Asymmetric Loss Functions for Forecasting in Criminal Justice Settings

Berk, Richard A.

doi:10.1007/s10940-010-9098-2

Cited by 38 publications

(28 citation statements)

References 41 publications

(27 reference statements)

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“…Here is where an asymmetric LF plays a key role because it assigns very small penalties to those individuals whose BV distributions are to the right of the hypothetical parental distribution. One simple asymmetric LF is the linear-linear loss (LinLin), whose behavior is linear on both sides of the target; it has the

α \in (0, 1)

term that induces different penalties (Berk 2011) and is the loss of the quantile regression. The LinLin LF is defined as

L (F_{Y}_{o}, α) = (α - 1 (e < 0)) e

where

e = μ_{s} - μ_{2} = S - R = σ i (1 - h^{2})

; then this LF is also a decreasing function of

h^{2}

.…”

Section: Methodsmentioning

confidence: 99%

A Bayesian Decision Theory Approach for Genomic Selection

Villar-Hernández

Pérez-Elizalde

Crossa

et al. 2018

G3 Genes|Genomes|Genetics

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Plant and animal breeders are interested in selecting the best individuals from a candidate set for the next breeding cycle. In this paper, we propose a formal method under the Bayesian decision theory framework to tackle the selection problem based on genomic selection (GS) in single- and multi-trait settings. We proposed and tested three univariate loss functions (Kullback-Leibler, KL; Continuous Ranked Probability Score, CRPS; Linear-Linear loss, LinLin) and their corresponding multivariate generalizations (Kullback-Leibler, KL; Energy Score, EnergyS; and the Multivariate Asymmetric Loss Function, MALF). We derived and expressed all the loss functions in terms of heritability and tested them on a real wheat dataset for one cycle of selection and in a simulated selection program. The performance of each univariate loss function was compared with the standard method of selection (Std) that does not use loss functions. We compared the performance in terms of the selection response and the decrease in the population’s genetic variance during recurrent breeding cycles. Results suggest that it is possible to obtain better performance in a long-term breeding program using the single-trait scheme by selecting 30% of the best individuals in each cycle but not by selecting 10% of the best individuals. For the multi-trait approach, results show that the population mean for all traits under consideration had positive gains, even though two of the traits were negatively correlated. The corresponding population variances were not statistically different from the different loss function during the 10th selection cycle. Using the loss function should be a useful criterion when selecting the candidates for selection for the next breeding cycle.

show abstract

α \in (0, 1)

term that induces different penalties (Berk 2011) and is the loss of the quantile regression. The LinLin LF is defined as

L (F_{Y}_{o}, α) = (α - 1 (e < 0)) e

where

e = μ_{s} - μ_{2} = S - R = σ i (1 - h^{2})

; then this LF is also a decreasing function of

h^{2}

.…”

Section: Methodsmentioning

confidence: 99%

A Bayesian Decision Theory Approach for Genomic Selection

Villar-Hernández

Pérez-Elizalde

Crossa

et al. 2018

G3 Genes|Genomes|Genetics

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show abstract

“…The kind of arrest really matters. In particular, arrests for crimes of violence are distinguished from other kinds of arrests. Forecasting errors that do not have equal costs can be introduced into the procedure at the beginning so that all of the results properly represent the preferences of stakeholders (Berk, ). Regularization is often built directly into the procedure to increase forecasting accuracy (Hastie et al., : Ch. 5, section 8.7). Highly unbalanced distributions for the classes to be forecasted create no special problems as long as the rare outcomes are important enough to be given extra weight in the analysis.…”

Section: Some Conceptual Fundamentalsmentioning

confidence: 99%

Statistical Procedures for Forecasting Criminal Behavior

Berk

Bleich

2013

Criminology & Public Policy

141

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“…7 7 The relative costs of type I and type II errors, which are context specific, drive whether a prediction exercise is justifiable from a policy perspective (Berk, 2011; Bushway, 2011). …”

mentioning

confidence: 99%