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Survival analysis is a statistical method used to analyze time-to-event data, often employed in fields such as medicine, engineering, and social sciences. One of the key challenges in survival analysis is dealing with incomplete data, a phenomenon known as "censoring." Censoring occurs when the event of interest (such as death, relapse, or system failure) has not occurred for some individuals by the end of the study period or is otherwise unobservable, and it might have many different...
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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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Time Series of Counts under Censoring: A Bayesian Approach.

Isabel Silva1, Maria Eduarda Silva2, Isabel Pereira3

  • 1Faculdade de Engenharia, Universidade do Porto, CIDMA, 4200-465 Porto, Portugal.

Entropy (Basel, Switzerland)
|May 16, 2023
PubMed
Summary
This summary is machine-generated.

This study addresses censored data in time series analysis using convolution closed infinitely divisible (CCID) models. Bayesian methods, including Approximate Bayesian Computation (ABC) and Gibbs sampler with Data Augmentation (GDA), are employed for accurate estimation and inference.

Keywords:
Bayesian estimationPoisson INAR(1) modelcensored time seriesconvolution closed infinitely divisible

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Area of Science:

  • Statistics
  • Time Series Analysis
  • Data Science

Background:

  • Censored data, common in environmental, medical, and economic fields, arise when observations are limited by detection thresholds.
  • Ignoring data censoring leads to biased statistical estimates and unreliable inferences.
  • Accurate statistical modeling is crucial for fields relying on observational data.

Purpose of the Study:

  • To develop and apply Convolution Closed Infinitely Divisible (CCID) models for time series count data with censoring.
  • To enhance estimation and inference techniques for censored time series data.
  • To provide robust statistical methods for handling restricted observational ranges.

Main Methods:

  • Utilized Bayesian approaches for statistical modeling.
  • Implemented Approximate Bayesian Computation (ABC) algorithms for parameter estimation.
  • Employed Gibbs sampler with Data Augmentation (GDA) for inference on censored count time series.

Main Results:

  • Demonstrated the effectiveness of CCID models in handling censored time series data.
  • Provided reliable parameter estimates and statistical inferences, mitigating bias from censoring.
  • Validated the performance of Bayesian methods (ABC and GDA) in this context.

Conclusions:

  • CCID models offer a robust framework for analyzing censored count time series.
  • Bayesian inference methods, specifically ABC and GDA, are suitable for addressing estimation challenges with censored data.
  • The study contributes advanced statistical tools for disciplines encountering data limitations.