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Precipitation Processes01:12

Precipitation Processes

2.4K
The experimental conditions in a gravimetric analysis should be optimized to maximize the particle size and purity of the obtained precipitate. Ideally, the concentration of the precipitating reagent should be low with effective stirring to maintain low relative supersaturation for the growth of large crystals. In homogeneous precipitation, the precipitant is slowly generated by a chemical reaction in the solution to avoid local reagent excesses. For example, urea decomposes gradually to...
2.4K
Prediction Intervals01:03

Prediction Intervals

2.7K
The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
2.7K
Precipitation and Co-precipitation01:17

Precipitation and Co-precipitation

3.2K
Precipitation and coprecipitation methods can be used to separate a mixture of ions in a solution. In qualitative inorganic analysis, ions that form sparingly soluble precipitates with the same reagent are separated based on the differences in solubility products. For example, consider the separation of Cu(II) and Fe(II) ions by precipitation as insoluble sulfides. First, copper(II) sulfide is precipitated by the addition of acidic H2S, where the dissociation of H2S is suppressed. Adding H2S...
3.2K
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

166
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...
166
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

2.0K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
2.0K
Steps in Outbreak Investigation01:18

Steps in Outbreak Investigation

330
In the ever-evolving field of public health, statistical analysis serves as a cornerstone for understanding and managing disease outbreaks. By leveraging various statistical tools, health professionals can predict potential outbreaks, analyze ongoing situations, and devise effective responses to mitigate impact. For that to happen, there are a few possible stages of the analysis:
330

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Related Experiment Video

Updated: Nov 17, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

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A framework for probabilistic weather forecast post-processing across models and lead times using machine learning.

Charlie Kirkwood1, Theo Economou1, Henry Odbert2

  • 1College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|February 15, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a machine learning framework to combine multiple numerical weather prediction (NWP) models. The method generates well-calibrated probabilistic forecasts for improved decision-making in weather forecasting.

Keywords:
artificial intelligencedata integrationdecision theorymodel stackingquantile regressionuncertainty quantification

Related Experiment Videos

Last Updated: Nov 17, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

10.8K

Area of Science:

  • Meteorology
  • Machine Learning
  • Data Science

Background:

  • Numerical weather prediction (NWP) models are increasing in complexity and number.
  • Combining forecasts from multiple NWP models with unique biases presents a challenge for operational meteorologists.
  • There is a need for well-calibrated probabilistic forecasts for effective decision support.

Purpose of the Study:

  • To demonstrate a machine learning framework for post-processing weather forecasts from multiple NWP models.
  • To bridge the gap between raw NWP model outputs and decision-support-ready probabilistic forecasts.
  • To improve the calibration and utility of weather forecasts for stakeholders.

Main Methods:

  • A three-stage machine learning framework was developed.
  • Quantile regression forests were used to learn individual NWP model error profiles.
  • Probabilistic forecasts were combined using quantile averaging and interpolated to form a predictive distribution.

Main Results:

  • The framework effectively learns and corrects for individual model biases.
  • Quantile averaging successfully combined probabilistic forecasts from different models.
  • The generated predictive distribution demonstrated properties suitable for decision support.

Conclusions:

  • The proposed machine learning framework offers an effective and operationally viable method for cohesive post-processing of weather forecasts.
  • This approach yields well-calibrated probabilistic outputs across multiple models and lead times.
  • The methodology enhances the usability of weather forecasts for critical decision-making.