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26 views

Why is the risk set convex, when we allow for randomized estimators

A randomized estimator $\delta^*(X)$ such that its loss function $L(\theta,\delta^*(x))=\int_\mathcal{D}L(\theta,a)\delta^*(x,a) \ da$, where $\delta^*(x, \cdot)$ is the estimator's density on the ...
3
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1answer
22 views

A uniformly optimal statistical procedure? an exercise from The Bayesian Choice

The previous exercise is from the book 'The Bayesian Choice', page 87. What does the author mean by uniformly optimal stat. procedure? This exercise refers to a Decision theory chapter, in a section ...
1
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1answer
45 views

How is the root node of a decision tree determined?

Almost all the examples I have found stated how the decision tree's split is based on how much purity/information can be gained (ie: via entropy and information gain) for internal node. But is the ...
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1answer
36 views

Random Forest explanation

I am having trouble understanding Random Forest, especially some terms. What is a node what is node size? What are ...
4
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0answers
56 views

How does an estimator that minimizes a weighted sum of squared bias and variance fit into decision theory?

Okay--my original message failed to elicit a response; so, let me put the question a differently. I will start by explaining my understanding of estimation from a decision theoretic perspective. I ...
4
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0answers
32 views

Optimal decision process to estimate Markov chain limiting distribution

Suppose there is a irreducible, reversible Markov chain with known states $1,\ldots,N$ and unknown transition matrix $T_{ij}$ and unknown limiting distribution $\pi_i$. I am able to repeatedly ...
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0answers
37 views

Statistical Decision Problem and Prior Sensitivity

At a critical stage in the development of a new aeroplane, a decision must be taken to continue or to abandon the project. The financial viability of the project can be measured by a parameter $\...
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0answers
12 views

Human behaviour and waiting times.

I was calling my phone company the other day about some issue. At some point I was told that I'd be put on hold for a few minutes. 5, 10, 15, 20 minutes went by and I was contemplating whether to hang-...
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2answers
32 views

What is the meaning of admissibility within a class, that every decision rule in a class is admissible in that class?

Suppose that I have that $X$ is a Poisson random variable with mean $\lambda$. Suppose a decision rule is to estimate $\lambda$ by using $\delta(Y) = aY$. Now, let $K$ be the class of all decision ...
2
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1answer
66 views

Non-probabilistic vs probabilistic frameworks for decision theory in metric spaces

I have a task to make a decision, say to classify an object as $X$ or $ \overline X$. However, $\overline X$ usually means everything else and you only have positive examples of $X$ and not so many ...
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0answers
8 views

Using Decision Rules to Make Cluster efect

I have a data set with 3 independent variables and 1 dependent variable. Dependent is play_golf Independents are Humidity, Pending_Chores, Wind I want to create "clusters" of rules and aggregate ...
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0answers
12 views

modeling sequential decisions

I am trying to model a 3 sequential decision. In my data context, there are two stores A and B. A consumer first decide to choose a store either A or B to visit, and then he decide to purchase a ...
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1answer
20 views

Bayes decision rule and thresholding

The best possible classification is for a set of samples drawn from any probability distribution is given by the Bayes decision rule. For any distribution, the rule is given by $f(x) = 1 ~if ~\eta(...
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2answers
47 views

Calculating the risk of an estimator using zero-one loss

Consider two observations where $$P_\theta(x=\theta+1)=P_\theta(x=\theta-1)=0.5,\ \ \theta\in\mathbb{R}$$Let $\mathbb{D}=\Theta=\mathbb{R}$ the decision space. Suppose that the associated loss ...
2
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1answer
49 views

Bayes factor (B) vs p-values: sensitive (H0/H1) vs insensitive data

The question of a beginner in Bayesian stats. As far as I understand, it is claimed (e.g. Dienes 2014) that B-based inference allows us to either confidently reject/accept the null, OR declare the ...
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0answers
2 views

Are Condorcet-way sorting method and Copeland method always identical?

