Statistical Inference Task

A Statistical Inference Task is an inference task that is a statistical task (which requires a statistical inference that is based on a population sample).

• Context:
  • It can (typically) require Core Statistical Elements, such as:
    • It can need random sampling from a target population.
    • It can involve probability model specification.
    • It can demand statistical assumption verification.
  • It can (typically) perform Inference Functions, such as:
    • It can estimate population parameters through sample statistics.
    • It can test statistical hypothesises about population propertys.
    • It can predict future observations based on observed patterns.
  • It can (often) utilize Statistical Methods, such as:
    • It can employ confidence intervals for parameter estimation.
    • It can use significance tests for hypothesis evaluation.
    • It can leverage prediction models for future value estimation.
  • It can range from being a Simple Inference Task to being a Complex Inference Task, depending on its inference complexity.
  • It can range from being a Parametric Inference to being a Non-Parametric Inference, depending on its distribution assumptions.
  • It can range from being a Single Parameter Inference to being a Multiple Parameter Inference, depending on its parameter scope.
  • ...
• Examples:
  • Parameter Estimation Tasks, such as:
    • Mean Estimation Tasks, such as:
      • Estimating population mean from sample data.
      • Calculating confidence intervals for mean estimates.
    • Proportion Estimation Tasks, such as:
      • Estimating population proportions from sample counts.
      • Determining market share from customer samples.
  • Hypothesis Testing Tasks, such as:
    • Group Comparison Tasks, such as:
      • Testing treatment effects in clinical trials.
      • Comparing product performance across market segments.
    • Relationship Testing Tasks, such as:
      • Analyzing correlation between variables.
      • Testing independence of categorical variables.
  • Predictive Inference Tasks, such as:
    • Point Prediction Tasks, such as:
      • Predicting future sales from historical data.
      • Estimating election outcomes from polling data.
    • Interval Prediction Tasks, such as:
      • Forecasting confidence bounds for economic indicators.
      • Predicting range of future values.
  • Model-Based Inference Tasks, such as:
    • Distribution Inference Tasks, such as:
      • Identifying probability distribution of random variables.
      • Testing goodness of fit for statistical models.
    • Causal Inference Tasks, such as:
      • Analyzing treatment effects in observational studys.
      • Identifying causal relationships in complex systems.
  • ...
• Counter-Examples:
  • Logical Inference Tasks, which use deductive reasoning rather than statistical methods.
  • Descriptive Statistics Tasks, which summarize observed data without population inference.
  • Data Visualization Tasks, which display data patterns without making statistical conclusions.
  • Database Query Tasks, which retrieve known information rather than make inferences.
• See: Statistical Method, Inference Algorithm, Probability Model, Sampling Theory, Statistical Analysis.

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References

2016

• (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/Statistical_inference Retrieved:2016-8-3.
  • Statistical inference is the process of deducing properties of an underlying distribution by analysis of data. Inferential statistical analysis infers properties about a population: this includes testing hypotheses and deriving estimates. The population is assumed to be larger than the observed data set; in other words, the observed data is assumed to be sampled from a larger population.

    Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and does not assume that the data came from a larger population.

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