Sensitivity analysis of agent-based models: a new protocol

Agent-based models (ABMs) are increasingly used in the management sciences. Though useful, ABMs are often critiqued: it is hard to discern why they produce the results they do and whether other assumptions would yield similar results. To help researchers address such critiques, we propose a systematic approach to conducting sensitivity analyses of ABMs. Our approach deals with a feature that can complicate sensitivity analyses: most ABMs include important non-parametric elements, while most sensitivity analysis methods are designed for parametric elements only. The approach moves from charting out the elements of an ABM through identifying the goal of the sensitivity analysis to specifying a method for the analysis. We focus on four common goals of sensitivity analysis: determining whether results are robust, which elements have the greatest impact on outcomes, how elements interact to shape outcomes, and which direction outcomes move when elements change. For the first three goals, we suggest a combination of randomized finite change indices calculation through a factorial design. For direction of change, we propose a modification of individual conditional expectation (ICE) plots to account for the stochastic nature of the ABM response. We illustrate our approach using the Garbage Can Model, a classic ABM that examines how organizations make decisions.

A Generalized Non-Parametric Instrumental Variable-Control Function Approach to Estimation in Nonlinear Settings

When the endogenous variables enter non-parametrically into the regression equation standard linear instrumental variables approaches fail. Two existing solutions are the non-parametric instrumental variables (NPIVs) estimators, which are based on a set of conditional moment restrictions (CMRs), and the control function (CF) estimators, which use conditional mean independence (CMI) restrictions. Our first contribution is to show that – similar to CMI – the CMR place shape restrictions on the conditional expectation of the error given the instruments and endogenous variables that are sufficient for identification, and we call our new estimator based on these restrictions the CMR-CF estimator. Our second contribution is to develop an estimator for non-linear and non-parametric settings that can combine both CMR and CMI restrictions, which cannot be done in either the NPIV nor the non-parametric CF setting. This new “Generalized CMR-CF” uses both CMR and CMI restrictions together by allowing the conditional expectation of the structural error to depend on both instruments and control variables. When sieves are used to approximate both the structural function and the CF our estimator reduces to a series of least squares regressions. Our Monte Carlos illustrate that our new estimator performs well across several economic settings.

CONFIDENCE INTERVALS OF THE ADJUSTED TAIL CONDITIONAL EXPECTATION RISK MEASURE FOR A STATIONARY SERIE

In this paper we present a semi-parametric estimator of the adjusted tail conditional expectation risk measure based on the theory of extreme values for a stationary serie. We prove its asymptotic normality and we construct the confidence intervals. The accuracy of these intervals is evaluated through a simulation study.

FMixFN: A Fast Big Data-Oriented Genomic Selection Model Based on an Iterative Conditional Expectation algorithm

Genomic selection is an approach to select elite breeding stock based on the use of dense genetic markers and that has led to the development of various models to derive a predictive equation. However, the current genomic selection software faces several issues such as low prediction accuracy, low computational efficiency, or an inability to handle large-scale sample data. We report the development of a genomic prediction model named FMixFN with four zero-mean normal distributions as the prior distributions to optimize the predictive ability and computing efficiency. The variance of the prior distributions in our model is precisely determined based on an F2 population, and genomic estimated breeding values (GEBV) can be obtained accurately and quickly in combination with an iterative conditional expectation algorithm. We demonstrated that FMixFN improves computational efficiency and predictive ability compared to other methods, such as GBLUP, SSgblup, MIX, BayesR, BayesA, and BayesB. Most importantly, FMixFN may handle large-scale sample data, and thus should be able to meet the needs of large breeding companies or combined breeding schedules. Our study developed a Bayes genomic selection model called FMixFN, which combines stable predictive ability and high computational efficiency, and is a big data-oriented genomic selection model that has potential in the future. The FMixFN method can be freely accessed at https://zenodo.org/record/5560913 (DOI: 10.5281/zenodo.5560913).

Conditioning

This chapter deals in depth with the concept of conditional expectation. This is defined first in the traditional “naïve” manner, and then using the measure theoretic approach. A comprehensive set of properties of the conditional expectation are proved, generalizing several results of Ch. 9, and then multiple sub‐σ‎‎‐fields and nesting are considered, concluding with a treatment of conditional distributions and conditional independence.