Design and Defend a Spatial Inference Plan

Chapter 6 practicum — Design and Defend a Spatial Inference Plan

Learning outcome

By the end of this practicum, you will be able to audit a spatial sampling design, define and compare neighbour hypotheses, quantify spatial dependence, validate interpolation and regression across separated geography, map uncertainty and unsupported domains, and issue a professional release decision whose statistical claims remain conditional on spatial support and design.

• Estimated time: 420–540 minutes
• Prerequisites: Lessons 2.31–2.34
• Portfolio output: Artifact 2.F — Spatial Inference and Validation Package
• Training status: every supplied coordinate, value and identifier is synthetic and released for instruction under CC0-1.0

Why this practicum matters

Spatial statistics can make an analysis appear sophisticated while concealing the most important decisions. A Moran statistic is incomplete without weights. A sample count is incomplete without a frame and inclusion mechanism. A kriging surface is incomplete without variogram evidence and spatial holdouts. A spatial-regression coefficient is incomplete without a process hypothesis and geographic validation.

In professional work, these components must form one claim–evidence system. The objective is not to use every method. It is to decide which evidence can support which inference, demonstrate sensitivity and refuse outputs whose confidence exceeds the sampling design.

Scientific brief

The Baltic coastal meadow research group asks:

Can the current synthetic plot evidence support a spatially continuous description of vegetation condition inside the core meadow frame, and what supplementary sampling is required before stronger ecological inference?

The team needs a planning product, not a publication-ready biomass map. You must evaluate accepted probability observations, roadside convenience records, inaccessible frame cells and the isolated targeted plot separately. You may release a restricted exploratory surface, or decide not to release one. Both outcomes are valid when supported by transparent evidence.

1. Required training assets

Use spatial-statistics/README.md first. Keep the supplied files unchanged:

• meadow_plot_observations.csv;
• sampling_frame.csv;
• spatial_validation_blocks.csv;
• SPATIAL_INFERENCE_QA_TEMPLATE.md;
• manifest.json.

Create a project structure:

spatial_inference_package/
├── README.md
├── environment.txt
├── inputs/
├── notebooks/
├── outputs/
│   ├── tables/
│   └── figures/
└── SPATIAL_INFERENCE_DECISION.md

Record software versions, random seeds and file checksums. Do not assign a real EPSG code to the synthetic local metric coordinates. The absence of a geographic CRS is intentional and prevents the instructional locations from being mistaken for field sites.

2. Gate A — define the inference target

Write the following before running a statistic:

• population or spatial domain;
• observation unit and physical support;
• time represented by each variable;
• response or target variable and units;
• estimand or prediction use;
• accepted, review and blocked evidence;
• strongest causal claim prohibited by the design.

Use one primary target:

Describe and predict synthetic accepted plot-level NDVI inside the accessible core sampling frame for survey planning.

This statement does not promise true 10 m vegetation condition, regional transfer or causal biomass explanation. The output grid represents prediction locations, while the evidence support remains plot level.

Check your understandingWhat must be declared before building a spatial prediction surface?

Choose one answer

The target population, observation support, prediction use and accepted analysis evidenceOnly the preferred colour paletteA requirement that every grid cell receive a value

Check answer

3. Gate B — audit frame, selection and realised observations

Create spatial_sampling_audit.csv with one row per frame or observed unit and these fields where applicable:

• stable identifier;
• source table;
• x and y coordinate;
• habitat and management strata;
• frame eligibility;
• accessibility and restriction reason;
• selected status and route;
• inclusion probability evidence;
• response/QA status;
• primary-analysis status;
• decision reason.

Report:

1. counts by habitat for the complete frame, accessible frame and accepted probability observations;
2. missing inclusion probability by sampling route;
3. nearest-neighbour distance by route;
4. spatial distribution of inaccessible cells;
5. the consequence of mixing roadside and probability observations;
6. whether P024 belongs to the core inference domain.

Propose six supplementary sample locations using a stratified random or spatially balanced design. Preserve the full frame, seed and non-selected rows. Define a replacement rule before simulating one inaccessible selection.

4. Gate C — make spatial weights inspectable

Build at least three scientifically plausible neighbour definitions for accepted core plots:

• four nearest neighbours;
• six nearest neighbours;
• a 170 m distance band.

For each definition, save:

• rationale;
• transformation;
• minimum, median and maximum neighbours;
• minimum, median and maximum link distance;
• symmetry status;
• island identifiers;
• edge observations;
• map filename.

Create weights_sensitivity.csv. Do not remove a definition because its result is weak or inconvenient. If P024 is included in a secondary analysis, record whether the distance rule exposes it as an island and how far k-nearest neighbours force it to connect.

5. Gate D — quantify spatial dependence cautiously

For accepted core NDVI and elevation:

1. standardise or transform only with a documented reason;
2. calculate global Moran's I under all three weights definitions;
3. use at least 999 permutations and a fixed seed;
4. retain observed I, expected I, permutation mean, permutation probability and z-score when available;
5. map the values beside the selected graph;
6. repeat with roadside review observations as a labelled sensitivity analysis;
7. write one possible environmental explanation and two alternatives;
8. state explicitly that autocorrelation does not establish cause.

