The decision-theory tag has no wiki summary.
2
votes
1answer
53 views
Value of Information for a simple investment problem
Assume the following problem: You're deciding whether to invest into an opportunity with uncertain cost $c$ and value $v$. The cost has been estimated to be normally distributed with 90% CI between 1 ...
1
vote
0answers
31 views
The meaning of translation completeness w.r.t a random variable
I stumbled upon this term in McFadden - Analysis of qualitative choice behavior (page 111).
It is said that
"A random Variable $X$ is translation complete if for a function h
of bounded ...
0
votes
0answers
9 views
How to find the tendency of a feature in decision trees?
I've trained a decision tree binary classifier and I have the most informative features based on the sum of information gain weighted by the number of samples at the node (scikit-learn ...
0
votes
0answers
22 views
Multiple-criteria decision analysis packages for Java
Does any multiple criteria decision analysis (MCDA) package/library exist in Java?
I work on ABM modelling and need to do use such a package to guide agents in their assessments. Previously I had ...
3
votes
1answer
120 views
What technical language to describe the degree to which probabilities are likely to be modified by future data?
I'm trying to reason about something I call "estimate stability," and I'm hoping you can tell me whether there’s some relevant technical language, so that I can learn about it and then write a ...
1
vote
0answers
32 views
Sampling to maximize model accuracy
Suppose you have a relatively small random sample and have a corresponding model
$\ Y$ ~ $\operatorname{Bernoulli}(p_i) $
$\ \operatorname{logit}( \hat{p_i} )=\hat{\beta}*X$ and now want to draw a ...
9
votes
2answers
250 views
Coin flipping, decision processes and value of information
Imagine the following setup: You have 2 coins, coin A which is guaranteed to be fair, and coin B which may or may not be fair. You are asked to do 100 coin flips, and your objective is to maximize the ...
0
votes
0answers
30 views
learn a decision tree classifier with uneven training data
Hi i have a set of data from which I wish to learn a decision tree classifier(binary) using id3. There is a 70:30 split between the classes should I expect the classifier to preform better on the ...
1
vote
0answers
23 views
Bandits without exploitation: finding the best items with incomplete information
I'm trying to analyze a general game. This is probably well-known, in which case pointers to relevant literature would suffice (but explanation would not be declined!). If it's not standard, of course ...
0
votes
1answer
283 views
Decision tree model evaluation for “training set ” vs “testing set ” in R
So I got my training set with 70% of my data called "train" / 30% "test"
I use ctree to get my decision tree model with something like this code below :
...
1
vote
0answers
61 views
Choosing which variable to sample to get a better model
Apologies if this question is long-winded and vague, but I'm really not familiar with the field and I'm having a hard time finding references.
We have a random variable $X$ which we assume is ...
0
votes
1answer
64 views
A constant as an admissible estimator
This is a homework question so I would appreciate hints. I believe I have the first part correct, but I fail to see how the second part is different.
Assume square error loss, $L(\theta ,a)=(\theta ...
0
votes
1answer
68 views
SVM decision function
our decision function e.g. in SVMs for binary classification (where the response is labeld by $y_i \in \{-1,1\}$) has the form:
$f(\mathbf{x}) = \text{sgn}(\mathbf{w}^\top \mathbf{x} + b)$ where ...
0
votes
1answer
56 views
Decision theory - reject option
In decision theory, we define a reject option ($\theta$) so that when making decision is difficult, the case will be ignored.
Suppose $1/k \leq \theta \leq1$:
If $\theta=1/k$ no cases will be ...
3
votes
1answer
71 views
Classification optimal decisions considering a loss function
Suppose we're given data from three different classes which are normally distributed with the following means and variances:
$C_1: \mu_1=(1,2)^T, \Sigma_1^{-1}=( \begin{array}{ccc}2 & 1 ...
0
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1answer
68 views
A logistic problem about decision theory
Belows is the question and the solution for part c which is the part that i don't understand. Can someone explains to me? I don't quite get how it gets $3\over 7$ and why does it needs to?Any hint ...
