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我试图在 PyMC3 中组合一个动态系统模型，以推断两个参数。该模型是基本的 SIR，常用于流行病学：

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，我根本无法走得很远。我见过的将这样的马尔可夫链组合在一起的唯一示例会产生关于递归太深的错误。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())

任何帮助将非常感激。谢谢 ！

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1 回答 1

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我会尝试定义一个新的发行版。类似于以下内容。但是，这不太有效，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())
于 2014-01-22T08:26:20.940 回答