Questions tagged [density-estimation]

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

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How to find density in behavior of people? [closed]

I have a list of numbers which represent speeds (Km/h) of some people when they crossing a street : [1, 2, 2, 3, 35, 70, 75, 80] When I want to find the density of ...
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32 views

What methods are there for estimating distributions based on histograms?

I recently worked on a consulting project where a client wanted to estimate gamma and weibull distributions based purely on histograms rather than raw-data. I have never worked with problems like that ...
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59 views

Convergence of kernel density estimate as the sample size grows

Let $X\sim\text{Normal}(0,1)$ and let $f_X$ be its probability density function. I conducted some numerical experiments in the software Mathematica to estimate $f_X$ via a kernel method. Let $\hat{f}...
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59 views

Point estimation, interval estimation, density estimation?

Frequentist statistics textbooks typically consider point and interval estimation but not density estimation of a parameter. Since the density (of the sampling distribution) of the estimator is ...
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Density estimation: the significance of smaller number of samples?

I'm reading Probabilistic Graphical Model: Principle and Techniques by Koller and Friedman. In section 18.5 Bayesian Model Averaging(p825), the author said If we are interested only in density ...
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15 views

Validity of Monte-Carlo method to estimate a probability distribution which follows a power law

I am using a Monte-Carlo method to estimate a probability distribution function (pdf). Basically, I have several input parameters following known distributions, from which I can draw samples, that I ...
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21 views

Combining estimated model distribution

I estimate separately a univariate model distribution $f_d(x;\widehat{\mu_{d}},\widehat{\sigma_{d}^{2}})$ with data of $d$ day. I have 5 models according with the 5 days of week. The behavior of ...
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22 views

Interval and density forecast in R with both heteroskedasticity and non-normality in time-series data

We tried to get both an interval and density forecast based on time-series data, which we found to be both non-normal and heteroskedastic, in R. We know that for non-normality, forecasts can be ...
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1answer
104 views

Why is K-Means a special case of Mean-Shift algorithm?

I have read the paper of Yizong Cheng about Mean Shift, Mean shift, mode seeking, and clustering , but I didn't understand exactly, how did he concluded that KMeans is a Special case of Mean Shift ...
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What is the resulting distribution of a data set that was originally normally distributed but has been quantized and had all negative values removed?

I am trying to benchmark a seasonal forecasting model and calculate not just the point forecasts but the forecast densities from the model. To do this, I generated a simulated data set in the ...
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Expected value and variance of KDE

I need to find the expected value and variance of KDE given that $$(i) E[u] = 0 \to \int u\phi(u)du=0\\ (ii)V[u] = \sigma^2 \to \int u^2\phi(u)du=\sigma^2$$ where $\phi$ is the kernel function. I've ...
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Hellinger Distance between 2 vectors of data points using cumsum in R

I have numerous vectors of data points and I want to compute the hellinger distance between the probability distributions of every 2 vectors. I am using this version of the Hellinger distance equation:...
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How to efficiently find spikes in 2D data projected to 1 axis

I have the following points: My goal is to find the be able to differentiate the yellow points from the purple ones. We can assume that the yellow points are aligned on the vertical axis. We cannot ...
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20 views

Fitting density through regression model

I found in a paper a way to fit a density through a regression model, and i wanted to know if you have some other referenes that uses it, or maybe the source of this idea. Here it goes : Suppose ...
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26 views

Using Parzen Window approach

When is preferable using Parzen Windows approach, so a nonparametric approach, instead to a parametric approach?
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How can probability be equal to pdf times volume of area?

I'm studying pattern recognition and I'm at the part about Kernel density estimators. During the introduction of the subject, the book I'm studying (Pattern Recognition & Machine Learning by ...
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54 views

Behavior of kernel density estimation

Consider the random variable $X=YZ$, where $Y\sim\text{Normal}(0,1)$ and $Z\sim\text{log-Normal}(0,1)$ are independent. I wanted to assess the accuracy of kernel density estimates for the density ...
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Difficulties with orthogonal density estimation

I am working on an implementation of an orthogonal density estimator, using the basis $$ \psi_0(t) = 1, \quad \psi_{2j}(t) = \sqrt{2}\text{cos}(2\pi j t), \quad \psi_{2j+1}(t) = \sqrt{2}\text{sin}(2\...
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Density estimation as an optimization problem

Density estimation is the estimation of a probability density function from observed data. Can some of the common approaches to density estimation, such as kernel density estimation, be formulated as ...
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21 views

“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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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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1answer
38 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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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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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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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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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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53 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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112 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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2answers
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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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1answer
47 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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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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17 views

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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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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10 views

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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47 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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1answer
70 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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1answer
92 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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1answer
37 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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133 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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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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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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2answers
175 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 ...