US federal Mathematical Statistician (series 1529) - USDA NASS and others · USA · USDA National Agricultural Statistics Service via USAJOBS (Office of Personnel Management rules)
Original practice questions written to the published syllabus · not past papersStatistics for data with a location: spatial autocorrelation, variograms and kriging, spatial regression, point patterns, area-frame sampling, accuracy assessment of crop maps and satellite-based area and yield estimation. Remote-sensing physics and GIS operations are taught in the Agricultural Engineering track; this is the statistics.
In the exams: AICE-JRF Agricultural Physics 'spatial statistics: variogram and interpolation' (present); national crop-estimation programmes (applied); light in national exams
US federal mathematical statistician (USDA NASS)
Area-frame construction and stratification, regression estimators combining surveys with classified imagery, and accuracy assessment of crop maps.
How our questions for US federal Mathematical Statistician spread across the units of Spatial Statistics, Geostatistics & Remote Sensing for Agriculture. Difficulty: 8 easy, 21 medium, 8 hard.
| Image classification as a statistical problem | 10 | |
| Accuracy assessment: error matrices and kappa; area estimation from maps | 9 | |
| Satellite-based crop area and yield estimation | 9 | |
| Area-frame sampling with satellite stratification | 8 | |
| Spatial data types: geostatistical, areal and point-pattern | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
District-wise average yields of maize for all districts of a state form which type of spatial data?
A. Areal (lattice) data
Values attached to fixed units that cover the region are areal or lattice data, analysed with spatial weights, Moran's I and SAR or CAR models.
Further reading: Cressie, Statistics for Spatial Data
An analyst reassigns several sampled segments to different strata after seeing their crop areas. What is wrong?
C. Strata must be fixed before sampling
Stratum membership and selection probabilities are defined by the design; changing them using the data invalidates the weights and variance estimates.
Further reading: FAO Handbook on Master Sampling Frames; Gallego (2004)
The maximum likelihood classifier for satellite images assumes that each land-cover class:
D. Is multivariate normal in the bands
Each class is modelled as multivariate normal with its own mean vector and covariance matrix; this makes the rule the quadratic discriminant of multivariate statistics.
Further reading: Congalton and Green; Johnson and Wichern (discriminant analysis)
How do prior probabilities change maximum likelihood classification of pixels?
B. Pixels go to the class of highest posterior
With priors, Bayes' rule multiplies each class likelihood by its prior; in doubtful pixels the more common class is favoured.
Further reading: Congalton and Green; Johnson and Wichern (discriminant analysis)
With rows = map and columns = reference, the user's accuracy for wheat is 80/100 = 0.80. What does it mean to a map user?
B. 80 per cent of mapped wheat is truly wheat
User's accuracy is the reliability of the map label (1 - commission error). The share of real wheat captured is producer's accuracy; overall accuracy covers all classes.
Further reading: Congalton and Green; Olofsson et al. (2014); Pontius and Millones (2011)
A rare crop occupies 2 per cent of a mapped region. Which design for reference samples ensures enough samples to estimate its accuracy?
B. Stratified random sampling by map class
Stratifying by map class guarantees a minimum sample in each class (often about 50 or more); simple random sampling would yield very few rare-crop points. Roadside and training samples are not valid probability samples.
Further reading: Congalton and Green; Olofsson et al. (2014); Pontius and Millones (2011)
The correlation between enumerated and classified crop area across sample segments is 0.8. Approximately how efficient is the regression estimator relative to the ground-only estimate?
D. 2.78 times
Variance ratio is about 1 - rho^2 = 0.36, so relative efficiency = 1/0.36 = 2.78. Using 1/(1 - rho) gives 5.00; rho^2 is the share of variance explained, not the efficiency.
Further reading: Gallego (2004); Cochran, Sampling Techniques
What does a Fay-Herriot model do in district-level crop estimation?
B. Combines each district's direct survey estimate with a satellite-based regression prediction
The area-level small-area model shrinks each direct estimate towards a covariate-based prediction, weighting by their precisions: districts with large samples rely on the survey, small-sample districts on the model.
Further reading: Gallego (2004); Cochran, Sampling Techniques
Field-level crop-cutting yields are regressed on NDVI, and the model's prediction intervals for district yield look very narrow. Which neglected feature is a likely cause?
A. Spatially autocorrelated residuals
Autocorrelated residuals mean fewer independent observations than assumed, so model-based standard errors and intervals are too small.
Further reading: Gallego (2004); Cochran, Sampling Techniques
Insurance payouts in a block depend on a satellite-assisted yield estimate. What is the most important statistical safeguard?
D. A documented probability design with stated uncertainty
Where money depends on estimates, the design, models and uncertainty must be documented and auditable; unvalidated sensors and post-hoc adjustment undermine credibility.
Further reading: Gallego (2004); Cochran, Sampling Techniques
Ten here, 37 in the app. The Laisha app has every practice question we have written to US federal Mathematical Statistician in this subject, marked as you go, with timed papers, a jump-to-unanswered list and a certificate when you pass at 70 per cent.
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