Question

Q2. New Zealand was the last major land mass to be settled by human beings. The Shag River Mouth in Otago (lower South 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 and Higham (2000) describe the Radiocarbon dating of well-preserved barracouta thyrsites atun bones found at the Shag River Mouth 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 (?.?.) distribution, where the standard deviation o- 40. The observations are: Observation 4 990 CRA 940 1040 910 (a) Use a normal ( 1000, 2009 prior for ?. Find the posterior distribution g(H?yi, J1). (b) Find a 95% credible interval for (c) To find the ?, the calibrated date, the Stuiver, Reimer, and Braziunas marine curve was used. We will approximate this curve with the linear function 0-2203-.835xu Find the posterior distribution of 0 given y?...y4. (d) Find a 95% credible interval for 0, the calibrated date

Answer 1

40 and dtomi 2. 102 a 900

40 200レ k. 久2 100 40000 400

dir :( Kt+9.uilly, g5% credeblende nal 0 025 ob y* sre 96 0015 g4 059.

H75553 (194:059, 1155:53. れ 835 835 2. N(810-198 276 129 95%-(Kdth ge-810-196-4-1-9-b-9. 6, e& 10-199 訂句

,77-62 2 842.76g 95T. credible derlr is (117 628, 842 79