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根据2014年5月、9~11月在威海市中心渔港拖网渔获物中采集的白姑鱼(Pennahia argentata)样本,利用一种稳健的贝叶斯方法研究了白姑鱼体长(全长、标准体长)与体重的关系。为得到可靠的参数估计值,将体长与体重关系式转化为线性模型,利用t分布建立参数的似然函数,通过数据标准化方法得到白姑鱼体长与体重关系式参数的后验概率分布。结果显示,本文方法可以较好估计白姑鱼体长与体重关系式参数的后验概率分布,由标准化数据计算的斜率和截距间不存在相关关系。t分布参数ν的估计值随体长与体重数据而发生变化,其分布范围为27.87~56.5。春季、秋季和全年白姑鱼的全长与体重关系式分别为W=2.540×10~(-3) TL~(3.4662)、W=4.308×10~(-3) TL~(3.3223)和W=3.963×10~(-3)TL~(3.3406),标准体长与体重关系式分别为W=1.083×10~(-2)SL~(3.2051)、W=1.498×10~(-2)SL~(3.1201)和W=1.403×10~(-2)SL~(3.1347)。春季与秋季白姑鱼的全长与体重关系、标准体长与体重关系存在显著性差异,春季白姑鱼参数b大于秋季,参数a小于秋季。威海近海白姑鱼属正异速生长种类,雌、雄群体的全长与体重关系和标准体长与体重关系均不存在显著性差异。黄海白姑鱼参数b的值与东海和南海北部白姑鱼b的值可能存在显著差异。本文的贝叶斯方法可用于估计鱼类体长与体重关系式参数及其不确定性。
According to a sample of Pennahia argentata collected from fishing trawls in the fishing port of Weihai City from May to September 2014 from November to November 2014, the body length (full length , Standard body length) and weight. In order to get a reliable parameter estimation, the relationship between body length and body weight was transformed into a linear model. The likelihood function of parameter was established by t distribution. The posterior probability distribution of body length and body weight parameter was obtained by data normalization . The results show that the proposed method can estimate the posterior probability distribution of the body length and body weight parameters better. There is no correlation between the slope and the intercept calculated from the standardized data. The estimated value of t distribution parameter ν varies with body length and weight data, and its distribution ranges from 27.87 to 56.5. The relationship between the total length and body weight of Paulus fulva in spring, autumn and year were respectively W = 2.540 × 10 -3 TL ~ 3.4662, W = 4.308 × 10 -3 TL ~ 3.3223 and W = 3.963 × 10 -3 TL ~ 3.3406. The relationship between standard body length and body weight were W = 1.083 × 10 -2 SL ~ 3.2051 and W = 1.498 × 10 -2 ) SL ~ (3.1201) and W = 1.403 × 10 ~ (-2) SL ~ (3.1347). There was a significant difference between the body length and the body length of P. boletus in spring and autumn. The parameter b of P. boletus in spring was larger than that in autumn and the parameter a was smaller than that in autumn. There was no significant difference in the relationship between full length and body weight of female and male population and the relationship between standard body length and body weight. There may be a significant difference between the value of parameter b in Pseudosciaena crocea and the value of b in white sand crab in the East China Sea and the North China Sea. The Bayesian method in this paper can be used to estimate the relationship between body length and body weight of fish and its uncertainty.