The primary report should focus on global structure. Optional local statistics may appear only in an appendix that documents multiple-testing control, weights and exploratory status.

Check your understandingThree scientifically plausible weights definitions produce different Moran results. What should be released?

Choose one answer

The complete sensitivity result and an evidence-based primary definitionOnly the definition with the smallest permutation probabilityThe average p-value without the weights

Check answer

6. Gate E — validate interpolation as a prediction task

Build an empirical variogram table for accepted core NDVI. Report distance-bin edges, midpoint, pair count and mean semivariance. Examine whether a broad coordinate trend, anisotropy or sparse long-distance pairs weaken a stationary interpretation.

Compare:

• inverse-distance weighting with a declared power and neighbour rule;
• ordinary kriging with a documented variogram model and parameters.

Use the same separated spatial blocks for both methods. Save interpolation_validation.csv with:

• plot ID and holdout block;
• observed value;
• method and full parameter label;
• prediction;
• residual;
• absolute and squared error;
• distance to nearest training observation;
• prediction variance when defined;
• inside/outside core support;
• QA note.

Report mean error, MAE and RMSE overall and by block. Map residuals with one common scale. If a method has a lower aggregate RMSE but systematic failure in one block, do not call it universally superior.

Create a prediction grid only inside a declared core domain. Map model-based uncertainty separately and add a support/extrapolation mask. The isolated plot must not cause the map to bridge an unobserved gap without warning.

7. Gate F — diagnose regression residuals

Fit a transparent baseline for synthetic biomass using accepted core NDVI and elevation. Document:

• response and predictors;
• units and support;
• ordinary diagnostics;
• coefficient interpretation as association;
• four-nearest residual Moran's I plus weights sensitivity;
• spatial-block validation performance;
• influential or edge observations.

Select only one spatial alternative for detailed comparison. It may be an SLX, spatial-error, spatial-lag or cautiously exploratory geographically weighted formulation. The decision must follow a process hypothesis, not whichever method removes residual Moran's I most strongly.

Save residual_diagnostics.csv and model_comparison.csv. If the selected library cannot generate valid out-of-sample predictions for the required geography, record that limitation and do not replace it with in-sample information criteria.

Check your understandingA smooth interpolation has low random-split error but poor separated-block validation. What is the correct decision?

Choose one answer

Restrict or block release because intended geographic transfer is not validatedPublish because the map is smoothReport only random-split error

Check answer

8. Build the decision matrix

Create one matrix connecting every claim to its evidence:

Claim area	Required evidence	Accepted result	Main sensitivity	Unsupported claim	Decision
Sampling representation	frame, inclusion mechanism, realised response
Spatial dependence	variable, weights, permutations, map
Interpolation	continuity model, spatial holdout, support mask
Regression	baseline, residual geography, alternative, validation
Ecological interpretation	measurement meaning and independent evidence

Use the statuses:

• accept: evidence supports the declared limited use;
• review: evidence is informative but a named uncertainty or sensitivity remains;
• block: the proposed use exceeds the current design or validation.

9. Produce the spatial inference map

Create spatial_inference_map.pdf with at least four coordinated panels:

1. accepted, review, inaccessible and proposed sampling locations;
2. selected neighbour graph and NDVI values;
3. preferred exploratory prediction surface with observation locations;
4. validation residuals and uncertainty/support mask.

The map must state that the coordinates are a synthetic local metric grid. Include units, an equal aspect ratio, an accessible colour scheme, clear missing/blocked symbology and a text description in the report. Do not add a geographic basemap or real place name.

10. Write the release decision

Create SPATIAL_INFERENCE_DECISION.md with a maximum of 1,000 words:

1. Question and intended use
2. Population, frame and realised sample
3. Spatial-dependence evidence
4. Interpolation and spatial-validation evidence
5. Regression diagnostic
6. Uncertainty and unsupported domain
7. Release status
8. Supplementary sampling priority

Choose one final status:

• release for exploratory survey planning;
• release only inside a restricted domain with prominent uncertainty;
• do not release a continuous surface.

State one interpretation the evidence supports and three it does not. Include a next action with an owner or responsible role.

11. Professional Mistakes — Spatial Statistics and Geostatistics

Use this as a final review table. Every row needs an explicit status and action in your notebook or decision record.

