Questions tagged [density-estimation]

Estimation of probability density functions, whether by kernel density estimation, log-spline estimation or other methods.

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“Simple” boundary correction method in kernel density estimation

I'm new to kernel density estimation and have a rough idea on boundary bias. When correcting for boundaries, I tried to use boundary correction method as "simple" which is available in R. Once I ...
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17 views

How density function of chi-squared has been found ? By who?

I want to understand how the chi-squared cumulative distribution function has been found. By who? Pearson? Other? I search to compute it without using formula found on the Web at Wikipedia but in ...
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29 views

How to generate random samples from a 2D dataset?

Suppose I'm given a data set consisting of many pairs of $(x,y)$ values which are correlated in some arbitrary complex way. How would I go about 'generating' more pairs of $(x,y)$ coordinates which ...
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McCrary test in PR election

I am exploring a RDD using the margin of victory of the winner over the runnner-up in a PR race with multiple candidates. It is not clear how/whether I should perform a density test as it is appeared ...
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49 views

How to fully estimate a probability density from only a sample of minimum values?

We are given a sample $\{ z_i \}$, $i=1,2,\ldots,N$, such that each value $z_i$ corresponds to the minimum of $n$ random variables $x$, i.e., $z = \min \{ x_1, x_2,\ldots,x_n \}$. By means of ...
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14 views

How to fit mixture of gaussians with identical mean?

Say I have data generated by a mixture of gaussians whose components have the same mean, but very different covariances, like the one generated by this code: ...
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31 views

Is there a name for this approach to find a class probability via density estimation?

I am studying a stochastic process that produces event 1 with a probability $p \ll 1$ and event 0 with probability $1 - p$. I have large amounts of data consisting of about $n=20$ features and ...
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8 views

Density estimation plot for large number of points when interested in the low frequency occurences?

I've made a triplet loss network, investigated my training data using it's losses to produce a "loss scatter". It was suggested that I try and use density estimation to investigate and visualize the ...
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26 views

How can one model the density of a distribution of choice?

I'm a bit new to stats, so I may be missing some fundamentals. I'm interested estimating the density of a discrete distribution, so that I can obtain the probability of an unseen outcome. I have ...
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51 views

Density estimation for big feature space

let's say I have a data set with 100 features and a couple million of samples. Whenever I get a new sample, I would like to estimate how many samples would have been around it in the original set (let'...
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How can a probability densitiy be estimated based on the maximum entropy principle, with constraints in the order statistics?

Let's say we are given a sample $\{ z_i \}$, $i=1,2,\ldots,N$, such that each value $z_i$ corresponds to the minimum of $n$ random variables $x$, i.e., $z = \min \{ x_1, x_2,\ldots,x_n \}$. The ...
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A comparison of the global optimal binwidth and local optimal binwidth of the histogram estimator

Suppose we have $X_1, \dots, X_n$ to be an i.i.d sample with unknown pdf $f(x)$ and cdf $F(x)$, and define $\hat{f} (x)$ to be the histogram estimator. We also define its Mean Integrated Square Error ...
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37 views

Kernel Density Estimation - Comparison Between different sets of samples

Is there a way for compare the distribution of different set of samples? For example, I have three sets, for example: X1 = N(0, 1); X2 = N(0.5, 1); X3 = N(1, 1). Each set is drown with a specific (...
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Likelihood proportional to several functions

Hi I have some probability density functions, $f_1$, $f_2$,... etc and know they are proportional to the following expressions: $f_1(X) \propto \frac{\frac{1}{p}^X}{(1-p)^X}$ $f_2(X) \propto \frac{1}{...
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44 views

state of the art in density estimation

I have seen density estimation methods which are pretty old. Specifically, I am referring to Parzen Window method. When I read the original Parzen's paper, I was amazed by it's beauty and I know that ...
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39 views

How to evaluate the accuracy of a probability distribution?

