Question

这个问题之前被问到并且没有得到回答（6月5日），但是将它放在上下文中更有意义。我已经使用两个lambdas完成了变换点教程并使用2个变换点进行了扩展，因此现在建模：

# the exp parameter expected is the inverse of the average from sampled series
alpha = 1.0 / count_data.mean() 
# regime 1 poisson
lambda_1 = pm.Exponential("lambda_1", alpha)
# regime 2 poisson
lambda_2 = pm.Exponential("lambda_2", alpha)

# regime 3 poisson
lambda_3 = pm.Exponential("lambda_3", alpha)

# change point is somewhere in between with equal probabilities
tau1 = pm.DiscreteUniform("tau1", lower=0, upper=n_count_data)
# change point is somewhere in between with equal probabilities
tau2 = pm.DiscreteUniform("tau2", lower=0, upper=n_count_data)

@pm.deterministic
def lambda_(tau1=tau1,tau2=tau2, lambda_1=lambda_1, lambda_2=lambda_2):
    out = np.zeros(n_count_data)
    out[:tau1] = lambda_1  # lambda before tau is lambda1
    out[tau1:tau2] = lambda_2  # lambda between periods is lambda2
    out[tau2:] = lambda_3  # lambda after (and including) tau2 is lambda3
    return out

observation = pm.Poisson("obs", lambda_, value=count_data, observed=True)

model = pm.Model([observation, lambda_1, lambda_2, tau1,tau2])

# markov monte carlo chain
mcmc = pm.MCMC(model)
mcmc.sample(40000, 10000, 1)

问题是，在确定性变量中，我如何实际告诉模型我只需要在tau1小于tau2时考虑？问题是当tau2在tau1之前时，存在时间对称性，这在计算上是不必要的。

欢迎任何帮助。

Answer 1

我没有测试过，但我认为你可以这样做：

# change point is somewhere in between with equal probabilities
tau1 = pm.DiscreteUniform("tau1", lower=0, upper=n_count_data)
# change point is somewhere in between with equal probabilities
tau2 = pm.DiscreteUniform("tau2", lower=tau1, upper=n_count_data)

这样tau2被限制为至少与tau1一样大。您可能需要考虑一下tau1和tau2是否应该重合。

Answer 2

在假设确定性差距的假设下，完整模型如下：

# the exp parameter expected is the inverse of the average from sampled series
alpha = 1.0 / count_data.mean() 
# regime 1 poisson
lambda_1 = pm.Exponential("lambda_1", alpha)
# regime 2 poisson
lambda_2 = pm.Exponential("lambda_2", alpha)
# regime 3 poisson
lambda_3 = pm.Exponential("lambda_3", alpha)

# change point is somewhere in between with equal probabilities
tau1 = pm.DiscreteUniform("tau1", lower=0, upper=n_count_data)
# change point is somewhere in between with equal probabilities
tau2 = pm.DiscreteUniform("tau2", lower=tau1+1, upper=n_count_data)

@pm.deterministic
def lambda_(tau1=tau1,tau2=tau2, lambda_1=lambda_1, lambda_2=lambda_2,lambda_3=lambda_3):
    out = np.zeros(n_count_data)
    out[:tau1] = lambda_1  # lambda before tau is lambda1
    out[tau1:tau2] = lambda_2  # lambda between periods is lambda2
    out[tau2:] = lambda_3  # lambda after (and including) tau2 is lambda3
    return out

observation = pm.Poisson("obs", lambda_, value=count_data, observed=True)

model = pm.Model([observation, lambda_1, lambda_2,lambda_3, tau1,tau2])

# markov monte carlo chain
mcmc = pm.MCMC(model)
mcmc.sample(40000, 10000, 1)

lambda_1_samples = mcmc.trace('lambda_1')[:]
lambda_2_samples = mcmc.trace('lambda_2')[:]
lambda_3_samples = mcmc.trace('lambda_3')[:]

tau1_samples = mcmc.trace('tau1')[:]
tau2_samples = mcmc.trace('tau2')[:]

也会尝试随机差距，看看它是怎么回事。

Answer 3

如果您愿意使用R解决相同的推理问题，则mcp包将为更改点问题提供更高级别的接口。默认情况下，它具有顺序受限的更改点参数。

这是三个拦截（两个变化点）的模型

model = list(
  count ~ 1,
  ~ 1,
  ~ 1
)

library(mcp)
fit = mcp(model, data, family = poisson())

更多信息：

about Poisson models in mcp。
priors in mcp包含有关更好地控制顺序限制的更多信息。

通过两个转换更改点检测

3 个答案: