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IRENE_DLL: a library to evaluate model performance Presented by: Gianni Fila Research Institute for Industrial Crops Agronomy Section g.fila@isci.it

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Topics 1. Background 2. Overview 3. Using the library: basic concepts 4. Special procedures 5. Application examples 6. Future developments

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1. Background

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Need of reliable model estimates No standard theory on model evaluation No standard boxes of tools Plethora of philosophical theories, statistical techniques, and software practices Why IRENE_DLL? IRENE_DLL: a set of tools all housed in a single, integrated component

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What IRENE_DLL can do Difference-based analysis: indices, test statistics Regression-based analysis: parameters, test statistics Patterns detection: Pattern Index Probability distributions: density functions, cumulative distributions (exceedence, non-exceedence) Aggregation: first level (module), second level (indicator) Shift analysis (Time mismatch)

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2. Overview

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IRENE_DLL in a nutshell IRENE_DLL is a library of methods and functions to compute a variety of statistics and statistical tests It consists of ten classes, containing data services, mathematical routines and some special data analysis procedures All IRENE_DLL classes can be accessed individually (no hierarchy)

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Overview Data objects DataSelections DataSelection Aggregation objects Module Indicator Accessory objects GeneralRoutines They store data to be processed, and expose properties to handle them. Each object holds a group of related functions. They contain methods to perform statistics aggregation Info-display routines Computing objects Pattern DistributionFunctions RegressionObject IndexObject Tests

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3. Using the DLL: basic concepts

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Handling data (1) To be accepted by any functions, data (estimated and measured) must be loaded into a DataSelection object External data E M DataSelection estimated measured (independent)

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Handling data (2) Whenever multiple series of data are to be processed, it is convenient to use a collective DataSelections object: External data E M E M E M DataSelection 1 DataSelection 2 DataSelection 3 DataSelections DataSelection 1 DataSelection 2 DataSelection 3

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Handling functions To use a particular function, you must call it from the parent object, then pass it the data (in the DataSelection format), and the necessary specifications: DataSelection Required Specs Outputs Computing object Function_1 Function_2 (….) Function_n Outputs from functions are aggregated in a single, collective variable

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Function modes Paired_Columns Paired_Rows Unpaired_Average Unpaired_One_to_One

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Handling outputs All functions in IRENE_DLL return a package of outputs A special collective variable is designed for each type of function Example: content of the Index_Variable:

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Example: computing regression Compute regression parameters for three arrays of estimated data against three corresponding arrays of measured data Array MyEstimated(1 to 365, 1 to 3) Array MyMeasured(1 to 365, 1 to 3)

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Example: (1) load data Start an instance of a DataSelection object, and transfer your data inside it through the Estimated and Measured properties Dim Nitrates As New DataSelection Loop through: Nitrates.Estimated(i, j) = MyEstimated(i, j) Nitrates.Measured(i, j) = MyMeasured(i, j)

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Example: (2) Compute Regression Start an instance of the RegressionObject, then call the function Regression_LS (least squares method) Dim RegrCalculator As New RegressionObject Dim RegrOutput As Regression_Variable RegrOutput = RegrCalculator.Regression_LS(Nitrates, Paired_Columns, Measured_Variable)

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Example: (3) Display results Outputs are returned as arrays of values Loop from j = 1 to 3 (the number of columns) Print RegrOutput.Intercept(j) Print RegrOutput.Intercept_StandError(j) Print RegrOutput.Intercept_Tvs0(j) Print RegrOutput.Intercept_Prob_Tvs0(j) Print RegrOutput.Slope(j) Print RegrOutput.Slope_StandError(j) Print RegrOutput.Slope_Tvs0(j) Print RegrOutput.Slope_Tvs1(j) Print RegrOutput.Slope_Prob_Tvs0(j) Print RegrOutput.Slope_Prob_Tvs1(j) Print RegrOutput.F(j) Print RegrOutput.Prob_F(j)

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4. Special procedures

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Aggregation of indices: the problem The need to define synthetic measures of model performance is a major topic of interest in the field of model evaluation. Giving a solid judgement is often complicated by the need to balance, for instance, departure of estimates from measurements, modelling efficiency, correlation measures, presence/absence of systematic behavior in the residuals, etc. The user may want to combine all such aspects in only one aggregated index.

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IRENEs approach Index/test aggregation is set up by IRENE, based on an expert system using decision rules, according to fuzzy logic This technique is robust when uncertain data are used (e.g. subjective judgements) and allows an aggregation of dissimilar statistics in a consistent and reproducible way.

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Aggregation levels hyerarchy IRENE_DLL supports two levels of statistics aggregation: First level: multiple indices/tests aggregated in one single index (Module) Second level: Multiple modules aggregated in one single index (Indicator)

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Module specifications Aggregation of statistics require the user to introduce specifications derived from his/her expert knowledge, and objectives For each index to aggregate, the user must specify: The DataSelection The Favourable and Unfavourable limit values The relative weight

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MyModule How to build a Module Add indices to aggregate, with the required specifications r_Pearson, DataSelection, 0.95, 0.90, 1 Add_Index: RMSE, DataSelection, 0.1, 0.8, 1 Add_Index: Pattern, DataSelection, 0.2, 0.75, 0.5 Add_Index: Finally, compute module value calling the function Module_Value Module_Value (a score between 0 and 1) RMSE r_Pearson Pattern Start an instance of the Module object

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Time mismatch analysis There are no specific indices to investigate the uncertainty about possible displacements (delay or acceleration) registered in time series. A time mismatch may be detected by an iterated procedure, shifting repeatedly the estimated points until optimal model performance values are found. Soil NH 4 (mg kg -1 )

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Finding a time mismatch Starting from an observed model performance as initial condition, the procedure runs as follows: 1.the simulated points are moved backward in time to the maximum anticipation chosen to evaluate the time mismatch 2.the desired evaluation indices are computed; 3.the simulated points of one time history are moved of one selected time step forward; 4.points 2 to 3 are reiterated until the maximum allowed time delay is reached. The time mismatch is identified by the time step (forward or backward) at which the best value of the evaluation indices are reached.

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Handling time mismatch in IRENE_DLL All functions exposed by IRENE_DLL have an optional ShiftN parameter: Ex., in the IndexObject object: –Public Function RMSE(Sel As DataSelection, Mode As Mode, [ByVal ShiftN As Long = 0], [ByVal Prob_level As Double = 0.05]) As Index_Variable By setting a ShiftN value <> 0, the index is computed shifting the estimated points. We can explore a range of ShiftN values by a loop

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5. Application examples

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Time mismatch analysis IRENE_DLL, sample applications Difference-based indices Pattern Index

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6. Future developments

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In the next future: Integration in IRENE interface Integration in development frameworks (MODCOM) Introduction of robust statistics (median-based). Introduction of randomization procedures (bootstrap) (….)

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How to get IRENE_DLL View documentation

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The people of IRENE_DLL Gianni Fila g.fila@isci.itg.fila@isci.it –Research Institute for Industrial Crops Gianni Bellocchi g.bellocchi@isci.itg.bellocchi@isci.it –Research Institute for Industrial Crops Marcello Donatelli m.donatelli@isci.itm.donatelli@isci.it –Research Institute for Industrial Crops Marco Acutis macutis@ideagate.itmacutis@ideagate.it –Department of Crop Science, University of Milan

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Thank you!

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