# 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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### Clarification Question from Berger's Statistical Decision Theory (Chapter 1, Exercise 12 a))

I have a CS background with intro stats courses, and currently, I am working through Berger's Statistical Decision Theory (the theoretical questions). I'd like to ask a clarification question: this is ...
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### Population bias in survey leading to inaction

This isn’t exactly an academic statistics question, but it is a real problem that I’m trying to understand with regards to bias in survey statistics leading to issues in real-world decision making. I’...
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### Questions regarding power of test and type II error

I´m preparing for a lecture in decision theory and I´m a little bit confused by the notation used by my prof. On the first slide under remark 3.2 point v) its written, that $\beta(\varphi)$ is equal ...
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### Majority vote method for regression trees when there are two peaks

For the majority vote method in statistical regression trees, I should get the most common occurrence in the data. However, there are two such peaks in the following data: ...
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### Modeling multiple-choice data

In my experiment, participants had to make a series of decisions between different options. On each trial, they were presented with a different number of options to choose from, and each option varied ...
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### N-ary decision tree with categorical features

I want to build an n-ary decision tree with categorical features. I am using ordinary ID3 algorithm to build a tree. Lets take the next dataset as a training dataset for building a decision tree: ...
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### Understanding what defines a Bayes optimal classifier in classification tasks

Say we are given a data-distribution $D$ over $\mathcal{X} \times \mathcal{Y}$, where $\mathcal{X}$ is our input/feature space and $\mathcal{Y}$ the set of (discrete) labels. Hence, $D$ is a joint-...
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### There is no decision theory that isn’t Bayesian... or is there?

David Manheim says in a comment under a blog post: If you’re not making decisions, there’s no need for Bayes. If you are, you’re Bayesian whether you like it or not – there is no decision theory that ...
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### James-Stein-style estimator when we place greater importance on some components

The James-Stein estimator allows us to get a better overall estimate of a mean vector (length $\ge 3$) than we would be able to get by estimating the components independently. My intuition is that, ...
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### Multiple hypothesis testing: lower bound for sample complexity of finding the different one

We have $m$ distributions $D_1,\dots,D_m$. We know that $m-1$ of them are $\mathcal{N}(\epsilon,\sigma^2)$ ($\epsilon>0$) and one of them is $\mathcal{N}(0,\sigma^2)$, but we don't know which one ...
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### Is a constant ever inadmissible?

For now, assume square loss. Let's estimate some parameter $\theta$, such as $\theta = \mu$ in $N(\mu, 1)$. Is there ever a case where there is no such $c$ to make $\hat{\theta} = c$ an admissible ...
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### Decision Theory: Why is it called a "least favorable prior"?

I'm currently reading the chapter on Statistical Decision Theory in Larry Wasserman's "All of Statistics". Reading the section 13.4 about Minimax Rules he introduces the so called Least ...
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### How is the threshold parameter practically selected for Scikit learn's decision tree algorithm and how to determine depth of tree?

I am referring to the so-called optimized CART algorithm that is explained on Scikit learn's website: https://scikit-learn.org/stable/modules/tree.html#mathematical-formulation I would appreciate if ...
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### Random forest that aggregates by taking the maximum over the trees instead of taking the average

I want to make a Random forest that aggregates by taking the maximum over the decision trees instead of taking the average. By default Sklearn is taking the average, and I couldn't find how to change ...
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### Better methodologies to make causal recommendations from correlated data?

I work as a data scientist at a SAAS company. We have an outcome variable, Y, that we consider "success" for our customers. We have a bunch of additional outcome variables X1, X2, X3 that ...
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