Professional mistake	Why it fails	Evidence that reveals it	Required recovery
Treating coordinates as spatially meaningful without units or CRS evidence	neighbour distance becomes ambiguous	metadata and coordinate audit	verify reference or retain documented local metric status
Selecting weights after searching for significance	inference becomes outcome-tuned	missing pre-analysis rationale	define plausible weights first and report sensitivity
Reporting Moran's I without W	the statistic cannot be interpreted	incomplete methods table	record neighbours, transformation and islands
Interpreting I against zero only	null expectation may differ	expected-I output	report expected value and permutation reference
Calling autocorrelation a cause	pattern does not identify mechanism	causal wording	separate description from competing explanations
Letting k-nearest neighbours hide an island	forced long links may be implausible	link-distance map	compare a distance rule and review the domain
Ignoring edge observations	neighbour structure differs near boundaries	neighbour-count summary	map and test edge sensitivity
Mixing accepted and review rows silently	QA and design conditions change	source-status reconciliation	retain statuses and run labelled sensitivity analysis
Calling roadside plots random	unknown inclusion mechanism is concealed	route and provenance audit	label convenience evidence and restrict inference
Deleting inaccessible frame units	target-frame gaps disappear	frame reconciliation	preserve restrictions and redefine domain honestly
Moving selected plots for convenience	selection probabilities become unclear	planned-versus-realised coordinates	use a predeclared replacement rule
Treating equal stratum sample counts as population proportions	unweighted estimates can be distorted	frame and sample shares	use design-aware estimates or stratum results
Interpolating an unsuitable variable	continuity assumption is unsupported	process review and variogram	refuse the surface or redesign the model
Choosing the smoothest interpolated map	appearance replaces validation	absent holdout results	compare identical spatial folds
Fitting a variogram before checking trend	non-stationary mean enters dependence model	value and residual maps	model trend or restrict domain first
Treating the nugget as sensor error only	microscale and support variation are ignored	replicate/support evidence	use cautious short-range-variance language
Ignoring variogram pair counts	sparse bins appear authoritative	lag table	report pair counts and sensitivity
Calling kriging variance observed error	it is conditional model uncertainty	holdout residuals	distinguish model variance from empirical error
Predicting across the P024 gap	output grid hides extrapolation	distance/support mask	restrict domain and flag unsupported cells
Validating with random neighbouring plots	local dependence leaks into test data	fold map and neighbour overlap	use separated blocks or sites
Selecting regression family from p-values	model lacks a process hypothesis	methods rationale	locate dependence in predictors, response or error conceptually
Interpreting spatial lag as an ordinary local coefficient	feedback creates indirect impacts	model definition	report appropriate direct/indirect impacts
Treating GWR maps as confirmed local mechanisms	local estimates may be unstable	bandwidth, collinearity and uncertainty	retain exploratory language and independent validation
Using in-sample R² as geographic validation	fit does not test transfer	absent block metrics	evaluate held-out geography
Eliminating residual autocorrelation at any cost	complexity may not improve science or prediction	cross-model comparison	balance diagnosis, transfer, stability and interpretation
Claiming NDVI causes biomass	observational association is not causal evidence	design and causal sketch	report association and required causal evidence
Publishing only the final surface	decisions and failures cannot be reconstructed	missing package files	deliver frame, weights, validation, uncertainty and decision record

12. Required deliverables

Submit all nine files:

1. README.md
2. spatial_sampling_audit.csv
3. weights_sensitivity.csv
4. interpolation_validation.csv
5. residual_diagnostics.csv
6. model_comparison.csv
7. spatial_inference_map.pdf
8. SPATIAL_INFERENCE_DECISION.md
9. spatial_statistics_practicum.ipynb

The notebook must run from top to bottom using relative paths and immutable inputs. It must preserve random seeds, rejected rows, sensitivity definitions and package versions. Screenshots may support review but cannot replace executable tables and code.

13. Assessment rubric

Dimension	Excellent evidence	Revision required
Technical correctness	weights, statistics, variogram, interpolation, residuals and validation are calculated with compatible rows and documented units	methods run but neighbourhood, support, folds or units are ambiguous
Conceptual understanding	sampling, dependence, continuity and residual processes are separated and linked to defensible hypotheses	methods are presented as interchangeable software choices
Reproducibility	frame, inputs, checksums, seeds, parameters, software, outputs and exclusions are traceable	selected locations or model defaults cannot be recreated
Scientific communication	maps and decision record distinguish observations, predictions, uncertainty, extrapolation and unsupported causation	smooth surfaces or coefficients are presented as ecological truth

Automatic revision is required if the submission:

• calls convenience locations random;
• omits the weights definition from an autocorrelation result;
• validates interpolation or regression only with random neighbouring rows;
• treats kriging variance as empirical accuracy;
• assigns a real CRS to the synthetic coordinates;
• reports causal NDVI–biomass language;
• hides inaccessible cells, review rows, islands or extrapolation.

14. Reflection and portfolio handover

Reflection

• Which single decision changed your conclusion most: domain, sampling set, weights, variogram or validation geography?
• What new field location would reduce the most important uncertainty?
• Which output is safe for survey planning but unsafe for ecological reporting?
• How will this chapter change the validation design of the final UAV and Satellite Analysis Pipeline?

Submission

Upload the nine required files, one screenshot of the rerun notebook, one screenshot of the map at readable scale and a 150-word handover note addressed to the scientist responsible for the next field campaign. The note must identify the release status, blocked interpretation, priority sample and file that contains full decision evidence.

Portfolio artifact

Add Artifact 2.F — Spatial Inference and Validation Package to the UAV and Satellite Analysis Pipeline. It should demonstrate that you can turn spatial observations into a restricted, validated inference without allowing maps, p-values or advanced model names to outrun the sampling design.