The decision-theory tag has no usage guidance.
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1answer
24 views
Relationship between “Logistic regression + L1 regularization” and PCA
This is the experiment I have done.
My data contain several hundreds of samples but with over 20k features per sample, so I used logistic regression + L1 regularization (LR+L1) to fit a linear ...
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23 views
Adaptive expereriment design with Bayes risk weighted by experiment time
Suppose I want to infer the parameter $\theta$ that has a likelihood function $L(\theta|x;e)=\Pr(x|\theta,e)$. Here, $x$ is the data and $e$ is the experiment type. For example, as a trivial example, ...
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63 views
Random interpretation of prediction
I am trying to build a binary classifier. Normally I'd build a model that predicts $P(y = 1 \mid x)$ and choose a threshold. I classify $1$ if predicted probability $\ge$ threshold.
What about this ...
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1answer
51 views
How to convert volatility of log returns into that of stock price? [on hold]
I have forecasted the volatility of the log return of stock prices using a GARCH model, but would like to use this to create a plot of the forecasted prices themselves, with confidence intervals based ...
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22 views
Bayesian Decision Theory - Self Study [duplicate]
Consider a naive Bayes classier with a binary class $Y ∈ {0, 1}$ and three binary features $X_1, X_2, X_3$ ∈
{0, 1}. You are given a set $D$ of $n$ training examples, i.e.
D={$(x^{(1)}_1, x^{(1)}_2, ...
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11 views
Utility theory approach in decision making for Gaussian variables
Consider the following problem:-
In nutshell there are 3 decisions $d_1,d_2,d_3$ and 3 effects $S_1,S_2,S_3$ after the decision has been made. Each effect can occur with a given probability. In ...
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16 views
Tools to combine n metrics for k elements
I am looking to combine n metrics to obtain 1 single unified metric. For example, let's say I have 2 metrics n1 and n2 for k elements. I am particularly interested in the one or two elements that have ...
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13 views
Beneficial Bias without Shrinkage
Suppose that we are interested in estimating a quantity $\theta$ with an estimator $\hat{\theta}$, and seek to minimize error in the $l_2$ sense, so our loss is $||\theta - \hat{\theta}||_2$.
It is ...
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25 views
Under what conditions is posterior expected 0-1 loss minimized by the MAP estimate?
Suppose we observe data $x$ from a distribution with density function $p_\theta(x)$ with unknown $\theta$, we have a prior density $\pi(\theta)$, and we want to minimize the following loss function:
$$...
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1answer
16 views
Classification with varying choice set (e.g. Auction)
I have the following situation: I am a customer and I search for a commodity to buy. I receive several offers from various companies and I must make a choice which one to buy. After some time I make ...
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19 views
Intuitively understanding the formulation of Utility as 1 - alpha of a reward
I was reading the construction of a utility function in "Statistical Decision Theory and Bayesian Analysis" by Jim Berger (page 52) -- below.
So I get that if say you have two outcomes -- one the ...
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1answer
49 views
Loss matrix to be included in decision tree? Rpart -R
For loss matrix, is it necessary to include it during the decision tree analysis ?
What will be the impact if this is excluded from the analysis e.g loss matrix (0,1,1,0) in Rpart-R? Do we usually ...
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1answer
156 views
Lower bound on smallest eigenvalue of covariance matrices
Assume that a class of $p\times p$ covariance matrices is characterized by a parameter $\theta$, i.e,
$$\mathbb{F} = \left\{\Sigma(\theta), \theta\in R\right\}$$
Also suppose we know the following
...
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24 views
Decision tree approach to optimization
Consider the rows of the following matrix (first row is the column names), consisting of values of variables “A”, “B” and the dependent variable “Revenue”. Now, revenue is some non-linear function of ...
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24 views
hypothesis testing to remove predictor
If we're working with a linear mixed model (fixed + random effects, normality assumptions) and are interesting in testing whether or not we can remove a fixed effect from the model, since standard ...
