Questions tagged [decision-theory]

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26 views

Explain Dempster Shafer Equation

I have a question about the Dempster Shafer theory application. I have four models where the output is of abstract level (crisp). I understand I have to use the confusion matrix (precision/recall) to ...
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1answer
25 views

How to quantify intangible costs for decision making

In many situations, decision-making requires weighing multiple losses. For example, you might determine the optimal threshold for a churn classification problem by comparing the cost of offering a ...
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1answer
25 views

Ordering list of items by two criteria

I have a list of items with two scores: scoreA and scoreB. To be more specific they represent the average of a list of accuracy scores and their maximum. Both of the scores range from 0 to 100%. I'm ...
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1answer
67 views

What is the best strategy for the simplified version of the multi-armed bandit?

Consider a simplified version of the multi-armed bandit problem, where: like in the standard multi-armed bandit: when you pull the lever of 1 bandit you win/lose some amount from that bandit ...
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8 views

Integrated AHP and Fuzzy logic for Supplier categorization

I am looking into a supplier classification problem. As I have a lot of vague and subjective criteria I am using Fuzzy Logic to classify suppliers on two dimensions. However not all criteria are ...
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1answer
33 views

How does Random Forest split?

Random forests or random decision forests are an ensemble learning method for classification, regression, and other tasks that operate by constructing a multitude of decision trees at training time ...
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0answers
26 views

Stochastic dominance and mean preserving spread

I need someones help on understanding the concepts of stochastic dominance and mean preserving spread. I have an exercise which could be used for explanation. Consider the following lotteries: L1 ={...
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37 views

Why does AdaBoost use decision stumps instead of 0-depth trees?

Why is it that AdaBoost uses decision stumps for the weak learners? It seems simpler to me to just use the weighted majority of the data points for the classification. Why shouldn't we do this?
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1answer
51 views

The proper way to compute the posterior distribution of a distribution

Suppose I am a Bayesian working with multi-level data, $j$ and $t$. I run a model using $t$ that calculates the posterior distribution of a parameter $\theta_j$ for each $j$, which I then use to ...
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24 views

Bayesian decision making

I have a real world problem which I have reformulated into a simpler problem which hopefully you can help me solve. Picture this, I have the option to build a factory next to a conservation park. The ...
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0answers
12 views

Decision making with respect to utility function

I am currently working on a small project targeted towards predicting survival times (red, green functions) of certain engine parts. The ultimate goal is to decide what part would be the best choice ...
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0answers
34 views

Why would a Bayesian want to maximize expectation? [closed]

A Frequentist interprets probability as an estimate of how frequent an event is giving that we can repeat the experiment many times. It is natural for them to try to maximize the expected utility ...
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33 views

Aren't multi-armed bandits basically the same things as the Von Neumann-Morgenstern utility theorem?

I can't seem to find any material connecting the two ideas. How would one who is more knowledgeable about these topics relate them to one another? Is it that multi-armed bandits are just one way of ...
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21 views

Modeling and updating the reliability of two sources of information

I do not know the general framework this might fall under, apologies for the vague title. Assume that a decision maker's choice is dependent on two sources of information $f_1$ and $f_2$. Assume for ...
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27 views

Are the following terminologies error/risk/marmgin/regret bounds related?

I recently come across papers with titles resembling "Error/Risk/Margin/Regret Bounds" and I can't help but wondering if there is any fundamental (mathematical) difference between these terminologies? ...
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48 views

Optimal decisions based on frequentist estimators

Consider a decision problem aimed at minimizing the expected loss1 where the argument is a parameter estimate. In a Bayesian setting, given a posterior distribution of the parameter and the loss ...
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12 views

Detection Theory minimax with non differentiable interior

The minimax is used in detection theory and decision theory for minimizing the overall average risk for the worst case prior. $$ \min_{\delta} \max_{\pi_0} r(\pi_0,\delta) = \max_{\pi_0} \min_{\delta}...
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2answers
41 views

Book on decision theory

I am from physics background. I know basics about statistics (upto 'Statistical Inference - Casella'). I came across some articles talking about terms like 'reciever operating characteristics curve', '...
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48 views

Bayesian Decision Theory - Rejection & Bishop plot

Reading through Bishop, I stumbled upon this picture on p. 42 top left under the topic of Bayesian classification, but I am unclear on how this can be two posterior distributions, as they seemingly do ...
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1answer
131 views

Differentiable programming for general Bayesian decision theory

It is my understanding that differentiable programming and thus libraries like TensorFlow (e.g. TFP) and JAX can be used to solve Bayesian decision theory problems where e.g. we have a probabilistic ...
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93 views

How to choose operation point from precision recall curves for multi-label classification

Is there a commonly accepted method for selecting an operating point for a multilabel classifier to optimize for each of these aggregate metrics: micro averaged recall at some minimal acceptable ...
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1answer
57 views

Bayesian estimator $\theta(x)$

Given a training set of $(X, Y )$'s where the $X$'s are the source variables and the $Y$'s are the targets, derive an estimator that minimizes the mean squared error between target values and ...
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27 views

How to use the likelihood-ratio to compute the error probability? [closed]

In Bayesian decision theory, There is an analytical form of error rate, which is $$P(e)=\int P(e|\bf{x})p(\bf{x})d\bf{x}$$. For binary classification, we can compute the type I error probability with: ...
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1answer
184 views

Admissible Empirical Bayes Examples

I would like to hear about a few simple empirical bayes estimators that are admissible for high (i.e. at least 3) dimensional parameter space. What are some textbook lollipop examples to study for ...
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2answers
134 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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31 views

Is the shrinkage of subgroup analyses in meta-analysis an example of Stein's paradox?

