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2
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1answer
38 views

A case of understanding customer behavior

Suppose I have a big online company, and many of my customers churned (i.e. they were paying, and then stopped). My goal is to understand why each of them churned. First I identify the complete set ...
1
vote
0answers
18 views

Given 3 discriminant functions I was able to classify 2D patterns, but how do I plot decision boundaries via matplotlib?

I have implemented the discriminant function and was able to classify the 2D patterns (via Python), but I have troubles thinking about an approach to plot the decision boundaries. Hope anyone has an ...
7
votes
1answer
81 views

Formal justification of Bayesian inference as a model for belief

I remember a proof that Bayesian probability theory is the only valid method for representing beliefs, it went something like we represent belief by some non-negative function over some domain of ...
0
votes
0answers
28 views

Best Methods for data-mining neuroimaging data with 1000 subjects

I am part of a team tasked with performing exploratory analysis of a large data set containing neuro-imaging scans. For each scan I will likely calculate some variable that relates to brain function - ...
0
votes
0answers
16 views

Plotting a decision boundary separating 2 classes using Matplotlib's pyplot

I could really use a tip to help me plotting a decision boundary to separate to classes of data. I created some sample data (from a Gaussian distribution) via Python NumPy. In this case, every data ...
1
vote
0answers
16 views

Admissibility and domination for estimators

Watching a video by the "mathematicalmonk" on the web, I was wondering how to answer this kind of questions: Given $X_1,\ldots,X_n\sim \mathcal{N}\left(\mu,\sigma^2\right)$. Assume that $\mu$ is ...
2
votes
0answers
33 views

What is a robust way to find the max of $n$ independent, non-identical random variates?

Suppose I observe $n$ random variates along with their variance (but not mean) and I'd like to select the one with the largest mean as frequently as possible. The procedure must be memoryless--you ...
3
votes
1answer
38 views

Given $n$ different univariate non-normal sample sets calculate for a new sample, $x$, which it most likely belongs to [duplicate]

Say you have $n$ different, non-normal, potentially overlapping data sets of samples. Maybe their densities look something like: and you are given a new sample $x$, how would you decide to which of ...
4
votes
0answers
56 views

Maximizing returns - A Bayesian approach

I want to design a Bayesian model for a simple asset allocation problem. Say I can buy $a_i$ amounts of $N$ assets. The return values of these assets are given by random variables $r_i$ with known ...
1
vote
1answer
65 views

How to incorporate constraints in random forest output

Suppose I am doing random forest classification of labels $A$,$B$,$C$,$D$. There is some theoretical ordering to this output such that when $A$ is more likely than $B$, $B$ is also more likely than ...
1
vote
0answers
69 views

Computing Confidence in A/B testing

First of all, I'm fairly new to Decision Theory and my question might be rather too simple for the experts. I am having some issues in computing confidence for A/B Testing. I will first explain the ...
0
votes
0answers
26 views

determining the number of variables in the kernal of a U-stat

I'm working through some problems on deriving U-statistics, and I am unsure about determining the number of samples (random variables?) that are needed for the kernel of a given U-stat. For example: ...
0
votes
0answers
49 views

Classification problem: admissible rule is a Bayes rule for some prior $\pi$

I have a classification problem where I want to place an observation $X$ into a population described by a pdf equal to either $f_1$ or $f_2$. Given $P_{f_i}(\frac{f_1(X)}{f_2(X)}=j)=0$ for all $j\in ...
0
votes
0answers
35 views

Decision rules based on amount of overlap between Bayesian probability intervals

My research hypothesis is that an intervention, I, results in greater scores than the control,C. If the intervals for these two don't overlap, I know I can make a clear-cut statement either accepting ...
1
vote
0answers
62 views

Showing that a statistic is ancillary for a parameter

Working through a HW problem, and a hint is that for a decision rule $$T(X) = \frac{X_{(1)} + X_{(n)}}{2}$$ Then $$T - \bar{X} $$ is ancillary. Intuitively this makes complete sense, but I am ...
0
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0answers
55 views

Admissible decision rule is always Bayes for some proper prior

I think I am able to visualize this graphically, but can't think of how to write this out. Some other literature online suggests drawing a picture, but I was looking for a concrete proof. I started ...
2
votes
1answer
99 views

How do I combine multiple prior components and a likelihood?

Lets imagine I am comparing two groups of animals (treatment/control). There is previous data from cell cultures indicating the treatment should have a positive effect. This gives me "prior component ...
0
votes
0answers
20 views

Markov Decision Process and its generality

My major is CS and I have a question about Markov decision process. I have been reading a book, planning with markov decision process an AI perspective. While reading it, I have a question regarding ...
2
votes
1answer
105 views

Prove/counter example: A minimax decision rule is always Bayes wrt some proper prior

Not sure whether the claim is true or false. If claim is true, intuitively, it might have something to do with "least favorable priors", but am not able to figure out the connection. If claim is ...
2
votes
1answer
69 views

What is a loss function in decision theory?

My notes define a loss function as the 'cost' incurred when the true value of $\theta$ is estimated by $\hat\theta$. What kind of cost is it talking about? monetary cost? or is it something related to ...
0
votes
1answer
71 views

Using decision trees with very infrequent outcomes

I am working on decision tree model and a value in dependent variable (churn) is very less. we have 1.5 lac records and only 1700 records have churn = 1. While using decision tree model, tree is not ...
0
votes
1answer
593 views

Decision boundary plot for a perceptron

I am trying to plot the decision boundary of a perceptron algorithm and am really confused about a few things. My input instances are in the form [(x1,x2),target_Value], basically a 2-d input instance ...
5
votes
0answers
42 views

Example Of Strict von Neumann Inequality

Let $r(\pi, \delta)$ denote the Bayes risk of an estimator $\delta$ with respect to a prior $\pi$, let $\Pi$ denote the set of all priors on the parameter space $\Theta$, and let $\Delta$ denote the ...
5
votes
0answers
70 views

Is the expected value a valid decision-making method in a very short term?

This might be related to game theory more than statistics, but I decided to ask this question here. Let's assume you're offered a lottery. There are a hundred balls in a bowl: 99 white balls and one ...
0
votes
0answers
49 views

Optimizing “twenty questions”-like decision tree queries

I'm looking for an algorithm which can optimize the selection of queries used to build a decision tree. However, unlike most decision trees, I am constrained to ask the same set of questions for every ...
0
votes
0answers
33 views

Modelling data of the form streets,timeofday,distance,duration?

I have data in the form of street name, time of the day, weekday/weekend, distance, duration for a lot of streets. I also have association of I went from street 1 to street 2 in a trip . For example: ...
2
votes
1answer
70 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
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0answers
57 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
12 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 ...
2
votes
1answer
60 views

Question about proof for luce choice axiom w.r.t. conditional probability

In Luce (1959) the choice axiom is definied, that for a finite subset $T$ of $U$ such that, for every $S\subset T$, $P_S$ is defined. If $P(x,y)\ne 0,1$ for all $x,y\in T$, then for $R\subset ...
0
votes
0answers
88 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 ...
4
votes
1answer
177 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
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0answers
37 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 ...
11
votes
2answers
371 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 ...
1
vote
0answers
35 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 ...
1
vote
1answer
1k 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
70 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 ...
1
vote
1answer
133 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
96 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
82 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
89 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
votes
1answer
79 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
157 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
893 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 ...
4
votes
1answer
113 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
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0answers
240 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 ...
45
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8answers
2k 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
2answers
378 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
93 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 ...
1
vote
0answers
138 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 ...