Sampling rate of spatial stochastic processes with independent components in modeling random search paths

Area of Science:

• Mathematical modeling
• Computational statistics
• Search theory

Background:

• Continuous-time random search models require rotation-invariant spatial components, which are computationally expensive.
• Independent component models offer a computationally feasible alternative but may have statistical disadvantages.

Purpose of the Study:

• To investigate if independent component models can approximate rotation-invariant models under specific conditions.
• To develop a criterion for selecting sampling rates to achieve this approximation.
• To reduce computational burden in continuous-time random search modeling.

Main Methods:

• Analysis of continuous-time random search models with independent spatial components.
• Comparison of statistical properties between independent component and rotation-invariant models.
• Development of a quantitative criterion for sampling rate selection.

Main Results:

• Disadvantages of independent component models are mitigated at lower frequencies.
• A quantitative criterion was established for choosing sampling rates where independent component models approximate rotation-invariant behavior.
• The proposed criterion enables simpler model selection.

Conclusions:

• Independent component models can effectively substitute for computationally intensive rotation-invariant models in continuous-time random searches under certain sampling conditions.
• The findings provide practical guidance for selecting appropriate sampling rates to balance computational efficiency and statistical accuracy.
• This research facilitates the use of simpler, less computationally demanding models for statistical inference in random search processes.