We want to sort criterion $C_1,C_2,C_3...$ for chemical substances. A group of participants has given us their preferences. Let's compute in the Condorcet way: we first compute the the majority ...
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1answer
46 views

Comparison between statistical decision theory and supervised learning [closed]

What are the differences and overlaps between statistical decision theory and machine learning ?
2
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0answers
37 views

What is a better political voting method? [closed]

We are in a season where some major elections are happening (e.g. U.S. elections) and I find it interesting to address. Objective When we decide "better", we need to define an objective. To be clear,...
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2answers
129 views

Does Bayesian Statistics have no concept of statistical hypothesis testing?

I was told that the framework of Bayesian Statistics has no concept of statistical hypothesis testing or confidence intervals. How does this make sense? Bayesian statistics only says that we ...
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0answers
9 views

ID3 Inductive Bias

In the text for ML class, it's stated that ID3 prefers shorter trees to larger trees. Is there any non-trivial class of decision trees for which an ID3 produced decision tree will be the (not ...
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0answers
74 views

Is a max Brier score really a max Brier score?

I am generating some random data to test out a function that calculates Brier and scaled Brier scores. See here for a reference (http://journals.plos.org/plosone/article?id=10.1371/journal.pone....
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0answers
31 views

Applying Markov Decision Processes to the Selling House Problem with waiting times

I'd like to apply the Markov Decision Process theory to this problem. We have a house to sell. Each day an offer of $X_n$ comes for the house. Each offer costs an amount $c$ to observe. You may think ...
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0answers
38 views

Find Bayes rule/action under given prior

I am able to solve for Bayes actions/rules with no data and am able to follow problems with simple data. However, I'm not sure how to solve a question where the data, $X$, is conditional on the state ...
2
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1answer
140 views

Which machine learning technique is appropriate for my problem?

I'm new in machine learning topics and I've problem in modeling my environment which has multi parameters with different value ranges and a few actions to perform when value of each parameter is not ...
1
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2answers
754 views

Is decision tree output a prediction or class probabilities?

A Random Forest works by aggregating the results of many decision trees. Recently, I was reading about how the RandomForest aggregates the results, and it made me question whether the results from ...
3
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1answer
74 views

On the proof of admissibility of constant estimators under squared loss

The question concerns the discussion in Wasserman, All of Statistics, Section 13.6. He defines: An estimator $\hat{\theta}$ is inadmissible if there exists another rule $\hat{\theta}'$ such that ...
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0answers
117 views

Email open-rate optimization

I am trying to maximize open rates of emails by selecting between two subject headlines {h1, h2} for a marketing campaing. The hypothesis is that different customers react to different headlines. ...
0
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0answers
38 views

Decision Theory

Patient X is worried that he may have disease Y. He goes to a doctor who performs some test and based on the test determines that the probability that X has disease Y is 0.3. The insurance company has ...
0
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0answers
49 views

How to draw a 3 nearest neighbour decision boundary

I have an exam tomorrow, and I can't seem to get my head around how to do this, nor can I find any information online for this particular case of a 3NN decision boundary. We are presented with sets of ...
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7answers
4k views

How much to pay? A practical problem

This is not a home work question but real problem faced by our company. Very recently (2 days ago) we ordered for manufacturing of 10000 product labels to a dealer. Dealer is independent person. He ...
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0answers
47 views

Decision Boundary for the following plot

How do I create a decision boundary for the following plot ? I would just want to highlight the points for which the class changes for a pair of specific values of petal width and sepal width. My ...
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0answers
55 views

Why is Wald's decision theory not universally recognized as the foundation of statistics?

This is somewhat ill-defined, but: Why is Wald's decision theory not universally recognized as the foundation of statistics? I gather (or maybe I infer) that it was formulated to put frequentist and ...
1
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1answer
47 views

Why is the MLE/OLS estimator so common in regression despite inadmissibility?

Why is regression so commonly used if the OLS estimator for the vector of regression coefficients is inadmissible under the squared error loss function? Is it because of its historical popularity or ...
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0answers
8 views

Transforming a bad predictor into a good one — Is there a general class of theories for this problem?

