MCMCpoisson  R Documentation 
This function generates a sample from the posterior distribution of a Poisson regression model using a random walk Metropolis algorithm. The user supplies data and priors, and a sample from the posterior distribution is returned as an mcmc object, which can be subsequently analyzed with functions provided in the coda package.
MCMCpoisson(
formula,
data = NULL,
burnin = 1000,
mcmc = 10000,
thin = 1,
tune = 1.1,
verbose = 0,
seed = NA,
beta.start = NA,
b0 = 0,
B0 = 0,
marginal.likelihood = c("none", "Laplace"),
...
)
formula 
Model formula. 
data 
Data frame. 
burnin 
The number of burnin iterations for the sampler. 
mcmc 
The number of Metropolis iterations for the sampler. 
thin 
The thinning interval used in the simulation. The number of mcmc iterations must be divisible by this value. 
tune 
Metropolis tuning parameter. Can be either a positive scalar or
a 
verbose 
A switch which determines whether or not the progress of the
sampler is printed to the screen. If 
seed 
The seed for the random number generator. If NA, the Mersenne
Twister generator is used with default seed 12345; if an integer is passed
it is used to seed the Mersenne twister. The user can also pass a list of
length two to use the L'Ecuyer random number generator, which is suitable
for parallel computation. The first element of the list is the L'Ecuyer
seed, which is a vector of length six or NA (if NA a default seed of

beta.start 
The starting value for the 
b0 
The prior mean of 
B0 
The prior precision of 
marginal.likelihood 
How should the marginal likelihood be calculated?
Options are: 
... 
further arguments to be passed. 
MCMCpoisson
simulates from the posterior distribution of a Poisson
regression model using a random walk Metropolis algorithm. The simulation
proper is done in compiled C++ code to maximize efficiency. Please consult
the coda documentation for a comprehensive list of functions that can be
used to analyze the posterior sample.
The model takes the following form:
y_i \sim \mathcal{P}oisson(\mu_i)
Where the inverse link function:
\mu_i = \exp(x_i'\beta)
We assume a multivariate Normal prior on \beta
:
\beta \sim \mathcal{N}(b_0,B_0^{1})
The Metropois proposal distribution is centered at the current value of
\theta
and has variancecovariance V = T (B_0 + C^{1})^{1} T
where T
is a the diagonal positive definite matrix formed from the
tune
, B_0
is the prior precision, and C
is the
large sample variancecovariance matrix of the MLEs. This last calculation
is done via an initial call to glm
.
An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package.
Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park. 2011. “MCMCpack: Markov Chain Monte Carlo in R.”, Journal of Statistical Software. 42(9): 121. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v042.i09")}.
Daniel Pemstein, Kevin M. Quinn, and Andrew D. Martin. 2007. Scythe Statistical Library 1.0. http://scythe.lsa.umich.edu.
Martyn Plummer, Nicky Best, Kate Cowles, and Karen Vines. 2006. “Output Analysis and Diagnostics for MCMC (CODA)”, R News. 6(1): 711. https://CRAN.Rproject.org/doc/Rnews/Rnews_20061.pdf.
plot.mcmc
,summary.mcmc
,
glm
## Not run:
counts < c(18,17,15,20,10,20,25,13,12)
outcome < gl(3,1,9)
treatment < gl(3,3)
posterior < MCMCpoisson(counts ~ outcome + treatment)
plot(posterior)
summary(posterior)
## End(Not run)
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