I've trained a Gaussian Bayesian Network. If I feed input values for the parent variables of my output variable, I get a normal distribution. How can I quantify the accuracy of this distribution when ...
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18 views

How can I estimate bivariate probability density for support restricted data?

I have a bivariate sample with the following kernel density estimation The issue is that there is actually a cutoff for log(Age) at about 2.5, so value greater than 2.5 has probability 0. The fitted ...
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Clustering timeseries subsequences (detection of modes)

I am working on a task that involves detecting different "clusters" of a timeseries signal. So basically I need to differentiate between "modes" (importantly, I do not know how many groups there will ...
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14 views

Have $(U,V)$ be a pair of Bivariate Gaussian variables with mean $0$, variance $1$ and $Cov(U,V) = p$ where 0 < ρ < 1 [duplicate]

Have $(U,V)$ be a pair of Bivariate Gaussian variables with mean $0$, variance $1$ and $Cov(U,V) = ρ$ where $0 < ρ < 1$ I'd like help finding the density of $U+V$ So far I have tried to use $...
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Is there an example reference for Density estimation using Triangular Kernel Function

Density estimation using Triangular Kernel Function
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Finding probability bucket which result in 90% correct classification

I have a dataframe of two columns, one of which contains probabilities of event X happening and the second column is whether or not X did occur as indicated by a 0,1. I would like to find the buckets ...
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44 views

Density Estimation Efficieny

My Question Let's say a set training samples like D from a discrete distribution like p(x) over a discrete variable vector like x is available. We don't have any prior knowledge about the form of p(x)...
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55 views

Estimate value with binomial distribution [closed]

We have some compound A diluted in a solution. In 200 trials, we find that when we mix $1$ $\mathrm{mm}^3$ our solution of A with some amount of some compound B, we get a reaction 185 times. How can I ...
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66 views

Density Estimation and Data Normalization

Is there any problem to first normalize data (for example, min-max one) then use kernel density estimation to get pdf of each sample? Thanks.
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Every point has the same probability?

I am reading "Pattern recognition and machine learning" by Cristopher Bishop. In Chapter 2.5.1 "Kernel density estimator", there is written that: Let us suppose that observations are being drawn ...
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32 views

Bayesian approach: ignoring the denominator leads to the conditional density equaling the joint density? [duplicate]

I know there are a lot of questions here about ignoring the denominator in a Bayesian approach, but I don't think mine is a duplicate of any of them. I am reading the book "Pattern recognition and ...
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59 views

What is the difference between probabilistic forecasting and quantile forecasting?

A probabilistic time series forecast outputs the entire distribution of the forecasted values for a given time point, instead of just a mean or a point forecast. A quantile forecast is a forecast ...
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29 views

Piecewise Pareto Distribution

What are the best practices for Piece-wise Pareto Distribution or maybe Pareto Mixture Model(?). Example: $x\in [0, 1) \Rightarrow \alpha=0.1$ $x\in [1, 10) \Rightarrow \alpha=0.5$ $x\in [10, 100) ...
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37 views

To what distribution it's similar? Looks like an exponential but it's not

To what distribution it's similar? Looks like an exponential but it's not. It's seems to have a property, that if I zoom it (xlim) then each time it has the same ...
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124 views

Can Kernel Density Estimation estimate an Exponential Distribution?

Can Kernel Density Estimation estimate an Exponential Distribution? I tried to performed to make experiments with various kernels like: "gaussian" and "exponential", but performance seems to be very ...
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Comparing Density Plot height (MachineLearning Classification)

I am working on a binary Machine Learning classification problem. My classifiers are really performing poorly because distribution of the 1 class is very similar to 0 class (dataset is imbalanced, 1 ...
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Substitution for unknown true density in 'Density Estimation Trees'

I'm having a hard time understanding parts of the derivation of the objective function for Density Estimation Trees (reference below) regarding the loss function. Taken from the article (Sec. 3.1): ...
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Conditional Density Estimate Loss. Why the double integral?

