Open House, ISM in Tachikawa, 2014.6.13統計数理研究所オープンハウス（立川）、H26.6.13ポスター発

Osamu Komori

小森 理

English

RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所 学術研究リポジトリ

2014年6月13日　統計数理研究所　オープンハウスFishery stock assessment based on asymmetric logistic modelOsamu Komori Department of Mathematical Analysis and Statistical Inference,Project Assistant Professor1 AbstractThe stock assessment data such as RAM legacy data is essential for construct-ing an estimation model because the biomass in that data reﬂects the abun-dance of marine stock status properly. However, the available assessmentdata has limited sample size due to intensive data requirements and largeamount of cost, and the ratio of collapsed stocks to non-collapsed stocks ishighly imbalanced (very few collapse stocks in comparison with large numberof non-collapse stocks). Moreover the stock status (collapse or non-collapse)is not deterministic, which is in fact estimated by stochastic biomass dynam-ics models such as age-structured model. To allow for the imbalancednessand uncertainty involved in the ﬁshery data, we propose a new binary regres-sion model with mixed eﬀects for estimation of stock status by employing anasymmetric model. In the proposed model, we assume that the small partof observations of the collapsed stocks are distributed in the same way asthose of the non-collapsed stocks, resulting in a mixture model of conditionalprobability of collapsed status given explanatory variables in ﬁshery-relateddata. In the estimation equation, we observe that the weights for the non-collapse stocks are relatively reduced, which in turn puts more importanceon the small numbers of observations of collapse stocks. As a result, the esti-mated collapse probabilities are much improved with a little degeneration ofthe estimated probabilities of non-collapsed stocks.2 Materical and methodsWe developed an aymmetric logistic regression with mixed eﬀects to con-struct a prediction model of ﬁshery status based on assessed stocks in RAMdata and applied it to estimate the global ﬁshery status based on unassessedstocks in FAO data. The asymmetric logistic regression means that we usean asymmetric logistic function as a link function in the generalized linearmixed model to allow for the imbalance in sample size and uncertainty ofclass labeling (collapse or non-collapse). The datset used for the predictionmodel consists of amout of catch, life history, major ﬁshing areas as well asbiomass information, which are commonly and widely investigated in preced-ing literature Thorson, Branch and Jensen (2012); Costello, Ovando, Hilborn,Gaines, Deschenes and Lester (2012). Some stocks in FAO data were identi-ﬁed to have high probability of being collapsed and those characteristics wereclariﬁed based on ﬁsh category and location information.2.1 Asymmetric logistic regressionAs seen in Figure 1, there are very few collapsed stocks in comparison with alarge number of non-collpased stocks in RAM data. In this case, the typicalstatistical method such as logistic regression model does not work properly.That is, it causes that the prediction for non-collapse stocks is accurate; whilethe prediction for collapse stocks is not accurate. As a result, the over-all errorrate could unresonably be estimated to be very low in a validation procedure.Our aim is to propose a robust method to that unregular situation for theprediction of stock status. Let y 2 f0; 1g be a class label for non-collapse(y = 0) and collapse (y = 1), which is determined every year during the ob-servation period, x and z be explanatory variables associated with the ﬁxedand random eﬀects, respectively. Then the conditional probability of y given(x; z) in a mixed-eﬀect asymmetric logistic regression is formulated asp(yjx; z; b; ±) = (1¡ ±) expfy(x>¯ + z>b)g + ±1 + ± + (1¡ ±) exp(x>¯ + z>b); (1)where ¯ and b are ﬁxed and random eﬀects, respectively. Note that if ± = 0,then it is reduced to a conditional probability in a usual logistic regressoinpL(yjx; z; b) =expfy(x>¯ + z>b)g1 + exp(x>¯ + z>b): (2)Then we havep(yjx; z; b; ±) =½w(x; z; ±)pL(0jx; z; b) if y = 0w(x; z; ±)f(1¡ ±)pL(1jx; z; b) + ±pL(0jx; z; b)g if y = 1 ;(3)wherew(x; z; ±) =1 + exp(x>¯ + z>b)1 + ± + (1¡ ±) exp(x>¯ + z>b): (4)We observe from (3) that p(yjx; z; b; ±) equals pL(yjx; z; b) when y = 0 apartfrom the normalizing constant w(x; z; ±), while p(yjx; z; b; ±) is a contami-nated model of pL(yjx; z; b) with the mislabel probability ± Copas (1988);Takenouchi and Eguchi (2004); Hayashi (2012). We assume for the tuningparameter ± to satisfy 0 · ± · 1. The conditional probability (1) morecorrectly reﬂects the present situation in probabilistic manner. We conﬁrmthat the likelihood ration is given byp(1jx; z; b; ±)p(0jx; z; b; ±) = (1¡ ±)pL(1jx; z; b)pL(0jx; z; b)+ ±; (5)which implies that the linear discriminant function x>¯ + z>b satisﬁes theBayes risk consistency.1953 1959 1965 1971 1977 1983 1989 1995 2001 2007number of stocks050100150200050100150200non−collapsecollapseFigure 1: Barplots of numbers of non-collapsed stocks (gray) and collapsed stocks (red)during the observation yearsTable 1: Mean 5-cross-validated AUC, TPR and TNR calculated for RAM legacy data set.Year catch method logistic model asymmetric modelAUC TPR TNR AUC TPR TNR AUC TPR TNR ±2000 0.906 0.013 0.999 0.891 0.093 0.988 0.892 0.100 0.984 0.0042001 0.860 0 1 0.879 0.087 0.988 0.878 0.093 0.987 0.0032002 0.877 0 1 0.908 0.165 0.982 0.905 0.165 0.981 0.0032003 0.828 0 1 0.822 0.133 0.992 0.858 0.378 0.964 0.0162004 0.839 0 1 0.825 0.10 0.987 0.860 0.365 0.969 0.0162005 0.865 0.009 0.997 0.870 0.293 0.973 0.884 0.475 0.951 0.0152006 0.885 0.134 0.97 0.879 0.267 0.966 0.884 0.303 0.956 0.0082007 0.852 0 0.99 0.852 0 0.984 0.853 0.01 0.982 0.006ReferencesCopas, J. (1988). Binary Regression Models for Contaminated Data. Journal of the Royal Statistical So-ciety: Series B. 50, 225–265.Costello, C., Ovando, D., Hilborn, R., Gaines, S. D., Deschenes, O. and Lester, S. E.(2012). Status and Solutions for the World ’s Unassessed Fisheries. Science 338, 517–520.Hayashi, K. (2012). A boosting method with asymmetric mislabeling probabilities which depend on covari-ates. Computational Statistics 27, 203–218.Takenouchi, T. and Eguchi, S. (2004). Robustifying AdaBoost by adding the naive error rate. NeuralComputation 16, 767–787.Thorson, J. T., Branch, T. A. and Jensen, O. P. (2012). Using model-based inference to evaluateglobal ﬁsheries status from landings, location, and life history data. Can. J. Fish. Aquat. Sci 69, 645–655.

Fishery stock assessment based on asymmetric logistic model

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Fishery stock assessment based on asymmetric logistic model

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Fishery stock assessment based on asymmetric logistic model

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