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Related Concept Videos

Sampling Plans01:23

Sampling Plans

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...
Cluster Sampling Method01:20

Cluster Sampling Method

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.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

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.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...

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Related Experiment Videos

Data-based stochastic subgrid-scale parametrization: an approach using cluster-weighted modelling.

Frank Kwasniok1

  • 1College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK. f.kwasniok@exeter.ac.uk

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|February 1, 2012
PubMed
Summary
This summary is machine-generated.

A novel data-driven method improves weather and climate models by using local models for unresolved processes. This cluster-weighted Markov chain scheme enhances prediction accuracy compared to existing methods.

Related Experiment Videos

Area of Science:

  • Atmospheric Sciences
  • Computational Science
  • Data Science

Background:

  • Numerical weather and climate prediction models require accurate parametrization of subgrid-scale processes.
  • Existing methods often struggle to capture the complex, state-dependent nature of these unresolved scales.

Purpose of the Study:

  • To introduce a new data-based stochastic parametrization approach for unresolved scales in prediction models.
  • To develop a subgrid-scale model conditional on the resolved scales using a collection of local models.

Main Methods:

  • A clustering algorithm in the resolved variable space was combined with statistical modeling of unresolved variables.
  • Clusters and subgrid model parameters were simultaneously estimated from data.
  • The approach was implemented using discrete Markov processes within the Lorenz '96 model framework.

Main Results:

  • The cluster-weighted Markov chain scheme demonstrated superior performance over simple parametrization methods.
  • The new scheme showed favorable comparisons with other advanced subgrid modeling techniques.
  • Effective for both long-term simulations and ensemble predictions.

Conclusions:

  • The proposed data-based stochastic parametrization offers a significant advancement for numerical weather and climate prediction.
  • Conditional Markov chains provide a robust framework for modeling unresolved processes.
  • This approach enhances the accuracy and reliability of climate and weather models.