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# Questions tagged [decision-theory]

Decision theory is the science of making optimal decisions in the face of uncertainty. Statistical decision theory is concerned with the making of decisions when in the presence of statistical knowledge (data) which sheds light on some of the uncertainties involved in the decision problem.

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### Random Forest explanation

I am having trouble understanding Random Forest, especially some terms. What is a node what is node size? What are ...
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### How does an estimator that minimizes a weighted sum of squared bias and variance fit into decision theory?

Okay--my original message failed to elicit a response; so, let me put the question a differently. I will start by explaining my understanding of estimation from a decision theoretic perspective. I ...
204 views

### Optimal decision process to estimate Markov chain limiting distribution

Suppose there is a irreducible, reversible Markov chain with known states $1,\ldots,N$ and unknown transition matrix $T_{ij}$ and unknown limiting distribution $\pi_i$. I am able to repeatedly ...
311 views

### What is the meaning of admissibility within a class, that every decision rule in a class is admissible in that class?

Suppose that I have that $X$ is a Poisson random variable with mean $\lambda$. Suppose a decision rule is to estimate $\lambda$ by using $\delta(Y) = aY$. Now, let $K$ be the class of all decision ...
161 views

### Non-probabilistic vs probabilistic frameworks for decision theory in metric spaces

I have a task to make a decision, say to classify an object as $X$ or $\overline X$. However, $\overline X$ usually means everything else and you only have positive examples of $X$ and not so many ...
1 vote
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### Is there a distribution where the data is generated from a decision process?

Sometimes my data is the result of the decisions each individuum of the observed population made: how much invest, how much gambled etc. The outcome would be a metric variable: money spent in total by ...
1 vote
Show that admissibility of a decision rule under weighted square error loss implies it's admissibility under square error loss. Weighted Square error loss = $\frac {(d(x) - \theta)^2}{\theta*(1-\... 2 votes 1 answer 946 views ### admissibility of bayes rule How to show that for a binomial(n, p) distribution, the MLE X/n is admissible under square error loss? The Bayes rule undr square error loss with beta($\alpha, \beta$) prior is X+$\alpha$/ (n +$\...
Suppose we are trying to estimate a real valued parameter under the linear exponential (LINEX) loss. Suppose we have some prior $g$ that has finite mean, variance and a moment generating function. ...