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All coins are biased. It's a question of how biased they are, but no coin has exactly equal chances of being heads or tails. In the frequentist approach, I think this calls for a test of equivalence: Decide how close to 0.50000 you will accept as unbiased. Do a power analysis to determine how many flips you will need to have a good (0.80? 0.90?) chance of ...


3

It means that you will need to confirm that this indeed is a global maximum by showing that the second derivative of the likelihood function and that point is negative and to test the values of the likelihood at the boundaries $θ→0^+$ and $ θ→∞$ as whuber pointed out in his comment.


3

The samples from the posterior allow you to compute expectations of the parameters. From Betancourt's A Conceptual Introduction to Hamiltonian Monte Carlo... Given sufficient time, the history of the Markov chain,$\{q_0,...,q_N\}$, denoted samples generated by the Markov chain, becomes a convenient quantification of the typical set....


2

Another perspective on this: Yes, of course you can do that, the only question in practice is how you do it. There's several options: You can work out the changes in variables etc. and explicitly define the implied priors on the untransformed variables. This is often impractical / requires a lot of work. If you can define your model in terms of the ...


2

While the CRLB is an inequality, and there is in general no reason for CRLB to hold with equality, it is in fact possible to say something about that possibility. A good book of theoretical statistics that does so, is Young and Smith: Essentials of Statistical Inference. I will try to review here what they do (around page 125.) Let $W(X)$ be an unbiased ...


1

The median is a smart choice here since it is pretty robust against outliers. It represents the value which splits the data between the lower half and the higher half - it can be read as the 50% percentile. https://en.wikipedia.org/wiki/Median


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Median, subsample mean, RPCA, any robust statistic operator...


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Consider the so-called final equation representation of a VAR in terms of an $ARMA(p,q)$. This builds on Zellner and Palm, J Econometrics 1974. Multiply the $n$-dimensional $VAR(p)$ $\Phi(L)y_t=\epsilon_t$ with $\Phi(L)^{adj}$, the adjoint matrix (or the adjugate) associated with $\Phi(L)$, in order to obtain the "final equations" $$ \det[\Phi(L)]y_t=\...


1

When you can not compute a posterior for $\mu$ because of missing information in the likelihood Below is a counterexample for a case where the likelihood function $p(y\vert \mu)$ is not uniquely defined by $\mu$, but depends in a more complex way on the vector $\theta$. Say you have the likelihoodfunction: $$Y \vert \theta_1+\theta_2 \sim N(\theta_1+\...


1

As I understand your question, I don't know weither this approach has a name ; expect maybe those of change-of-variable. Indeed, by defining a prior on $g(\theta)$, you are simply defining a prior on $\theta$ (assuming $g$ is monotonic, or bijective in multidimensional setting). More formally, using change of variable relationship gives: $$ p(\theta|y) \...


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