Created
April 21, 2019 16:40
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A simple Poisson state-space model with seasonality and overdispersion
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| data { | |
| int<lower=1> n; // n = 2632 | |
| int y[n]; // number of shootings per day | |
| } | |
| transformed data { | |
| int<lower=1,upper=365> yday[n]; | |
| for (i in 1:n) yday[i] = i % 365 + 1; | |
| } | |
| parameters { | |
| vector[n] mu_innovations; | |
| vector[365] seasonal_innovations; // yearly seasonality | |
| vector[n] u_overdispersion; | |
| real<lower=0> sigma_mu; | |
| real<lower=0> sigma_yday; | |
| real<lower=0> sigma_overdispersion; | |
| real baseline; | |
| } | |
| transformed parameters { | |
| // zero-mean seasonal term | |
| vector[365] y_seasonal; | |
| vector[n] mu; | |
| { vector[365] seasonal_with_trend; | |
| real trend; | |
| seasonal_with_trend = cumulative_sum(seasonal_innovations); | |
| trend = seasonal_with_trend[365]; | |
| for (i in 1:365) | |
| y_seasonal[i] = sigma_yday/100 * (seasonal_with_trend[i] - trend * i/365.0); } | |
| mu = sigma_mu/100 * cumulative_sum(mu_innovations); | |
| } | |
| model { | |
| seasonal_innovations ~ normal(0, 1); | |
| mu_innovations ~ normal(0, 1); | |
| u_overdispersion ~ normal(0, 1); | |
| y ~ poisson_log(baseline + mu + y_seasonal[yday] + sigma_overdispersion * u_overdispersion); | |
| sigma_mu ~ lognormal(-3.5 + log(100), 2); | |
| sigma_yday ~ lognormal(-3.5 + log(100), 2); | |
| sigma_overdispersion ~ lognormal(0, 2); | |
| } |
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