我目前正在 JAGS 中实现足球结果预测模型。实际上，我已经实现了几个，但我已经遇到了迄今为​​止最困难的挑战：Rue & Salvesen 在他们的论文“Prediction and retrospective analysis of football matches in a League”中描述的一个模型。他们的模型使用混合模型来截断以 5 个进球后攻击/防守强度为条件的泊松分布。他们还采用了 Dixon & Coles (1997) 的一项法则，以增加低分比赛中 0-0 和 1-1 结果的概率。

我的问题如下，我正在尝试实现混合模型：

$$\pi_{g1}(x_{A,B},y_{A,B}|\lambda_{A,B}^{(x)},\lambda_{A,B}^{(y)}) = \kappa(x_{A,B},y_{A,B}|\lambda_{A,B}^{(x)},\lambda_{A,B}^{(y)})Po(x_{A,B}|\lambda_{A,B}^{(x)})Po(y_{A,B}|\lambda_{A,B}^{(y)})$$ 在哪里$x_{A,B}$表示主队在 A 队和 B 队之间的比赛中的进球数，并且$log(\lambda_{A,B}^{(x)})$表示球队的实力。我试图通过使用 0-ones 技巧在 JAGS 中实现这两个定律，但到目前为止没有运气（error: illegal parent values）。到目前为止，我的 JAGS 模型：

data {
    C <- 10000

    for(i in 1:noGames) {
        zeros[i] <- 0
    }

    homeGoalAvg <- 0.395
    awayGoalAvg <- 0.098

    rho <- 0.1
}

model {

    ### Time model - Brownian motion
    tau ~ dgamma(10, 0.1)
    precision ~ dgamma(0.1, 1)

    for(t in 1:noTeams) {
        attack[t, 1] ~ dnorm(0, precision)
        defence[t, 1] ~ dnorm(0, precision)

        for(s in 2:noTimeslices) {
            attack[t, s] ~ dnorm(attack[t, (s-1)], (tau * precision) / 
                                         (abs(days[t,s]-days[t,s-1])))
            defence[t, s] ~ dnorm(defence[t, (s-1)], (tau * precision) / 
                                          (abs(days[t,s]-days[t,s-1])))
        }
    }

    ### Goal model
    gamma ~ dunif(0, 0.1)

    for(i in 1:noGames) {

        delta[i]            <-  (
                                attack[team[i, 1], timeslice[i, 1]] + 
                                defence[team[i, 1], timeslice[i, 1]] -
                                attack[team[i, 2], timeslice[i, 2]] - 
                                defence[team[i, 2], timeslice[i, 2]]
                            ) / 2

        log(homeLambda[i])  <-  (
                                    homeGoalAvg + 
                                    (
                                        attack[team[i, 1], timeslice[i, 1]] - 
                                        defence[team[i, 2], timeslice[i, 2]] -
                                        gamma * delta[i]
                                    )
                                )

        log(awayLambda[i])  <-  (
                                    awayGoalAvg + 
                                    (
                                        attack[team[i, 2], timeslice[i, 2]] - 
                                        defence[team[i, 1], timeslice[i, 1]] +
                                        gamma * delta[i]
                                    )
                                )

        goalsScored[i, 1] ~ dpois( homeLambda[i] )
        goalsScored[i, 2] ~ dpois( awayLambda[i] )

        is0X[i] <- ifelse(goalsScored[i, 1]==0, 1, 0)
        isX0[i] <- ifelse(goalsScored[i, 2]==0, 1, 0)
        is1X[i] <- ifelse(goalsScored[i, 1]==1, 1, 0)
        isX1[i] <- ifelse(goalsScored[i, 2]==1, 1, 0)
        is00[i] <- is0X[i] * isX0[i]
        is01[i] <- is0X[i] * isX1[i]
        is10[i] <- is1X[i] * isX0[i]
        is11[i] <- is1X[i] * isX1[i]

        kappa[i] <- (
                        is00[i] * ( 1 + (homeLambda[i] * awayLambda[i] * rho) ) + 
                        is01[i] * ( 1 - (homeLambda[i] * rho                ) ) + 
                        is10[i] * ( 1 - (awayLambda[i] * rho                ) ) + 
                        is11[i] * ( 1 + rho                                     ) + 
                        1 -       ( is00[i] + is01[i] + is10[i] + is11[i]     )
                    )

        # This does not work!
        zeros[i] ~ dpois(-log(kappa[i]) + C)
    }

}