Question

我正在尝试将一个动态系统模型放在PyMC3中，以推断出两个参数。该模型是流行病学中常用的基本SIR：

dS / dt = - r0 * g * S * I

dI / dt = g * I（r * S - 1）

其中r0和g是要推断的参数。到目前为止，我根本无法走得太远。我见过的唯一一个将像这样的马尔可夫链组合在一起的例子会产生关于递归过于错误的错误。这是我的示例代码。

# Time
t = np.linspace(0, 8, 200)

# Simulated observation
def SIR(y, t, r0, gamma) :
    S = - r0 * gamma * y[0] * y[1]
    I = r0 * gamma * y[0] * y[1] - gamma * y[1]
    return [S, I]

# Currently no noise, we just want to infer params r0 = 16 and g = 0.5
solution = odeint(SIR, [0.99, 0.01, 0], t, args=(16., 0.5))


with pymc.Model() as model :
    r0 = pymc.Normal("r0", 15, sd=10)
    gamma = pymc.Uniform("gamma", 0.3, 1.)

    # Use forward Euler to solve
    dt = t[1] - t[0]

    # Initial conditions
    S = [0.99]
    I = [0.01]

    for i in range(1, len(t)) :
        S.append(pymc.Normal("S%i" % i, \
                         mu = S[-1] + dt * (-r0 * gamma * S[-1] * I[-1]), \
                         sd = solution[:, 0].std()))
        I.append(pymc.Normal("I%i" % i, \
                         mu = I[-1] + dt * ( r0 * gamma * S[-1] * I[-1] - gamma * I[-1]), \
                         sd = solution[:, 1].std()))

    Imcmc = pymc.Normal("Imcmc", mu = I, sd = solution[:, 1].std(), observed = solution[:, 1])

    #start = pymc.find_MAP()
    trace = pymc.sample(2000, pymc.NUTS())

非常感谢任何帮助。谢谢！

Answer 1

我会尝试定义一个新的发行版。像下面这样的东西。但是，这不太合适，而且我不太确定我做错了什么。

class SIR(Distribution): 
def __init__(self, gamma, r0,dt, std): 
    self.gamma = gamma
    self.r0 = r0
    self.std = std
    self.dt = dt

def logp(self, SI):
    r0 = self.r0 
    std = self.std 
    gamma = self.gamma 
    dt = self.dt

    S=SI[:,0]
    I=SI[:,1]

    Si = S[1:]
    Si_m1 = S[:-1]
    Ii = I[1:]
    Ii_m1 = I[:-1]

    Sdelta = (Si - Si_m1)
    Idelta = (Ii - Ii_m1)

    Sexpected_delta = dt* (-r0 * gamma * Si_m1 * Ii_m1)
    Iexpected_delta = dt * gamma * Ii_m1 *( r0 * Si_m1 - 1 )


    return (Normal.dist(Sexpected_delta, sd=std).logp(Sdelta) +
            Normal.dist(Iexpected_delta, sd=std).logp(Idelta))


with Model() as model: 
    r0 = pymc.Normal("r0", 15, sd=10)
    gamma = pymc.Normal("gamma", 0.3, 1.)
    std = .5
    dt = t[1]-t[0]


    SI = SIR('SI', gamma, r0, std,dt, observed=solution[:,:2])

    #start = pymc.find_MAP(start={'gamma' : .45, 'r0' : 17})
    trace = pymc.sample(2000, pymc.NUTS())

PyMC3中的简单动态模型

1 个答案: