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Related Concept Videos

Prediction Intervals01:03

Prediction Intervals

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. 
The...
Random Variables01:09

Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
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)...
Random Error01:04

Random Error

Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...

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Related Experiment Videos

Accident prediction models with random corridor parameters.

Karim El-Basyouny1, Tarek Sayed

  • 1Dept. of Civil Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z4. basyouny@civil.ubc.ca

Accident; Analysis and Prevention
|August 12, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces random parameter count models for analyzing urban road accident frequencies. A Poisson-lognormal model revealed that corridor-specific effects significantly impact accident rates, improving model fit and understanding.

Related Experiment Videos

Area of Science:

  • Transportation Engineering
  • Statistical Modeling
  • Traffic Safety Analysis

Background:

  • Accurate analysis of accident frequencies is crucial for urban road safety.
  • Traditional count models may not fully capture spatial heterogeneity in accident data.
  • Random parameter models offer a potential improvement for analyzing complex accident data.

Purpose of the Study:

  • To assess the impact of corridor-specific effects on accident frequencies using advanced statistical models.
  • To compare alternative model specifications for analyzing accident data on urban arterials.
  • To identify significant covariates influencing accident frequencies and their spatial variability.

Main Methods:

  • Utilized a dataset of urban arterials in Vancouver, British Columbia, comprising 392 segments clustered into 58 corridors.
  • Estimated proposed models within a Full Bayes context using Markov Chain Monte Carlo (MCMC) simulation.
  • Compared model goodness of fit and inference across different specifications, including Poisson-lognormal (PLN) models with random parameters.

Main Results:

  • Several covariates were found to significantly influence accident frequencies.
  • These covariates exhibited random parameters, indicating significant variation in their effects across different corridors.
  • The Poisson-lognormal (PLN) model incorporating random corridor effects provided the best fit to the data.

Conclusions:

  • The inclusion of random corridor effects significantly improves the goodness of fit for accident frequency models.
  • This approach enhances understanding of how covariates influence accident frequencies and accounts for unobserved heterogeneity.
  • Accounting for corridor effects can lead to more robust model inference by explaining significant variation in accident data.