Statistical Inference - Parameter Space

**simplemts** · 10-24-2012 12:06 AM

"Suppose that ( $x_1$ , ... , $x_n$ ) is a sample from a Bernoulli( $\theta$ ) distribution with $\theta$ an element of [0,1] unknown.
We take the parameter space to be [0,1], the set of all possible values for $\theta$ .
We parametize the model by "Characteristic" - ln{ $\theta/$ / (1 - $\theta$ )
Record the statistical model using this parameterization, i.e. record the probability function using "characteristic" as the parameter and record the relevant parameter space.

I'm trying to figure out: 1) Just what the hell this is asking 2) How to start it.

**Dason** · 10-24-2012 08:05 AM

My guess is that they want you to write something like $\eta = -\log(\frac{\theta}{1-\theta})$ and then only use $\eta$ when writing the pmf. Then it wants to know what is the valid parameter space for $\eta$ . Does that make it a little more clear?

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