Suppose that today I was interested in finding out whether the next ball in roulette game was going to come up red or black (assuming no green). To do this, I find several people and have them go ...
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40 views

Decision Tree Modeling

Hello and thanks for taking a look at this problem. I am interested in using some type of decision tree model for determining how a particular outcome (product revenue) is generated through a series ...
3
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1answer
192 views

Quadratic loss function implying conditional expectation

I am reading Bishop's pattern recognition book. In the decision theory part he first derives that using a quadratic loss function implies that our estimate $y(x)$ should be the conditional expectation ...
1
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1answer
124 views

What is an appropriate machine learning model for a dice game?

I'm having trouble thinking of the correct way to pose the following problem: Say a dice game (like Yahtzee) involves throwing up to 5 6-sided die in three rounds. After three rounds, a score is ...
4
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2answers
88 views

Decision tree with equal points

Suppose I have a decision tree built, and in the training set there are two points, say $x_1$ and $x_2$, which are completely equal. What happens if I remove exactly one of them from the training data?...
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0answers
321 views

Difference b/w KNN and Decision Tree

What are the differences between KNN classifier and Decision tree classifier? How do one choose between them for solving a classification problem?
2
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1answer
21 views

Struggling with payoff matrix

I've been struggling finding the loss functions, $L(\theta,d_1)$ and $L(\theta,d_2)$, for the following question: Items I manufacture are either independently flawed with probability, $p$, or perfect....
1
vote
1answer
67 views

Random effects in Bayesian network or Decision Tree

I wonder if we can incorporate a random effect model (as it is used a function..for example linear or logistic regression) to other machine learning algorithms such as Bayes network or decision tree? ...
2
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0answers
30 views

Simple question on graphical representation of minmax decision rule

In the picture below, I cannot understand why the minmax decision rule is on the line $R_1=R_2$. $R_i=R(\theta_i,d)$, where $\theta_i$ is the parameter and $d$ is the decision rule. $S$ is the risk ...
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0answers
65 views

How to find the threshold that minimizes the (weighted) mis-classification rate?

To use a logistic regression model for doing prediction, let \begin{equation} \hat Y_i= \begin{cases} 1 &\mbox{if $P(Y_i=1|X_i)>\alpha$}\\ 0 &\mbox{if $P(Y_i=1|X_i)\leq\alpha$} ...
3
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1answer
186 views

How to make optimal decisions with uncertain outcomes: achieving a “Yahtzee”

The game of Yahtzee is a poker-like game played with dice. Each move consists of three rolls of five (ordinary, fair, six-sided) dice. After each of the first two rolls the player may designate any ...
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2answers
788 views

Aside from Durbin-Watson, what hypothesis tests can produce inconclusive results?

The Durbin-Watson test statistic can lie in an inconclusive region, where it is not possible either to reject or fail to reject the null hypothesis (in this case, of zero autocorrelation). What other ...
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2answers
485 views

Admissible Estimator for Linear Regression

Is there an admissible estimator for a linear regression model with many parameters without restricting the parameter space? Admissibility will be with respect to Mean Square Error on the regression ...
4
votes
1answer
70 views

showing that $\bar{X}$ is inadmissible by comparing with $\max(\bar{X},2)$ under squared error loss function

suppose $X_1,X_2,\ldots,X_n$ be a random sample of $N(\theta,1), \theta>2$. how can I show $\bar{X}$ is inadmissible estimator Compared to $\max(\bar{X},2)$ under Squared error loss function
3
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1answer
78 views

Does maximum likelihood minimize a kind of generalized “0-1 loss”?

A very good point was raised here about how the optimal betting strategy under 0-1 loss was to bet on the mode, while under MSE loss the optimal strategy was to bet on the mean. Maximum likelihood is,...
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1answer
204 views

What would be an example of when L2 is a good loss function for computing a posterior loss?

L2 loss, together with L0 and L1 loss, are three a very common "default" loss functions used when summarising a posterior by the minimum posterior expected loss. One reason for this is perhaps that ...
3
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1answer
108 views

Why are inf and sup used in the definition of minimax estimators?

An estimator $\hat{\delta}$ is minimax iff $$\sup_\theta R(\theta,\hat{\delta})=\inf_\delta\sup_\theta R(\theta,\delta)$$ or in english iff out of all estimators it has the least maximum risk. For ...