This paper writes (edited for concision): Consider, a doctor in Germany confronted by a meta-analysis of long term‚ $\beta$ blockade after myocardial infarction. Although a robust beneficial effect ...
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37 views

Cannot understand a notation detail in ESL's Statistical Decision Theory EPE minimization

In The Elements of Statistical Learning, at page 18 the authors explain that, in order to minimize the EPE (Expected Prediction Error defined as the mean of the loss function: $\text{EPE}(f) = \mathbb{...
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1answer
57 views

Bayes Decision Theory With 3 Classes

I'm trying to create a Bayes classificator in 1 dimension with 3 classes. I have created the following graph, where you can see that from zero to $x_{bnd1}$ is the first area $R1$, then from $x_{bnd1}$...
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21 views

Understanding Randomized Estimators in Statistical Decision Theory

I'm reading through The Bayesian Choice by CP Robert with a particular focus on understanding randomized decision rules vs non-randomized statistical rules in the Bayesian context. In Section 2.3, he ...
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128 views

Compute the Risk function

Suppose we are given $(X_1,...,X_n)$ random variables which are iid. from $\mathcal{N}(\mu,\theta)$ and finite variance. Let $Y=\frac{1}{n}\sum_{i=1}^n(X_i-\overline X)^2$ and define a loss function $...
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4answers
191 views

Getting all answers correct by taking the same exam for fewest times

Rain never studies, so she is completely clueless during the midterm even though it consists of Yes/No questions only. Fortunately, Rain's professor allows her to re-take the same midterm as many ...
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1answer
70 views

Optimal classification rule given data, model and loss function

Setup Suppose I have a data set with a categorical variable $Y$ (with possible values $j=1,\dots,J$) and another variable $X$. I wish to classify $Y$ based on the information in $X$. For simplicity, ...
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29 views

Expected utility maximization when beliefs are inaccurate

In the framework of maximization of expected utility (MEU), is it somehow optimal or justifiable to make choices based on the subjective probability distribution when we know it may be inaccurate (...
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83 views

Two class bayesian decision theory

I'm new to decision theory, but in the many "intro to bayesian decision theory" tutorials, the two-category classification example is usually given. It boils down to deciding action 1 if it's risk is ...
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1answer
95 views

In what sense does interim monitoring of clinical trials “cost” a Bayesian?

I have read (and will seek a specific reference on the subject) that unlike Frequentist trials, Bayesians can continually monitor data as it accrues. A Frequentist tries to control, and thus ...
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2answers
488 views

Minimizing expected brier score and Brier score interpretation

For a probabilistic binary forecast, the BS (Brier score) is given by $$ \text{BS}= \begin{cases} (1-f_i)^2\\ f_i^2\\ \end{cases} $$ Where $f$ is the forecast. If the event occurs with probability $...
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1answer
45 views

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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1answer
47 views

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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0answers
40 views

Does intended model use affect Bayesian parameter estimation?

Bayesian parameter estimation results in a posterior distribution for model parameters. The user may or may not be interested equally much in all properties of the distribution. Perhaps the user ...
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0answers
20 views

What does it mean when Risk function turns out to be a number?

I have a statistical decision making theory problem.I have to calculate the Risk Function for each of 4 decision rules.However,it turns out that the fourth Risk function is not a function of θ and it ...
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1answer
60 views

Why is the maximum risk of an estimator independent of a prior distribution over the parameter?

One way of choosing an estimator $\delta(x)$ for data $X$ distributed as $P_{\theta}(X)$, where $\theta \in \Theta$ is: $$minimize \sup_{\theta \in \Theta} Risk(\delta(x), \theta)$$ In this case why ...
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2answers
39 views

Bayesian (In)Decision

Let $A_j$ be the action of person $j$, $A_k$ be the action of person $k$, and $p(A)$ be the probability of an action. Using Bayes Rule, $$p(A_j=x|A_k=y)=\frac{p(A_k=y|A_j=x)p(A_j=x)}{p(A_k=y)}$$ If $...
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0answers
58 views

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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0answers
46 views

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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126 views

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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0answers
58 views

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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1answer
30 views

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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1answer
215 views

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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163 views

Decision Tree from Agglomerative Clustering

I have agglomerative clustering done. I want to convert it to a decision tree so I can figure out the cluster very quickly. How to do so? A tedious approach (bad, I know): Take the top ...
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1answer
201 views

Admissibility does not imply minimax

The answer to minimax estimator explains why minimax does not imply admissibility. The relevant statement is from https://www.stat.berkeley.edu/~yuekai/201b/lec6.pdf which says, minimaxity does not ...

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