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15 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
26 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 ...
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0answers
41 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 ...
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2answers
46 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
22 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
99 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
31 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
32 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 ...
49
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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
35 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
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0answers
45 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
37 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
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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 ...
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0answers
30 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
118 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
69 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
59 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
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0answers
96 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
20 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
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1answer
49 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? ...
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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 ...
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0answers
24 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
59 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
142 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
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2answers
431 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
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2answers
381 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
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1answer
67 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
65 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 ...
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1answer
150 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
96 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
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1answer
60 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
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0answers
28 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
128 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 ...
3
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1answer
69 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 ...
2
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1answer
111 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
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1answer
141 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
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1answer
59 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 ...
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0answers
39 views

Incorporating Risk Aversion in Bayesian Expected Loss functions

In Berger's Statistical Decision Theory and Bayesian Analysis, he presents the following expected loss function for decision theory: $\rho(\pi^*,a)=\int_\Theta L(\theta,a)d\pi^*(\theta)$ Where ...
0
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1answer
41 views

Association rules or classifier for product modeling for queries

I have a set of products P {1...n} which are rated on a goodness scale G ={1...100} (G10 is more good than G5). Each product has a set of features F {1....m}, now I want to learn a model for ...
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0answers
35 views

Are these independent: the sample, randomized rule, and random variable having the prior distribution on the parameter space?

In section 1.3 of Bickel and Doksum's Mathematical Statistics 2006, the risk function of a nonrandomized rule $d$ is the expectation of loss of the rule wrt the random sample. $$ R(\theta, d) := ...
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1answer
44 views

Is there a distribution where the data is generated from a decision process?

Sometimes my data is the result of the decisions each individuum of the observed population made: how much invest, how much gambled etc. The outcome would be a metric variable: money spent in total by ...
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0answers
51 views

admissibility under weighted error loss implies admissibility under square error loss

Show that admissibility of a decision rule under weighted square error loss implies it's admissibility under square error loss. Weighted Square error loss = $\frac {(d(x) - ...
-1
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1answer
158 views

admissibility of bayes rule

How to show that for a binomial(n, p) distribution, the MLE X/n is admissible under square error loss? The Bayes rule undr square error loss with beta($\alpha, \beta$) prior is X+$\alpha$/ (n ...
1
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1answer
359 views

Bayes estimator under LINEX loss?

Suppose we are trying to estimate a real valued parameter under the linear exponential (LINEX) loss. Suppose we have some prior $g$ that has finite mean, variance and a moment generating function. ...
1
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1answer
29 views

Bayesian calculation of parameter multiplying normal

I am interested in a model like: $y_{i} = \sum_{k\in K}{\beta_{k} z_{k}}$, with $z_{k} \tilde{} N(\mu_{k}, \sigma_{k})$. where $\beta \equiv(\beta_{k})_{k\in K}$ is not known, but all else is. I ...
0
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1answer
105 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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2answers
132 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
17 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 ...
0
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0answers
62 views

Intuition behind the Stein's paradox [duplicate]

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
285 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 ...