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1answer
29 views

Detecting a consistent pattern in a dataset via Decision Trees and cross-validation

Assume a classification problem where there are two classes and the aim is to detect a consistent pattern which successfully separates the input dataset regardless of how we divide it into training / ...
2
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3answers
115 views

Is 'fair statistics' a thing?

Given that statistics can often be abused to deliberately present 'facts' to support a pre-existing viewpoint. (Lies, damned lies and statistics). And given confirmation bias. Is there an ...
1
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0answers
11 views

Optimal Number of Entries in Contest of Skill

Objective: I'm looking for the optimal number of unique entries in a contest of skill with monetary prizes. Description: The contests vary from as little as 20 entries up to 10,000+ entries. You ...
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0answers
7 views

How does weka's decision table handle numerical (continuous) output and numerical inputs?

I've been using WEKA's decision table majority classifier in order to do a feature selection on a data set with both numerical (continuous) and categorical inputs, and numerical (continuous) output. ...
0
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0answers
36 views

Intuition behind the Stein's paradox

I had read wiki and some sources. jmanton's blog, Wasserman's blog the background is that: You have Xi ∼ N(θi, 1), and we want to estimate the each θi. Where Xi are ...
5
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2answers
191 views

Drawing numbered balls from an urn

PROBLEM There is an urn with a set of balls where each ball is labeled with a different integer. The numbers on the balls are known and are not a range of integers. For example the set of balls could ...
3
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2answers
83 views

Bayes decision theory: Classification error probability

In Bayesian decision theory: Given $\omega_1$ and $\omega_2$ as two classes for classification, $P\left( \omega_1 \right)$ and $P\left( \omega_2\right)$ their prior probabilities, $x$ the feature ...
3
votes
1answer
49 views

Loss function that relates ROPE with HDI?

In Doing Bayesian Data Analysis (link to the book) and Bayesian Estimation Supersedes the t-Test, J. Kruschke proposes using the following criterion to reject or accept the null hypothesis in a ...
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0answers
29 views

bayes optimum decisions and loss functions

In this question, one of the comments discusses the benefits of using Bayes optimum decision rules coupled with loss functions rather than using other performance metrics such as sensitivity. My ...
2
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1answer
53 views

Decision function problem based on the logistic function

Suppose we have a bunch of a sampled pairs $(x_1,y_1)...(x_n,y_n)$ with the $y_i =\pm1$. Then consider the decision function $h(x) = -1$ if $p(x)=\frac{1}{1+e^{-x}}\leq0.5$, and $h(x) = 1$ if $p(x) ...
0
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0answers
15 views

Rearranging 2 discriminant function to solve for 1 parameter (to derive a decision boundary)

I have a task where I want to classify patterns from 2 classes where the samples are drawn from a bivariate Gaussian distribution. I use the 2 discriminant functions ($g_1$ and $g_2$) to classify the ...
2
votes
1answer
90 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
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0answers
41 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
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1answer
88 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
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0answers
43 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
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0answers
58 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
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0answers
20 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
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0answers
38 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
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1answer
43 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
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0answers
71 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 ...
2
votes
1answer
95 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
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0answers
100 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 ...
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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: ...
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0answers
56 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
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0answers
53 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
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0answers
76 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 ...
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0answers
64 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
138 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 ...
1
vote
1answer
34 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
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1answer
125 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
96 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
90 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
1k 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
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0answers
46 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
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0answers
102 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
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0answers
65 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 ...
2
votes
1answer
71 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
72 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 ...
2
votes
1answer
68 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 ...
4
votes
1answer
178 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
41 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
393 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
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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
2k 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
71 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
151 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
105 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
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1answer
95 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
95 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
80 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 ...