-1
votes
1answer
142 views
Why $T=X_1X_2$ is not a sufficient statistic?
Why $T=X_1X_2$ is not a sufficient statistic?
Suppose I want to show $T=x_1x_2$ is sufficient and with this distribution
$$ x \sim \frac{\theta^xe^{-\theta}}{x!}$$
Chug and plug, you will get ...
3
votes
1answer
497 views
What are complete sufficient statistics?
I have some trouble understanding complete sufficient statistics?
Let $T=\Sigma x_i$ be a sufficient statistic.
If $E[g(T)]=0$ with probability 1, for some function $g$, then it is a complete ...
3
votes
1answer
84 views
Expectation notations
In Statistical Decision Theory, one often studies the following two measures (from "The Bayesian Choice"):
Average loss (aka the frequentist risk):
$R\left(\theta,\delta\right) = ...
1
vote
0answers
162 views
Sufficient, Complete Sufficient, UMVUE, Rao-Blackwell, Admissible. What are ties between these?
I am taking stat inference course. I have some trouble understanding some these terms:
Sufficient Statistics: a stat that does not depend on the parameter, say $\Sigma X$ for normal distribution
...
36
votes
6answers
1k views
The Sleeping Beauty Paradox
The situation
Some researchers would like to put you to sleep. Depending on the secret toss of a fair coin, they will briefly awaken you either once (Heads) or twice (Tails). After each waking, ...
3
votes
1answer
289 views
Bayes decision boundary of Figure 2.5 in Elements of Statistical Learning
When I read "Elements of Statistical Learning", I met some difficulty in calculating the Bayes decision boundary of Figure 2.5. In the package ElemStatLearn, it ...
2
votes
1answer
86 views
Absolute error loss minimization
From Robert (The Bayesian Choice, 2001), it is proposed that the Bayes Estimator associated with the prior distribution $\pi$ and the multilinear loss is a $(k_2/(k_1+k_2))$ fractile of ...
0
votes
1answer
178 views
What are the advantages of different classification algorithms? [closed]
For example, when should one use the decision trees over logistic regression (or vice versa) for classification?
1
vote
0answers
112 views
Loss functions, decision theory for hyperparameters, or estimating the variance of an unknown prior
How I got here
I was originally interested in point estimation and the Bayes risk of some distribution $\pi$
$$
r(\pi) = \mathbb{E}_{\pi(x)}[ \mathbb{E}_{\Pr(y|e,x)}[L(x,\hat x(y|e))]],
$$
where ...
2
votes
0answers
140 views
Cramer-Rao type bound for Information Gain
I am interested in the Bayes risk of some distribution $\pi$
$$
r(\pi) = \mathbb{E}_{\pi(x)}[ \mathbb{E}_{\Pr(y|d,x)}[L(x,\hat x(y|d))]],
$$
where $L$ is some loss function and $\hat x$ is the ...
7
votes
1answer
276 views
What is the decision-theoretic justification for Bayesian credible interval procedures?
(To see why I wrote this, check the comments below my answer to this question.)
Type III errors and statistical decision theory
Giving the right answer to the wrong question is sometimes called a ...
11
votes
1answer
441 views
A hair dresser's conundrum
My hairdresser Stacey always puts on a happy face, but is often stressed about managing her time.
Today Stacey was overdue for my appointment and very apologetic. While getting my haircut I wondered:
...
2
votes
1answer
106 views
Algorithm to evaluate whether you should buy now or wait [closed]
I'm currently in search of an algorithm that can determine whether or not it's time to buy something (an item, a stock, a service, etc.) given an history of prices (30, 50, 100, ...).
My idea is ...
6
votes
1answer
142 views
Given two responses for two groups, how to decide what to test on response or profit?
For many years I have been conducting t-tests on response to mailing activity. Recently I was challenged that we should infact be conducting tests on profit rather than response.
So, let me put this ...
5
votes
1answer
375 views
What is the relation between statistics theory and decision theory?
I was wondering how statistics and decision theory are related?
It looks to me all the statistics problems/tasks can be formulated in decision theory. Also problems in decision theory can be ...
