Morris MethodEdit

The Morris Method, sometimes referred to in literature as the Morris screening method, is a widely used approach to global sensitivity analysis in computational modeling. It provides a pragmatic way to identify which input factors are most influential on a model’s outputs while keeping the computational cost modest. By focusing on elementary effects—the impact of small, discrete changes in inputs along a sequence of model evaluations—the method offers a quick diagnostic tool for prioritizing data collection, model refinement, and risk assessment in a variety of fields, from engineering to environmental policy.

In practice, the Morris Method sits at the intersection of simplicity and insight. It does not pretend to deliver the exact, quantitative fingerprint of every interaction among inputs; instead, it flags which factors merit serious attention before investing in more intensive analyses. This makes it especially useful in early-stage modeling, when resources are limited and decisions must be made about where to devote effort. The approach also aligns well with a conservative, efficiency-minded mindset that favors proven ROI in research and policy work. global sensitivity analysis is the broader framework in which Morris operates, and the method connects naturally with related ideas such as elementary effects and factorial design.

Overview

The core idea of the Morris Method is to probe a high-dimensional input space by constructing several random, one-at-a-time (OAT) trajectories through the space of input values. Each trajectory steps the value of one input at a time, while other inputs remain fixed, and records the resulting change in the model output. From these trajectories, one extracts elementary effects for each input: the change in the output produced by a unit perturbation in that input, along a given path. Aggregating many elementary effects across multiple trajectories yields summary statistics that indicate an input’s overall influence and its tendency to interact with other factors.

Two summary statistics are central:

The mean (often the absolute mean, mu*) of the elementary effects, which signals the overall importance of a factor.
The standard deviation (sigma) of the elementary effects, which signals nonlinearity or interaction with other inputs.

Together, mu* and sigma help distinguish factors that consistently drive outputs from those whose influence is sporadic or context-dependent. These ideas connect to broader concepts in uncertainty analysis and statistical method development, but the Morris approach keeps the implementation straightforward enough to be run with modest computer resources. For readers exploring how this fits with other sampling ideas, see Latin hypercube sampling and factorial design as related design strategies in experimental design.

Methodology

Design a grid of input levels for each factor and generate several random trajectories through the input space. Each trajectory is a sequence of single-factor moves, designed so that a perturbation in one factor is assessed across many baseline contexts. The result is a collection of elementary effects for each factor.
Compute the elementary effects for each factor across all trajectories. The primary outputs are the mu* (mean of absolute elementary effects) and sigma (standard deviation of elementary effects). High mu* suggests that the factor often has a large effect on the model output, while a high sigma points to nonlinear behavior or interactions with other inputs.
Use these statistics to rank factors by importance and to decide where to invest in more detailed sensitivity analyses or data collection. The method’s emphasis on screening makes it a practical first pass in resource-constrained settings.

In this framework, the Morris Method is especially compatible with scenarios where the model is expensive to run, or where a rapid triage of input factors is valuable. It complements other methods in the global sensitivity analysis toolkit, such as variance-based techniques rooted in Sobol' sensitivity indices and more exhaustive sampling strategies, by offering speed and interpretability.

Advantages and practical value

Computational efficiency: Morris requires far fewer model evaluations than many full-spectrum sensitivity analyses, making it attractive when simulations are time-consuming or costly. This efficiency supports timely decision-making in industry and public policy.
Intuitive interpretation: The concepts of elementary effects and the mu*/sigma pair are straightforward to communicate to stakeholders, engineers, and policymakers who must understand how inputs drive outcomes without wading through dense mathematical formalism. This clarity helps in prioritizing model improvements and data collection.
Effective screening: By highlighting the most influential inputs early, Morris guides where to allocate scarce resources—such as laboratory experiments, field measurements, or higher-fidelity simulations—without committing to a single, rigid modeling assumption about interactions.
Compatibility with iterative modeling: As a preliminary step, the Morris Method integrates smoothly into an iterative workflow where models are progressively refined, validated, and subjected to more rigorous analyses as needed.

In discussions of sensitivity analysis within uncertainty analysis frameworks, proponents emphasize Morris as a pragmatic starting point—especially when time, budget, or data are limited. Critics, meanwhile, remind users that the method’s approximate nature means it should not be treated as the final word on a model’s behavior.

Limitations and criticisms

Approximate nature: Morris is a screening method, not a complete characterization of input-output relationships. It trades depth for speed, so its ranking of factors may be imprecise in complex, highly nonlinear systems with strong interactions. For more precise quantification, analysts often turn to Sobol' sensitivity indices or other variance-based approaches.
Sensitivity to design choices: The results can be influenced by the number of trajectories, the size of perturbations, and the input space partitioning. In practice, practitioners must balance sampling density with computational constraints, and may need to perform robustness checks across different designs.
Dimensional challenges: In very high-dimensional models, even a screening-oriented method like Morris can require substantial calibration to ensure that the elementary effects capture meaningful information about the input landscape. Critics argue that reliance on simple OAT trajectories may miss certain multi-factor interaction patterns that only emerge when several inputs vary together.
Dependence on input distributions: The interpretability of mu* and sigma can hinge on how input ranges are specified. If ranges are poorly chosen, influential factors might be overlooked or overemphasized. This points to the broader principle in risk assessment that input specifications matter as much as the analysis technique itself.

From a practical policy perspective, some observers argue that screening methods should be supplemented with more robust analyses when the stakes are high—for example, in climate risk assessments or critical infrastructure planning. Advocates of Morris counter that the method’s speed and transparency make it invaluable for triage and for engaging stakeholders in a productive discussion about where to focus deeper investigation.

Applications and real-world use

The Morris Method has found application across engineering design, environmental modeling, economics, and public policy analytics. In engineering, it helps engineers identify which material properties, boundary conditions, or loading factors most influence performance outcomes, enabling better design decisions under uncertainty. In environmental risk assessment, the method can spotlight key drivers of ecosystem or water quality responses, informing monitoring priorities and regulatory planning. In economic modeling, it supports rapid sensitivity screening of policy levers and exogenous shocks before investing in more computationally intensive simulations.

Its flexible, low-cost nature makes Morris appealing to organizations that must balance rigor with practicality. It also serves as a teaching tool, illustrating the intuitive idea that not all inputs matter equally and that some influences are consistent while others depend on context or interactions. In ongoing debates about how best to allocate resources for scientific modeling, Morris is often cited as a rational first step that aligns with a disciplined, fiscally prudent approach to analysis.

In the academic literature, the method sits alongside other landmark ideas in factorial design and variance-based sensitivity analysis, and it is frequently discussed in the context of model verification, calibration, and uncertainty quantification. The ongoing evolution of sensitivity analysis continues to refine how practitioners understand and manage the trade-offs between speed, accuracy, and interpretability.