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Questions tagged [isotonic]

isotonic means monotone, either increasing or decreasing. Use this tag for isotonic regression (monotone regression) and other forms of order-restricted inference, like hypothesis testing with ordered alternatives.

9
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2answers
125 views

How to test whether $\mu_1 < \mu_2 <\mu_3$?

Suppose I have three independent groups, with mean $\mu_1,~ \mu_2,~\mu_3$ respectively. How can I test whether $\mu_1 < \mu_2 <\mu_3$ or not using $n_1,~n_2,~n_3$ samples from each group? I ...
1
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1answer
34 views

Hypothesis test testing for monotonic group mean change

I wonder if there is a statistical hypothesis test testing whether group average monotonically increases across groups? For example, I have four treatment groups, A, B, C and D. I would like to test ...
5
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1answer
383 views

What are drawbacks of isotonic regression?

I have been reading about isotonic regression and it seems like a great method that will give one a monotone regression function estimator and, moreover, is free of any tuning parameters. Why are ...
0
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1answer
18 views

Seeking method for isotonic regression with bound constraints

I would like to fit an isotonic regression (with respect to "ordinary" linear ordering) to observations y_1, ..., y_n subject to the additional constraints that a <= y_1^* and y_10^* <= b where ...
1
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0answers
30 views

Multinomial classification where the response variable is monotonic over time

I have a set of feature and response variables measured for multiple subjects, each having multiple visit. Let's define $X_t^p$ as the feature variable at the $t^{th}$ observation of subject $p$, $...
2
votes
1answer
111 views

Estimate monotone function from noisy obsersations

Assume that $y=f(x)$ is an unknown monotonically increasing function of variable $x$. We have access to $N$ observations of this function given as tuples $(x_i,y_i)$, such that $y_i=f(x_i)$. The ...
1
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1answer
2k views

recursive feature elimination: why select subset based on AUC vs sensitivity/specificity

I have a small dataset of 25 observations with a classification variable (factor 0,1) and 82 features scaled to have values between 0 and 1. I used the rfe() ...
0
votes
1answer
26 views

How can I refute a monotonic correlation

I have a binary target T and a continuous variable I expect to correlate with it. I expect some monotonic correlation, as the explaining variable increases I expect P(T) to increase. I collect some (...
4
votes
1answer
118 views

What's the correct method to rank populations?

I want to rank ten or so sources based on their respective error measurements. A few notes on the sources and measurements: The sources do not have the same number of measurements The number of ...
1
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0answers
40 views

Recalibrating a model predictions to incidence in coarse resolution, and measuring that its calibrated

I have a model that predicts a rare disease (1% prevalence) with good discrimination (AUC). However, the predictions it is giving can not be interpreted as probabilities. I want to recalibrate the ...
3
votes
3answers
133 views

statistical test for two populations of proportions

I performed an experiment in which I measured the equilibration of a protein across two nuclei in a binucleated cell. This equilibration is expressed in percentages or proportions. I measured this for ...
2
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1answer
40 views

Likelihood of Ordered Binomials

I have four numbers ($k_1 \dots k_4$) that come from 4 binomial trials with parameters $n$ and $\theta_1 \dots \theta_4$. I want to test (via likelihood ratio test) the hypotheses $$H_0: \theta_1 = \...
0
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1answer
411 views

Calibration after up and downsampling

I am experimenting with different techniques to deal with imbalanced classes in a classification problem. I am comparing upsampling the minority class with downsampling the majority class. Furthermore ...
1
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1answer
585 views

Predicting the probability of product to be bought

I want to predict using statistical/machine-learning methods the probability of a person to buy a product on a website knowing the characteristics of the product and the other products it is compared ...
2
votes
1answer
82 views

Multiplying SVM-derived probabilities with different levels of support

Let's assume there is a function of interest: y = abc ...where a, b, and c are the probabilities of independent events. I've created classification algorithms (specifically, SVMs) to estimate those ...
0
votes
3answers
175 views

Multiclass classification question

I am working on applying Random Forests to a multiclass classification problem, where I have a set of 11 predictor variables and a response that can take the values of "Yes", "No", and "Maybe". In my ...
1
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1answer
118 views

Comparing and evaluating win probabilities in sports from different settings

Background I'm trying to predict the probability that the home teams wins a certain sports game, for each minute of the game. Taking these win probabilities together produces a nice visual of the ...
2
votes
1answer
177 views

Normalize logistics regression scores

I have four logistic regression model that predicts likelihood that customer make a purchase in 4 product categories(purchase event is rare and oversampled 50-50 for each model). Is there way to ...
1
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0answers
672 views

Machine Learning: how do we usually select the best combination of parameters to obtain well-calibrated probabilities instead of classification task?

