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Questions tagged [decision-theory]

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Role of expected loss of the best forecast in decision theory

Suppose we have a random variable $Y$ with an unknown distribution $P$. We model it with a distribution $Q$. We are asked to make a point forecast under some type of loss $L$. We choose the loss ...
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Value of using a better normal distribution

I tried to derive this on my own, but my stats education proved too far back… (This is a problem in Bayesian decision theory – if that makes you uncomfortable, feel free to reformulate it) Let's say ...
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Is it rational to select a parameter posterior value because it maximizes utility, even if probability is low?

I did Bayesian parameter estimation and I have now an estimate of the posterior distribution for my model parameters (say I have 2000 samples). Now I would like to make the optimal decision under my ...
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Response time of sequential probability ratio test for continuous-time observation process?

I hope to simulate the response time of a binary decision problem given continuous-time observation using sequential probability ratio test (SPRT). Traditionally with discrete-time SPRT, we calculate ...
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How to prove that the prior for which Bayes rule is also the minimax rule, is the least favorable prior?

I have read in the book Mathematical Statistics: A Decision Theoretic Approach by Thomas Ferguson that The prior for which the Bayes rule is also minimax rule, then that prior is Least favorable prior....
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Questioning the axiom of continuity in Von Neumann–Morgenstern utility theorem

In my previous question, I aksed about they we care so much about expected utility, rather than e.g., the variance in utility (Why care so much about expected utility?) From the helpful answers, I ...
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bayesian decision making - comparing expected loss

The problem is like this: Suppose that I am considering which country should I invest on, country A and country B, based on their GDP growth rate $\alpha$. There are two possible choices for each ...
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Choose one of two normal distribution that will give the probability of biggest value when sampling it

Suppose you have two (or more) normal distributions with different mean and variance. You can draw only one sample of only one of the available distributions. Your goal is to get the biggest value ...
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What is minCases in C5.0Control using R

from Package (C5.0 Decision tree Using R ) definition "minCases : an integer for the smallest number of samples that must be put in at least two of the splits." I very confuse about it . Please ...
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How to categorize data as others if training set is not available?

I run into a problem. I am using the decision tree to classify the incident category based on the short description the user has used while logging the ticket. I have the training data only for 5 ...
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Model fitting vs minimizing expected risk

I'm confused about the mechanics of model fitting vs minimizing risk in decision theory. There's numerous resources online, but I can't seem to find a straight answer regarding what I'm confused about....
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Why is the risk function defined to be the expectation of loss function?

In decision theory, we define the risk associated with a particular predictor function as the expected value of the loss function. Since the input and output are considered random variables therefore ...
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Decision tree without the “tree”

I would like to construct something like a decision tree. However, instead of using "recursive partitioning" to build a tree, I would like to find an optimal set of "global" splits. For example, in a ...
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Can additional iterations of backward induction as described affect optimal policy?

Consider a game with the following properties: Single player Finite number of game states (after the player arrives at a terminal state, he or she can begin again from the start state; the player can ...
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Hypothesis testing using spectra

How does hypothesis testing work when a measurement is not a single number, but an entire spectrum? For instance, suppose we want to distinguish a species of plant based on its absorption spectrum. ...
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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 ...
295 views

Bayes estimate with weighted square error loss

First, let $T(x)$ be an estimator of $g(\theta)$ and assume we have a square error loss function defined as $$L[g(\theta),T(x)]=[g(\theta)-T(x)]^2$$ Then the posterior expected risk of $T$ is \...
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Minimize mis-classification - 0 - 1 output

I am studying logistic regression from the book Advanced Data Analysis from an Elementary Point of View which states the following on page 280: “We minimize the mis-classification rate by ...
322 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 ...
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Multidimensional Bayes point estimates

Consider the posterior distribution $p(\theta|x)$. We aim to find a "good" estimate of the random variable $\theta$. The Bayes risk associated with the loss function $L(\hat{\theta}, \theta)$ is ...
301 views