# 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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### Does scoring rules really only apply to categorical outcomes?

The wikipedia article on scoring rule says that It is applicable to tasks in which predictions must assign probabilities to a set of mutually exclusive outcomes or classes. The set of possible ...
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### Drift-diffusion model: Can the accumulated evidence be expressed as probability?

For a reaction-time model, I am considering whether I can compare 1) a probabilistic classifier or survival model and 2) a drift-diffusion model (DDM). I am interested in predicting reaction ...
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### In Bayesian Parameter Estimation - How Is The Parameter's Priori PDF Found? [duplicate]

I wish to explain my confusion through an example, so I understand all the contextuals aswell: Say I want to predict the chance of someone being a European man $C_M$ based on their height $x_i$. I.e I ...
1 vote
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### A Proper Conjugate Model for A/B Test for Revenue per Click (RPC)

What would be a proper Conjugate Posterior model for Earning / Revenue per Click in A/B test? The data is the total number of visitors and the total revenue per day per variant (A and B). What are the ...
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### James-Stein estimator with multiple samples

Let $X_1, \dots, X_n \in \mathbb{R}^p$ be i.i.d. samples from the $p$-normal distribution $N(\theta, \tau^2 I)$. Suppose we are interested in estimating $\theta$ with known variance $\tau^2$. Take the ...
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### Does a high-listed attribute in a Decision Tree represent a major cause for the target class?

I am wondering about two questions: Let us assume we have a Decision Tree, which wants to predict health. If the attribute "smoking (yes/no/occasionally)" is listed relatively high in the ...
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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 ...
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### Which predictive models output the posterior distribution?

In a supervised learning context, the posterior distribution of the target given the predictors is often discussed in foundational treatments of the subject. One way this comes up is in decision ...
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1 vote
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### Why do we have a Neyman-Pearson lemma for type one error but not an analogous one for precision and recall of a classifier?

We fix alpha to .05 in statistical testing. We never fix the precision or recall of a test. There's no decision theory lemma that guarantees we can find a decision region with fixed precision or ...
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### Please help me understand a Figure in Bishop's "Pattern Recognition and Machine Learning", Sec 1.5.1 Minimizing the misclassification rate

The figure is Figure 1.24 on page 40 of Bishop's "Pattern Recognition and Machine Learning", Sec 1.5.1 Minimizing the misclassification rate: I don't understand this figure, starting from &...
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The sentence is in section 1.5.1 "Minimizing the misclassification rate" (page 39), underlined in red: The author thinks this statement is "clear", but I just can't understand. ...
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### A Frequentist approach to modeling uncertainty around decision optimization

I'm curious about how a Frequentist would approach an optimization problem, where said problem is constructed using inferred parameters. As an example, I'll use price optimization given a demand curve....
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### Computing the Bayesian Estimator with Jeffreys prior for the Gamma distribution

Question: Let $X_1, · · · , X_n$ be a random sample from $Gamma(1, θ)$. The population mean is $θ$. Assume that the Jeffreys prior is used. Find the generalized Bayesian estimator of θ under the SEL (...
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### Generalized Bayesian estimator (rule) of θ

Question: Let $X_1, · · · , X_n$ be a random sample from $Poisson(θ)$. The prior for θ is $G(α, β)$ Find the Bayesian estimator (rule) of θ under the SEL(squared error loss). Find the generalized ...
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1 vote
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### Why do we need the concept of Risk in Bayesian Decision theory?

I'm studying Bayesian decision theory as introduction to machine learning and I see the concept of Risk in a lot of places. In the course I read, they define risk as: Risk is the expected error ...
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### How to interpret the results of the DCA curve?

I have a large sample of data, but only a small number of people have an event. I want to use a certain indicator to predict the occurrence of the event, but when I draw the DCA curve, I found a ...
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### Summarization and resources for Bayesian decision theory

Looking for textbooks and/or resources to get familiar with Bayesian decision making. I have the book, Statistical Rethinking, by Richard McElreath and I've found this to be a really great resource ...
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### Bayes Risk Not Connected to Observed Data

It puzzles me that the Bayes risk seems not connected to the observed data. Let me illustrate this with an example. Let a coin toss follow a Bernoulli distribution with a hidden parameter $\theta$ and ...
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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 ...
29 views

### 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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### Maximising the utility when I have a large number of discrete decisions mixed with continuous decisions

I have an optimisation problem which is potentially quite tricky. Consider the problem of allocating a discrete number of resources (in my case, they are spare mechanical components for a large ...
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1 vote
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### Bayes classifier expected classification error for multiclass case

Assume a feature $x \in [a,b]$ and two classes $\omega_1, \omega_2$ with prior probabilities $P(\omega_1), P(\omega_2)$ and likelihood functions $p(x | \omega_1), p(x | \omega_2)$. Then, the expected ...
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### Checking whether Brier score is a strictly proper scoring rule

I want to check whether Brier Score is a strictly proper scoring rule based on some definition I found here. Since the paper is behind a paywall, I provide the definition here: A scoring rule assigns ...
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### Decision tree: how you would expect the next split based on a set of variables?

I'm trying to understand the logic behind a question I was given during a mock test. Can somebody help me please? I am not sure I can understand the concept, hence be able to make it right in a ...
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