The Houhora site in Northland (top of North Island) New Zealand is one of the sites of
Question:
The Houhora site in Northland (top of North Island) New Zealand is one of the sites of early human inhabitation that New Zealand archeologists have investigated, in trying to determine when the Polynesian migration to New Zealand occurred and documenting local adaptations to New Zealand conditions. Petchey (2000) describe the Radiocarbon dating of well-preserved snapper Pagrus auratus bones found at the Houhora site. They obtained four acceptable samples which were analyzed by the Waikato University Carbon Dating Unit. Assume that the conventional radiocarbon age (CRA) of a sample follows the normal (µ, σ2) distribution where the standard deviation σ = 40 is known. The observations are:
Observation 1 234 CRA 1010 1000 950 1050
(a) Use a normal (1000, 2002) prior for µ. Find the posterior distribution g(µ|y1,...,y4).
(b) Find a 95% credible interval for µ.
(c) To find the θ, the calibrated date, the Stuiver, Reimer, Braziunas marine curve was used. We will approximate this curve with the linear function θ = 2203 − .835 × µ . Find the posterior distribution of θ given y1,...,y4.
(d) Find a 95% credible interval for θ, the calibrated date.
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