这是一份贝叶斯统计推断作业代写的成功案

$$
y_{t} \sim \operatorname{Normal}\left(\log \left(q K P_{t}\right), \sigma^{2}\right), \quad t=1, \ldots, n=23,
$$
where $q, K$, and $P_{t}$ denote the “catchability parameter,” “carrying capacity” of the environment, and biomass in year $t$ expressed as a proportion of the carrying capacity, respectively. In addition, the biomass dynamics are given by
$$
\log P_{t}=f\left(P_{t-1}\right)+u_{t}, \quad f\left(P_{t-1}\right)=\log \left[P_{t-1}+r P_{t-1}\left(1-P_{t-1}\right)-\frac{C_{t-1}}{K}\right],
$$
where $u_{t} \sim \operatorname{Normal}\left(0, \omega^{2}\right), r$ is the “intrinsic growth rate,” and $C_{t-1}$ denotes the total catch, in kilotonnes, during year $t-1$. To avoid the issues discussed above, we will express this, instead, as
$$
\log P_{t} \sim \operatorname{Normal}\left(f\left(P_{t-1}\right), \omega^{2}\right), \quad t=1, \ldots, n .
$$

STAT 770/BIOS 805/BIOSTAT695/PSY 525/625/SOCI612/STA 4504/STA 517 COURSE NOTES ：

$$
\psi_{i j}=\frac{D}{V_{i}} \exp \left(-\frac{C L_{i}}{V_{i}} t_{i j}\right)
$$
This is the unique solution to the following differential equation and initial condition, at time $t=t_{i j}$ :
$$
\frac{d C(t)}{d t}=-\frac{C L_{i}}{V_{i}} C(t), \quad C(t=0)=\frac{D}{V_{i}}
$$