I have always dealt with Machine Learning problems involving classification tasks. I now have the following problem: obtain the purchasing probabilities of users given a certain dataset. Reading the ...
1
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1answer
36 views

Testing for a non-zero, monotonic trend amongst 3 groups in a repeated-measures design

For each subject, we repeatedly measure 3 conditions for a scalar dependent variable. The research hypothesis is that there is a monotonic positive trend - that is, either 1<2<3 or 1=2<3 or 1&...
4
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1answer
183 views

Why bother looking at an omnibus ANOVA when I have a priori hypotheses about group differences?

I am examining three independent groups that were measured on a continuous outcome variable. I have a priori belief that the result should be Group 1 < Group 2 < Group 3. I've been told to do an ...
7
votes
2answers
4k views

Is it right to consider the output of the neural network as its confidence in predicting the output?

Suppose I have a single output sigmoid (tanh) that is producing an output ranging [-1, +1]. Is it right to consider this output as its confidence measue of predicting the output. The output value ...
1
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1answer
246 views

What does monotone polynomial plot represent?

I am trying to understand monotone and isotonic regression. I believe they will produce curve which are monotonely increasing or decreasing. In most of what I read on the net, the change is shown in a ...
3
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1answer
1k views

Fit monotone polynomial to data

I want to fit monotone polynomials to data. Murray, Müller and Turlach (http://dx.doi.org/10.1007/s00180-012-0390-5) provide an implementation in R (http://cran.r-project.org/web/packages/MonoPoly/...
3
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1answer
1k views

Applying isotonic regression calibration (using PAV) to new model predictions

I'm working on classifying models for a few different projects. Several papers on the subject of calibration all suggest using isotonic regression (using PAV) to adjust the model probabilities. I ...
2
votes
1answer
923 views

Chi-Square test: one-sided implementation?

I need to compare two samples and I would like to know if the distribution of the first stochastically dominates that of the second one. I'm not sure whether with the Chi-Square test I can verify ...
11
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2answers
14k views

Is it “okay” to plot a regression line for ranked data (Spearman correlation)?

I have data for which I calculated the Spearman correlation and want to visualize it for a publication. The dependent variable is ranked, the independet variable is not. What I want to visualize is ...
2
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1answer
85 views

Would multiple t-tests be appropriate

I have reaction time data from four different age groups, and I am hoping to prove that reaction time improves with age. I know that ANOVA would be preferred to determine if age has an effect, but I ...
6
votes
1answer
2k views

why is adaboost predicting probabilities with so little standard deviation?

I'm using several algorithms to predict a binary target. So far I tried Gradient Boosting, Random Forest, Extra Random Trees and adaboost from scikit learn. All of these algorithms appear to predict ...
0
votes
2answers
522 views

Convert linear SVM answers to class probability?

How to do this? I use SVMlight that returns me some scores (which say how sure SVM is that something belongs to a class?) The questions is - can I do something to convert it to a % probability? Any ...
3
votes
0answers
1k views

Estimators for linear regression when multicollinearity is present

I have a multicollinearity problem in a linear regression model and ridge regression was suggested as a solution. So I have spent quite some time researching different ridge regressors in the ...
2
votes
1answer
1k views

1D weighted Isotonic Regression (PAV): a simple description of the algorithm

I have to use IsotonicRegression class from scikit-learn with non-uniform point weights: in method IsotonicRegression.fit parameter ...
1
vote
2answers
180 views

One-way table largest proportion test

Suppose I've a one-way table with three categories (A, B and C), and let $p_a$, $p_b$ and $p_c$ be the true proportion of observations in each category, i.e. $p_a+p_b+p_c=1$. How can I conduct a ...
5
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1answer
849 views

Fitting constrained hierarchical models in JAGS

I have been doing some research on constrained models and have recently read the paper: Gunn and Dunson (2005) "A Transformation Approach for Incorporating Monotone or Unimodel Constraints", ...
7
votes
3answers
735 views

Binomial data analysis with all 0 responses for some treatment groups

We have a series of experiments where we measure virus transmission to plants when exposed to virus-infected insects for different time periods, so all of the experiments have similar types of ...
6
votes
1answer
450 views

Any good reference books/material to help me build a txn level fraud detection model?

I am looking for a book/case study etc on how to build a fraud detection model at the transaction level. Something applied rather than theoretical would be really helpful.
4
votes
1answer
324 views

Quantifying the degree of consistency of two fitted curves

I previously asked how to estimate the latent potential of a runner who ran the 100 metres each day for 200 days. Latent skill was defined as "the latent time it would take the individual to run if ...
7
votes
3answers
191 views

Estimating latent performance potential based on a sequence of observations

Context you have 200 observations of an individual's running time for the 100 metres measured once a day for 200 days. Assume the individual was not a runner before commencement of practice Based on ...