# 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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### Interpreting by dividing up results of AB test

at my company we are doing AB tests (with 95% confidence) for features of our game (mobile app, hyper-casual game, Global scale). After the tests had ran its course, we have a practice of dividing up ...
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### Sample mean of Bernoulli trials is admissible under squared loss

Let $X_1,\ldots,X_n$ be i.i.d. Bernoulli trials with probability $\theta\in(0,1)$, and let $L:(0,1)\times[0,1]\to\mathbb{R}$ be the squared loss function, i.e. $L(\theta,a)=(\theta-a)^2$. I am trying ...
• 155
10 views

### What time window to use for independent variables?

I have 10000 listings on various days. My y variable is % of transactions that happened 7 days before listing with a loss > 0 is 30% or more then 1 else 0. Now losses can happen before listing also....
• 1
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### Difference between generalisation error (Vapnik risk) and frequentist (statistical) risk

I'm reading these lecture notes: http://www.iro.umontreal.ca/~slacoste/teaching/ift6269/A19/notes/lecture5.pdf I always learned: "risk is the expected loss". In these lecture notes I see two ...
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62 views

155 views

### How to estimate when an event of interest is overdue?

I'm looking for a principled way to estimate when an event of interest is overdue (a binary decision/alert), not just predicting when it is supposed to happen. In the survival analysis literature I ...
• 3,471
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### How did the probability change to integral in bishop's 1.78 formula

In the equation R is the decision region and C is the classification. I don't understand how did he go from probability to integral!
315 views

### kNN Classifier Asymptotic Error Rate versus Bayes Error Rate

Suppose we are in the realm of $M$ class classification, $M \in \mathbb{N}$. I have seen the following result stated many times, but only proven for the case $k = 1$. I would like to prove it for ...
• 183
1 vote
267 views

### How do I build a decision tree model with a dataset that only has categorical values

kI'm trying to build a decision tree model on a dataset that only has categorical values, an example fragment of the dataset is below. My training dataset consists of 40 observations ...
70 views

### Randomly choose between options with multiple criteria

Here's the problem: I have some options. Each is represented with three attributes or say criteria (with normalized values between 0 and 1). I want to randomly choose one of these options based on ...
• 13
1 vote
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### Are there any (exponential) families without a minimal sufficient statistic?

Bahadur's theorem says that if a minimal sufficient statistic exists, then a complete sufficient statistic is also minimal sufficient. Are there any (homogenous, identifiable) families with a complete ...
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### How to eliminate constant to derive the decision rule in terms of the sufficient statistic $\bar{X}$ for normal distribution means hypothesis test?

Suppose that we have a random sample, of size $n$, from a population that is normally-distributed. Both the mean, $\mu$, and the standard deviation, $\sigma$, of the population are unknown. We want to ...
229 views

### 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 ...
1 vote
107 views

### At what value of p are you indifferent between action A and action B?

Problem statement: Suppose you are deciding between two actions, A, and B, and are testing between two mutually exclusive hypotheses, H1 and H2. If you choose action A, you receive 1 dollar if H1 is ...
1 vote
75 views

### 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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379 views

### 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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