ensure sample representativeness through selection criteria.
    • It can maintain selection efficiency through algorithmic optimization.
  • It can (typically) support Sampling Objectives, such as:
    • It can enable population inference through representative samples.
    • It can reduce computational costs through data reduction.
    • It can facilitate statistical analysis through manageable subsets.
  • It can (often) handle Sampling Challenges, such as:
    • It can address population size issues through efficient selection.
    • It can manage bias control through randomization techniques.
    • It can ensure sample quality through validation methods.
  • It can range from being a Probability Sampling Algorithm to being a Non-Probability Sampling Algorithm, depending on its selection method.
  • It can range from being a Simple Sampling Algorithm to being a Complex Sampling Algorithm, depending on its computational complexity.
  • It can range from being a Single-Stage Sampling to being a Multi-Stage Sampling, depending on its selection process.
  • ...
• Examples:
  • Probability Sampling Methods, such as:
    • Simple Random Samplings, such as:
      • Random Number Based Selection for uniform probability.
      • Systematic Random Selection with fixed intervals.
    • Stratified Samplings, such as:
      • Proportional Allocation across population subgroups.
      • Optimal Allocation based on stratum variances.
  • Advanced Sampling Methods, such as:
    • Monte Carlo Samplings, such as:
      • Importance Sampling for rare events.
      • Metropolis-Hastings Algorithm for complex distributions.
    • Sequential Samplings, such as:
      • Reservoir Sampling for streaming data.
      • Progressive Sampling with increasing sizes.
  • Specialized Sampling Methods, such as:
    • Cluster Samplings, such as:
      • Single-Stage Cluster Sampling of natural groups.
      • Multi-Stage Cluster Sampling with hierarchical selection.
    • Weight-Based Samplings, such as:
      • Consistent Weighted Sampling for weighted elements.
      • Probability Proportional Sampling to element sizes.
  • Adaptive Sampling Methods, such as:
    • Dynamic Samplings, such as:
      • Thompson Sampling for online learning.
      • Adaptive Cluster Sampling based on observed patterns.
    • Hybrid Samplings, such as:
      • Mixed Mode Sampling combining multiple methods.
      • Adaptive Stratification with dynamic boundarys.
  • ...
• Counter-Examples:
  • Complete Enumeration Algorithms, which process entire populations.
  • Deterministic Selection Algorithms, which use fixed criteria without randomization.
  • Exhaustive Search Algorithms, which examine all possibilitys.
  • Sorting Algorithms, which order elements rather than sample them.
• See: Statistical Sampling, Random Selection, Population Analysis, Sample Design, Data Reduction.

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References

2009

• http://en.wikipedia.org/wiki/Sampling_(statistics)
  • Sampling is that part of statistical practice concerned with the selection of individual observations intended to yield some knowledge about a population of concern, especially for the purposes of statistical inference. Each observation measures one or more properties (weight, location, etc.) of an observable entity enumerated to distinguish objects or individuals. Survey weights often need to be applied to the data to adjust for the sample design. Results from probability theory and statistical theory are employed to guide practice. In business, sampling is widely used for gathering information about a population. [1]
• http://en.wikipedia.org/wiki/Sampling_(statistics)
  • • 4 Probability and nonprobability sampling
    • 5 Sampling methods

         o 5.1 Simple random sampling
         o 5.2 Systematic sampling
         o 5.3 Stratified sampling
         o 5.4 Probability proportional to size sampling
         o 5.5 Cluster sampling
         o 5.6 Matched random sampling
         o 5.7 Quota sampling
         o 5.8 Mechanical sampling
         o 5.9 Convenience sampling
         o 5.10 Line-intercept sampling
         o 5.11 Panel sampling
         o 5.12 Event Sampling Methodology

2006

• (Yves Tillé, 2006) ⇒ Yves Tillé. (2006). “Sampling Algorithms." Springer. ISBN:0387308148.
  • A sampling algorithm is a procedure used to select a sample. If the sampling design is known and if the population size is not too large, sa sample can be selected directly by enumerating all the samples as explained in Section 3.3. Nevertheless, when [math]\displaystyle{ N }[/math] is large, the number of possible samples becomes so large that it is practically impossible to enumerate all the samples. The objective of a sampling algorithm is to select a sample by avoiding the enumeration of all the samples. The main difficult of these implementation is thus the combinatory explosion of the number of possible samples.
  • Definition 31. A sampling algorithm is a procedure allowing the selection of a random sample.
  • Definition 32. A sampling algorithm is said to be enumerative if all the possible samples must be listed in order to select the random sample.
  • An efficient sampling algorithm is by definition a fast one. All enumerative algorithms are therefore inefficient.

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