I read RFCDE: Random Forests for Conditional Density Estimation. Just like it sounds, these folks trained random forests for making conditional density estimates. At inference time, density estimates ...
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25 views

bandwidth setting for density comparison

I intend to compare a list of density distributions. Following one published paper (with similar type of data and same objective), I learned that I have to use Gaussian kernel density estimator, and a ...
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62 views

Properties of Kernel Density Estimators

Given Let $X \in \mathbb{R}$ be a real-valued random variable with theoretical probability density function (pdf) $f(x)$ and corresponding cumulative distribution function (cdf) $F(x)$. Let $X_1, X_2,...
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Integration of Kernel and density product

Im considering kernels of the form $$K_s(u) = A(s)k_s(u)I[\lvert u \lvert \leq 1]$$ and $$k_s(u) = (1-u^2)^s$$ with $r$'th derivative $$K_s^r(u) = A(s)\frac{d^r k_s(u)}{du^r}I[\lvert u \lvert \leq ...
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36 views

Expectation of derivative of kernel density estimator

I am trying to calculate the expectation of the $s$'th derivative of a kernel density estimator. This problem arises naturally when trying to estimate the derivative of a density, because one approach ...
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55 views

Is There an Optimal Bandwidth for Kernel Density Estimation at One Point

I am trying to estimate the density of a 2D distribution using KDE, but I only care about the accuracy right at the origin. I have read about methods to estimate the optimal bandwidth matrix when you ...
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19 views

Function dependent to nth order on a sample

From this paper: ... every multivariate density estimator that is in any reasonable sense nonparametric may be written in the form: $$ \hat{f}(y) = \frac{1}{n}\sum_{i=1}^n K_n(x_i, y) $$ ...
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317 views

Difference between function and distribution?

I know this is dumb question, but i am confused to understand it. I have constant function as $$y = exp(-x^2)$$ This also represent gaussian distribution with mean zero and variance of 0.5 Now if ...
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62 views

Are vanishing bias and variance enough for pointwise consistency for KDE-based estimation?

Question: Is the condition that asymptotic bias and asymptotic variance goes to zero for infinite samples sufficient to guarantee the pointwise consistency of an estimator based on plug-in kernel ...
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84 views

Can kernel density estimation be used to estimate a radial probability density?

I am trying to estimate the PDF of the radius of points distributed in a 2D plane. The points are distributed like this: I can produce a histogram of the radius data which looks like this: I want ...
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123 views

Credibility evaluation - how to model conditional continuous density from multiple variables of various types?

I recently got dataset for 37000 households with declared income and a few dozens of other variables of various types: continuous, discrete, binary. The task is to automatically (unsupervised) ...
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Weighted kernel density

I would like to produce a 3-d plot based on density of 2-d data. This can be achieved for example in R using the kde2d function from the ...
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2answers
147 views

GLMM species count data with transects

I am trying to create a GLMM model which explains differences in abundance/count of three species of scorpion around a field reserve in different forest types. -I have 7 trails in different forest ...
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195 views

How to get a density from a forecast with prediction interval

Some reproducible code to have in your environment a time series and a possible forecast: ...
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Choosing Gaussian PDF basis bandwidth depending on number of bases and range of data

Summary (details below!) I have a basis expansion of $m$ (univariate) Gaussian PDFs to model the density of a sample $X$. The means of these PDFs are spaced equidistantly through the domain of $X$ ...
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Principled estimate of joint PDF given marginals and first and second-order statistics

(Trying to solve the same underlying problem as this.) Let's say we know the marginal probability density functions $p_i(x)$ of a set of zero-mean random variables $\{X_i\}_{i=1}^N$ as well as the ...
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173 views

Normal Kernel Estimation in R [closed]

I'm given the following data: ...
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96 views

How long is a distribution considered normal?

I have a dataset of metric distances ($n=5800$) and plotted those as a histogram. My initial thought was that this distribution looks normal. But after performing a Shapiro Wilk test and plotting the ...