Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Application of Rates of Change01:18

Application of Rates of Change

64
The movement of a car along a highway can be examined through key principles of calculus and kinematics. As the car travels, its position varies over time and can be represented mathematically as a function of time. Analyzing the rate of these changes enables the measurement of velocity and acceleration, fundamental aspects of motion analysis.Velocity describes how position changes over time. The average velocity during a specific time interval is calculated by dividing the change in position...
64
Rates of Change01:20

Rates of Change

33
The rate of change is a central concept in mathematics that quantifies how one variable varies in response to another. It serves as a foundational tool in modeling dynamic systems across disciplines such as physics, biology, economics, and engineering. Understanding both average and instantaneous rates of change enables the analysis of behavior in functions that describe real-world phenomena.Average Rate of ChangeFor a function f(x) defined over an interval [x1,x2], the average rate of change...
33
Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

1.1K
Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...
1.1K
Relative Velocity in One Dimension01:10

Relative Velocity in One Dimension

9.7K
The understanding of the concept of reference frames is essential to discuss relative motion in one or more dimensions. When we say that an object has a certain velocity, we must state the velocity with respect to a given reference frame. In most examples, this reference frame has been Earth. For instance, if a statement reads that a person is sitting in a train moving at 10 m/s east, then it implies that the person on the train is moving relative to the surface of Earth at this velocity,...
9.7K
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

861
In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
861
Related Rates01:18

Related Rates

22
When two or more physical quantities are linked by a single relationship, a change in one variable necessarily affects the others. This interdependence forms the basis of related rates analysis, which examines how different quantities change with respect to time. A classic physical example is an expanding balloon, where the size of the balloon changes continuously as air is added.For a hot air balloon, the inflated envelope is commonly idealized as a perfect sphere to simplify mathematical...
22

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

On prior smoothing with discrete spatial data in the context of disease mapping.

Statistical methods in medical research·2025
Same author

Spatial Modeling With Spatially Varying Coefficient Processes.

Journal of the American Statistical Association·2024
Same author

Mechanistic modeling of climate effects on redistribution and population growth in a community of fish species.

Global change biology·2023
Same author

Assessing Disparity Using Measures of Racial and Educational Isolation.

International journal of environmental research and public health·2021
Same author

Spatial Joint Species Distribution Modeling using Dirichlet Processes.

Statistica Sinica·2019
Same author

Alternating Gaussian Process Modulated Renewal Processes for Modeling Threshold Exceedances and Durations.

Stochastic environmental research and risk assessment : research journal·2018
Same journal

Instrumental Variable Estimation of Marginal Structural Mean Models for Time-Varying Treatment.

Journal of the American Statistical Association·2026
Same journal

Semiparametric Joint Modeling for Survival Analysis with Longitudinal Covariates.

Journal of the American Statistical Association·2026
Same journal

Dimension Reduction for Large-Scale Federated Data: Statistical Rate and Asymptotic Inference.

Journal of the American Statistical Association·2026
Same journal

Facilitating Heterogeneous Effect Estimation via Statistically Efficient Categorical Modifiers.

Journal of the American Statistical Association·2026
Same journal

Nonparametric Density Estimation of a Long-Term Trend from Repeated Semicontinuous Data.

Journal of the American Statistical Association·2026
Same journal

Functional Integrative Bayesian Analysis of High-dimensional Multiplatform Clinicogenomic Data.

Journal of the American Statistical Association·2026
See all related articles

Related Experiment Video

Updated: Jan 17, 2026

Measuring Attention and Visual Processing Speed by Model-based Analysis of Temporal-order Judgments
13:00

Measuring Attention and Visual Processing Speed by Model-based Analysis of Temporal-order Judgments

Published on: January 23, 2017

10.3K

Directional Rates of Change Under Spatial Process Models.

Banerjee Sudipto1, Alan E Gelfand2, C F Sirmans3

  • 1Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455.

Journal of the American Statistical Association
|September 18, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces methods for analyzing spatial surface changes using directional finite difference and derivative processes. These techniques are applied within a Bayesian framework for real estate and simulated data analysis.

Keywords:
GradientMatèrn correlation functionOrthonormal basisScale of resolutionSlice Gibbs samplerStationary Gaussian process

More Related Videos

Methods to Explore the Influence of Top-down Visual Processes on Motor Behavior
09:49

Methods to Explore the Influence of Top-down Visual Processes on Motor Behavior

Published on: April 16, 2014

26.8K
High-Throughput Analysis of Optical Mapping Data Using ElectroMap
07:36

High-Throughput Analysis of Optical Mapping Data Using ElectroMap

Published on: June 4, 2019

10.0K

Related Experiment Videos

Last Updated: Jan 17, 2026

Measuring Attention and Visual Processing Speed by Model-based Analysis of Temporal-order Judgments
13:00

Measuring Attention and Visual Processing Speed by Model-based Analysis of Temporal-order Judgments

Published on: January 23, 2017

10.3K
Methods to Explore the Influence of Top-down Visual Processes on Motor Behavior
09:49

Methods to Explore the Influence of Top-down Visual Processes on Motor Behavior

Published on: April 16, 2014

26.8K
High-Throughput Analysis of Optical Mapping Data Using ElectroMap
07:36

High-Throughput Analysis of Optical Mapping Data Using ElectroMap

Published on: June 4, 2019

10.0K

Area of Science:

  • Spatial statistics
  • Geostatistics
  • Environmental modeling

Background:

  • Spatial process models are crucial for data inference across various fields.
  • Interest often lies in quantifying the rate of change (gradients) of spatial surfaces.
  • Examples include environmental gradients and digital elevation model assessments.

Purpose of the Study:

  • To formalize directional finite difference and derivative processes for spatial surfaces.
  • To develop a complete distribution theory for these processes under Gaussian assumptions.
  • To present a Bayesian inference framework for analyzing spatial rates of change.

Main Methods:

  • Building upon mean square differentiability concepts.
  • Assuming stationary Gaussian process models for data or spatial random effects.
  • Employing a Bayesian framework for inference.

Main Results:

  • Complete distribution theory results are obtained.
  • The Bayesian approach offers advantages for this type of spatial analysis.
  • Methodology demonstrated on simulated and real estate datasets.

Conclusions:

  • The proposed methods provide a robust framework for analyzing directional changes in spatial surfaces.
  • The Bayesian inference is effective for spatial process modeling.
  • The approach is applicable to diverse real-world datasets, including property prices.