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- W1000422594 abstract "Consider a simple mixture experiment conducted in two stages as follows: V is a positive random variable with density pV(v); in the first stage of the experiment the value v of V is observed; at the second stage, a random sample X(n) = (X1, X2,..., Xn) is drawn from a normal density with an unknown mean α and variance v. Our aim is to draw inference about α. If we consider (X(n),v) as our sample the joint likelihood is given by $$left{ {{p_{{X(n)}}}|{V^{{(x(n)|V = v;alpha )}}}} right}{p_{V}}(v)$$where we assume that pV is free from α. The usual conditionality principle (see e.g. Cox and Hinkley (1974), p.38) then suggests that the inference about θ should be based on the density pX(n) | V where the value of v is known. Suppose now that the value v is unknown to the experimenter even though it is known that the first stage of the experiment has been performed. We then have only X(n) as our sample and the information that the experiment on V has been performed. The conditionality principle will still be in force; we may treat v as an unknown nuisance parameter and use the density pX(n) | V for inference about α." @default.
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- W1000422594 date "1983-01-01" @default.
- W1000422594 modified "2023-09-27" @default.
- W1000422594 title "Mixture Experiments and Conditional Inference" @default.
- W1000422594 doi "https://doi.org/10.1007/978-1-4612-5505-5_5" @default.
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