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Estimates Configuration

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Estimates configuration

This part of the nFIESTA functionality formalises the search for the best possible data (field as well as auxiliaries if available) and the corresponding estimation technique which can be used given the user specification of:

  • target parameter – variable e.g. total forest area
  • estimation cell – representing a geographical area (denoted by D) for which the best possible estimate of the specified target parameter needs to be identified as well as the dataset allowing for its calculation
  • inventory year(s) – to which the estimate should (ideally) correspond
  • parametrisation region – a region D_+ \supseteq D in which a working model can potentially be parametrised and used to increase the precision of target parameter estimate

The configuration process is captured by schema in Figure 3. In this schema the orange nodes correspond to user defined inputs (left part of the schema). The central rectangle corresponds to purely design-based estimation, while in the right one leads to model-dependent or mixed (i.e. for some sampling strata model-dependent and design-based for other). Section 6 of the report by ene_et_al_2018 provides a better insight in terms of estimation methods to be used for each of the possible paths between nodes No. 1 and 10.

The blue and gray diamonds to decisions made by nFIESTA (potentially user-assisted decision) and the thin blue or gray rhomboids represent dataset available for the calculation of the estimate(s). The only green end point corresponds to a state when the estimate of the respective target parameter can be calculated. Reaching the red end point will stop the whole process because no viable configuration (estimation method) exists for the user inputs.

The estimate configuration logic can be described following the nodes of the schema in figure:

Figure 3: Schema of nFIESTA estimates configuration logic.

  • Node No. 1 – the user chooses the target parameter (total or ratio, target variable), the reference year(s), the estimation cell and parametrisation area type (to be able to test whether auxiliary data can be used for estimation). For a given estimation cell and parametrisation region type (defining a set of spatially congruent parametrisation areas) a particular parametrisation region is easily determined based on an explicit linkage to estimation cells (the unions of which define parametrisation regions).
  • Node No. 2 – automatic check whether there the necessary target variable(s) is (are) available on all plots within the automatically identified parametrisation region of given type. The check is done irrespective of the reference year.
  • Node No. 3 – because the requested target variable(s) is not available for the whole or part of parametrisation region no estimates can be produced. From here the user has always the chance to come back to node No. 1 and choose another type of parametrisation region (possibly the one corresponding to the estimation cell itself) and continue with second iteration of the configuration. In fact such a logic could be implemented automatically, but at the moment it is has not been implemented by nFIESTA.
  • Node No. 4 – Data identified in node No. 4 is reduced to a subset corresponding to the desired reference year(s). Then the size of the subset is compared to the minimum sample size requirement.
  • Node No. 5 – plot data (organised to sampling panels) which fits spatially as well as temporarily to the requested target parameter, cell and parametrisation region.
  • Node No. 6 – system check whether the found plot data represents the full sampling grid surveyed in the field. The purpose of this check is to separate situations when a single-phase estimation can be performed and no potentially better estimation technique exists (using wall-to-wall auxiliaries is considered also a kind of single-phase estimation here).
  • Node No. 7 – user assisted decision whether auxiliary data obtained from wall-to-wall maps can be used to improve precision of the target parameter estimate(s).
  • Node No. 8 – the user has to specify auxiliaries and all the terms of a linear regression model which will be used for the estimation.
  • Node No. 9 – the dataset necessary for the particular estimator type i.e. \boldsymbol{\tilde{G}_{\beta_{t+}}} matrices and auxiliary totals for the extent of the given estimation cell. The gbeta-matrices can either be reused (if available) or they have to be evaluated by nFIESTA right at this moment.
  • Node No. 10 – nFIESTA calculates the respective estimate the type of which depends on the path through which the node has been reached.
  • Node No. 11 – system checks whether there are more panels representing various reference years in the dataset identified in node No. 5. If yes an additional check is performed to find out whether for each of the reference years at least one panel exists which has been remeasured. If both conditions are met a two-phase estimator can be constructed combining the panels for the requested years and panels which were measured in the past (or future in some cases).
  • Node No. 12 – data corresponding to full sampling grid (all yearly panels not necessarily form the same inventory campaign) which can be used for two-phase estimation (to improve precision, old plot data can be used as non-exhaustive auxiliaries). Wall-to-wall auxiliaries may also enter the game if a positive answer in node No. 7 is obtained. In such a case the resulting estimator would actually be a three-phase one.
  • Node No. 13 – either there was no suitable data found in node No. 5 or the data does not correspond to the full sampling grid and the available panels do not allow for two-phase estimation (node No. 11). In the former case one can try an interpolation of plot values between two measurement years or using the unchanged plot values corresponding to the next preceding survey (if an interpolation between two field survey occasions is not possible). This corresponds to model-based or mixed inference. In the later case (i.e. when reaching node No. 13 from node No. 11) the default system behavior is to continue to node No. 7 (avoiding interpolation at the end a design-based estimation is pursued).
  • Node No. 14 – the system creates a plot dataset which contains the original as well as some artificial panels with interpolated plot data. Currently only a linear interpolation can be used. This can be improved by disturbance maps and growth models (once they are available for large territories). From here the configuration goes to node No. 7 to check whether wall-to-wall auxiliaries can be used to improve precision of the estimate. Estimates using interpolated data should not be considered generally unbiased. The interpretation of the respective variance estimates should reflect this circumstance.
  • Node No. 15 – a situation of no data measured in specified reference year(s) and no interpolation possible. Check if there are is wall-to-wall auxiliary data corresponding to the measurement year(s) of field data identified in node No. 5 and at the same time, if there is another (generation) of the same auxiliary data corresponding to the user specified reference year(s).
  • Node No. 16 – field data identified in node No. 5 and the pair(s) of wall-to-wall auxiliaries corresponding to the field data and the requested reference year(s). Next step is the parametrisation (calculation of G_Beta) based on the auxiliary corresponding to the only available field data followed by a synthetic estimation using the fitted model but auxiliaries corresponding to the user requested reference year(s). This method is not implemented in nFIESTA because of lack of suitable auxiliaries with a regular update frequency and large spatial coverage.
  • Node No. 17 – there is no other option than to take the inventory data identified in node No. 5 as it is and potentially try to improve precision by incorporation of wall-to-wall auxiliaries (timely indifferent approach).

At the moment the assessment of all the above conditions is done in a way that a positive answer is obtained only in case the conditions are met for each sampling stratum encroaching the parametrisation region. This approach basically means that we head toward the same type of estimate in all strata found within the given estimation cell. This constraint can be relaxed in the future implementation but for the moment a more transparent approach was preferred.