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4
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2answers
31 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
votes
1answer
53 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 ...
0
votes
0answers
4 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 ...
0
votes
0answers
10 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 ...
0
votes
1answer
17 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 ...
3
votes
2answers
45 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 ...
2
votes
1answer
46 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 ...
0
votes
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 ...
0
votes
1answer
41 views

Comparison between statistical decision theory and supervised learning [closed]

What are the differences and overlaps between statistical decision theory and machine learning ?
2
votes
0answers
36 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 ...
2
votes
2answers
117 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 ...
0
votes
0answers
6 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 ...
1
vote
0answers
53 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 ...
0
votes
0answers
24 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 ...
0
votes
0answers
35 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
votes
1answer
118 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
vote
2answers
261 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
votes
1answer
67 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 ...
0
votes
0answers
109 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
votes
0answers
36 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
votes
0answers
41 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 ...
57
votes
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 ...
0
votes
0answers
43 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 ...
5
votes
0answers
51 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
vote
1answer
42 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 ...
0
votes
0answers
7 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 ...
0
votes
0answers
35 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
votes
1answer
160 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
vote
1answer
91 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
votes
2answers
77 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 ...
0
votes
0answers
231 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
votes
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 ...
1
vote
1answer
60 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? ...
0
votes
0answers
15 views

Optimizing two decision trees with dependent labels

I might need help phrasing the question. I'll start with a simplified example. I have 20 cars with color, height, year, and width attributes. My attributes are in two groups: A (color, height) and B ...
2
votes
0answers
28 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 ...
1
vote
0answers
61 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
votes
1answer
165 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 ...
8
votes
2answers
604 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 ...
3
votes
2answers
447 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
votes
1answer
74 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 ...
7
votes
1answer
178 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
votes
1answer
104 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 ...
2
votes
1answer
61 views

Choosing a line/plane to separate two classes of binned data

In high energy physics I know it is common task to find the best separation point between two classes of data, usually signal and noise. This separation point is usually determined by first binning ...
0
votes
0answers
38 views

Decision tree indicating payoffs

I need to draw a decision tree to represents these requirements : The research and development manager in an old oil company, which is considering making some changes, lists the following courses of ...
2
votes
1answer
169 views

Minimizing the misclassification rate

I am reading the book Pattern Recognition and Machine Learning, and have a specific question from a text snippet. I'll state a few lines in the text Suppose that our goal is simply to make as few ...
4
votes
1answer
85 views

Intuitive interpretation of Bayes risk $R(\delta, \lambda) = \int_{\Omega}R(\theta, \delta) \lambda(\theta) d\theta$

Consider the risk function R of an estimator (statistic) $\delta(X)$ trying to estimate parameter $\theta$: $$R(\theta, \delta) = E_{X \sim P_{\theta}}[Loss(\theta,\delta(X)]$$ Which can be ...
3
votes
1answer
131 views

How are statistical decision theory and statistical learning theory related?

This paper attempts to contrast the basic elements of statistical learning theory and statistical decision theory, but I'm still confused about how the two are related.
2
votes
1answer
150 views

minimax property of sample mean

Suppose $X_1,X_2,\ldots,X_n$ are iid $\mathcal{N}(\mu,\sigma^2)$, where $\sigma$ is known, but $\mu$ is not. We wish to construct a confidence interval of length $L$ (given) for $\mu$. Is it true that ...
1
vote
1answer
66 views

Is summing posterior probabilities valid for classification problems?

A classification for two mutually exclusive problem can be formulated by having a decision hinge on whether $P_0(x) > P_1(x)$ or $P_0(x) < P_1(x)$ where $P_0(x)$ and $P_1(x)$ are posterior ...