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Related Concept Videos

Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
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Estimating Population Standard Deviation01:26

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
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The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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"Exact" and Approximate Methods for Bayesian Inference: Stochastic Volatility Case Study.

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  • 1Institute for Computing and Information Sciences, Radboud University Nijmegen, Toernooiveld 212, 6525 EC Nijmegen, The Netherlands.

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Summary
This summary is machine-generated.

This study compares Bayesian inference methods for stochastic volatility models, finding particle Markov Chain Monte Carlo (MCMC) and other techniques vary in performance and adaptability. Fair assessment requires diverse data-generating processes for accurate model comparison.

Keywords:
Bayesian inferenceMarkov Chain Monte CarloRiemann Manifold Hamiltonian Monte CarloSequential Monte Carlofixed-form variational Bayesintegrated nested laplace approximationstochastic volatility

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Area of Science:

  • Computational Statistics
  • Econometrics
  • Bayesian Inference

Background:

  • Stochastic volatility models are crucial for financial econometrics, but their estimation presents computational challenges.
  • Bayesian inference methods offer a powerful framework, yet their performance can vary significantly.
  • Understanding the efficiency and adaptability of different Bayesian techniques is vital for practical applications.

Purpose of the Study:

  • To empirically evaluate and compare various Bayesian inference methods for estimating stochastic volatility models.
  • To assess the impact of different particle filtering techniques on the variance of estimated likelihoods.
  • To examine the adaptability, scalability, and feasibility of these methods in different model specifications and dimensions.

Main Methods:

  • Comparative case study of Bayesian inference techniques: particle Markov Chain Monte Carlo (MCMC), RMHMC, fixed-form variational Bayes, and integrated nested Laplace approximation.
  • Focus on estimating the posterior distribution of parameters in stochastic volatility models.
  • Evaluation criteria include adaptability to model specifications, scalability to higher dimensions, and multivariate feasibility.

Main Results:

  • Different classes of Bayesian inference methods exhibit varying performance in estimating stochastic volatility models.
  • Particle filtering methods significantly influence the variance of the estimated likelihood.
  • A fair assessment necessitates considering various data-generating processes for robust method comparison.

Conclusions:

  • No single Bayesian inference method is universally superior; choice depends on model complexity and desired properties.
  • The study highlights the importance of adaptability and feasibility for multivariate stochastic volatility models.
  • A challenging multivariate stochastic volatility model specification is presented as a practical benchmark for future method development.