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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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34k views

The situation Some researchers would like to put you to sleep. Depending on the secret toss of a fair coin, they will briefly awaken you either once (Heads) or twice (Tails). After each waking, they ...
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### Why care so much about expected utility?

I have a naive question about decision theory. We calculate the probabilities of various outcomes assuming particular decisions and assign utilities or costs to each outcome. We find the optimal ...
12k views

### What are complete sufficient statistics?

I have some trouble understanding complete sufficient statistics? Let $T=\Sigma x_i$ be a sufficient statistic. If $E[g(T)]=0$ with probability 1, for some function $g$, then it is a complete ...
1k views

### How to make optimal decisions with uncertain outcomes: achieving a "Yahtzee"

The game of Yahtzee is a poker-like game played with dice. Each move consists of three rolls of five (ordinary, fair, six-sided) dice. After each of the first two rolls the player may designate any ...
21k views

### Understanding the Bayes risk

When evaluating an estimator, the two probably most common used criteria are the maximum risk and the Bayes risk. My question refers to the latter one: The bayes risk under the prior $\pi$ is defined ...
2k views

### What is the decision-theoretic justification for Bayesian credible interval procedures?

(To see why I wrote this, check the comments below my answer to this question.) Type III errors and statistical decision theory Giving the right answer to the wrong question is sometimes called a Type ...
3k views

### What is a loss function in decision theory?

My notes define a loss function as the 'cost' incurred when the true value of $\theta$ is estimated by $\hat\theta$. What kind of cost is it talking about? monetary cost? or is it something related to ...
1k views

### Is a loss function the flip side of a coin to a utility function, or are they not related?

I'm trying to get a grasp on utility and loss functions, and at first I thought that a utility function was the flipside of a loss function and vice versa. Kind of like how if you know the probability ...
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### Different definitions of Bayes risk

I'm having trouble understanding the proper definition of Bayes risk. Let the data/variate $x \sim P(X|\theta)$, $\theta\in \Theta$, $\pi$ be a distribution on $\Theta$ (prior), $\hat \theta(x)$ be ...
4k views

### Aside from Durbin-Watson, what hypothesis tests can produce inconclusive results?

The Durbin-Watson test statistic can lie in an inconclusive region, where it is not possible either to reject or fail to reject the null hypothesis (in this case, of zero autocorrelation). What other ...
221 views

### What problem or game are variance and standard deviation optimal solutions for?

For a given random variable (or a population, or a stochastic process), mathematical expectation is the answer to a question What point forecast minimizes the expected square loss?. Also, it is the ...
998 views

### What is the relation between statistics theory and decision theory?

I was wondering how statistics and decision theory are related? It looks to me all the statistics problems/tasks can be formulated in decision theory. Also problems in decision theory can be ...
867 views

### Does a density forecast add value beyond a point forecast when the loss function is given?

Density forecasts are more universal than point forecasts; they provide information on the whole predicted distribution of a random variable rather than on a concrete function thereof (such as ...
805 views

### Drawing numbered balls from an urn

PROBLEM There is an urn with a set of balls where each ball is labeled with a different integer. The numbers on the balls are known and are not a range of integers. For example the set of balls could ...
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### Quadratic loss function implying conditional expectation

I am reading Bishop's pattern recognition book. In the decision theory part he first derives that using a quadratic loss function implies that our estimate $y(x)$ should be the conditional expectation ...
988 views

### Uniform random variables and optimal strategy

This comes from Fivethirtyeight's riddler weekly challenge... Toddler poker is played by two players. Each is dealt a “card,” which is actually a number randomly chosen uniformly from the ...
146 views

### Machine learning methods for exploring relationships for a continuous response variable

I would like to explore a model to predict the value of a continuous response variable, from a set (around 100) of explanatory variables. I do not want to apply PCA like feature reduction, because I ...
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### Is summing posterior probabilities valid for classification problems?

A classification for two mutually exclusive problem can be formulated by having a decision hinge on whether $P_0(x) > P_1(x)$ or $P_0(x) < P_1(x)$ where $P_0(x)$ and $P_1(x)$ are posterior ...
700 views

### Derivation of Bayes classifier in Murphy's book

I am reading Kevin Murphy's Machine Learning book (MLAPP, 1st printing) and want to know how he got the expression for the Bayes classifier using minimization of the posterior expected loss. He wrote ...
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### How to Build a Model with Correlation / Statistical Dependency for Bayesian A / B Testing

I use the Beta Binomial model for A/B testing. I wonder if there a way to build a model in PyMC which models correlation between the conversion rate of group A with ...