All Questions
Tagged with nonparametric bayesian
60
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33
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Is bootstrapping inherently Frequentist? If so, how do we do a Bayesian non-parametric two-sample test?
I normally use frequentist statistics but I now want to use Bayesian statistics as I want to carry out a two-sample (randomised control trial) test that includes prior information. I have an existing ...
- 913
4
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1
answer
52
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In what ways is Gaussian Process Regression both parametric and non-parametric?
Gaussian Process Regression is considered a "non-parametric" model. However, the term "non-parametric" is often used imprecisely to mean different things, leading to questions ...
- 847
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30
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Fisher information or Bayesian Uncertainty for non-parametric distributions
This question sounds ridiculous, let me clarify motivation:
Fisher information & Bayesian inference uncertainty seemed very cool to me because they can effectively tell you "how ...
- 411
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26
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BART with non-parametric heteroscedastic noise?
Is there a variant of BART that robustly captures noise that is both heteroscedastic and non-parametric (or has an a-priori unknown parametric form)?
For example, a BART that could fit this test data:
...
- 467
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65
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Bayesian analysis of non-normally distributed variable
I would like to use an Bayesian approach to compare a continuous non-normally distributed variable taking values between -1 to 1 between two populations. The measurements are not paired.
Overall my ...
- 101
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0
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61
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How can I combined Bayesian and non-parametric techniques?
I'd like to combine Bayesian and non-parametric (e.g. XGBoost) models, with the goal of getting a probability distribution over my target variable rather than a point estimate. I have a prior, and I ...
- 851
2
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4
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235
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good intermediate-level textbook for undergraduate applied statistics in data science?
I will be teaching an applied statistics course for the first time and the main audience will be 2nd and 3rd year undergraduates, mostly data science majors. They will have an intro statistics course ...
1
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61
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trace class of prior covariance operator in Bayesian inference problem
I'm interested in certain Bayesian inference problems where the vector space $Q$ where the parameters $\theta$ live is infinite-dimensional.
These show up all the time in the geophysical sciences -- ...
- 143
1
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136
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Deciding the Number of Clusters : Standard Methods vs. Non-Parametric Methods
I was watching this video over here (https://www.youtube.com/watch?v=UBiaLq5V7mE) that discussed a Non-Parametric based Bayesian approach for deciding the number of clusters in a dataset.
Essentially, ...
2
votes
0
answers
73
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MCMC fitting of Dirichlet Process or Polya Tree prior to residuals in (simple linear regression)/(2-independent-samples) problem
Consider a simple location-shift semi-parametric model with two mutually-independent samples (in what follows, $F$ is a cumulative distribution function (CDF) on $\mathbb{ R }$, the $C_i$ and $T_j$ ...
- 69
2
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140
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MCMC fitting of a Dirichlet Process or Polya Tree prior to the residuals in a (simple linear regression)/(2-independent-samples) problem
Consider a simple location-shift semi-parametric model with two mutually-independent samples (here $F$ is a cumulative distribution function (CDF) on $\mathbb{ R }$, the $C_i$ and $T_j$ are real-...
- 69
2
votes
1
answer
854
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KNN as a crude prototype of Gaussian Process Regression?
I've heard it said before that K-Means-Clustering is a prototypical method for Expectation-Maximization algorithm. Where KM Clustering returns a hard cluster assignment, EM returns soft assignments, ...
- 3,382
2
votes
0
answers
41
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Unexpected zero on posterior density of Dirichlet process mixture
I was reading this notebook from the PyMC3 documentation about Dirichlet Process Mixtures and, on the last figure, the estimated density reaches almost zero for a particular value, despite the ...
- 2,680
2
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73
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distance for abc - nonparametric likelihood
When fitting models using abc, data is simulated using parameters drawn from the prior. The distance between the simulated data and the observed data is calculated, and typically if less than a ...
- 33
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2
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1k
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Is there a Bayesian Non-Parametric one-way ANOVA?
The rough idea is that I am trying to compare linguistic properties (e.g. readability) between pieces of texts from two authors essentially. For this, I thought using an ANOVA would be appropriate. ...
0
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27
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Question about possible typo in a tutorial about the stick-breaking model of the Dirichlet distribution
I am reading a tutorial on the Dirichlet distribution: http://mayagupta.org/publications/FrigyikKapilaGuptaIntroToDirichlet.pdf
and I think there is a typo in Step 2 of the stick-breaking model of ...
1
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31
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Is data modeled by dirichlet process mixture exchangeable?
Consider DPM model:
$$
\begin{aligned} X_{i} | \phi_{i} & \sim F\left(x;\phi_{i}\right) \\ \phi_{1}, \phi_{2}, \cdots | & P \stackrel{iid}{\sim} P \\ P & \sim D P(\alpha G_0) \end{aligned}
...
- 241
1
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28
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Estimation hardness results in Bayesian inference?
Frequentist statistics has a series of fundamental hardness results that are encountered by beginning statistics students. In non-parametric statistics, a famous hardness result for the normal means ...
- 53
2
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0
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46
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Directly applying residual bootstrap to the predictions vs. inferring the parameters?
My friend has a procedure where he does the following:
Given a dataset $(x_1,y_1),\ldots,(x_n, y_n)$ Fit $f$ according to $\hat{y_i} = f(x_i) + \epsilon_i$ where $f$ is the regression function.
...
- 203
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1
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514
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Do Stochastic Processes such as the Gaussian Process/Dirichlet Process have densities? If not, how can Bayes rule be applied to them?
The Dirichlet Pocess and Gaussian Process are often referred to as "distributions over functions" or "distributions over distributions". In that case, can I meaningfully talk about the density of a ...
3
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2
answers
233
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Simulating the Posterior Density of a Transformed Parameters
I am reviewing an example (p. 180-181, Example 11.3 and 11.4) from All of Statistics by Larry Wasserman. The example intends to illustrate that the posterior can be found analytically and can be ...
- 159
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2
answers
72
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Likelihood term in Bayesian inferencing versus the general definition
In general we say that the likelihood function is defined as some $L(\theta|x)$, so that it is a function over some parameters: $\theta$ given some data: $x$. That is, $\theta$ is free to vary whilst $...
- 545
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133
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Smooth regression algorithms that produce zero training error
I am looking to fit three regression functions $f_1, f_2, f_3:\mathbb{R}^2 \to \mathbb{R}$. For example, let's say $X_1$ is time, $X_2$ is geographic latitude, $f_1$ is the temperature, $f_2$ is the ...
- 201
4
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1
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530
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Is parametric Bayesian inference a special case of nonparametric Bayesian inference?
I'm thinking about univariate density estimation.
Original Question
In parametric inference, you assume the data are generated from a density that can be summarized by finitely-many parameters. You ...
- 1,425
4
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1
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958
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Is there a loss function when estimating a model using MCMC?
I am trying to understand how fitting a model using MCMC works. Is there a loss function that is optimized?
Or is it simply a case of more draws from the distribution amount to a more complete ...
- 12.1k
1
vote
0
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64
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Bayesian posterior from pairwise comparison of observations
Say I have $n$ observations of group $A$ and $m$ observations of group $B$ and a function $f: A\times B \rightarrow C$ mapping a pair of observations to one of $k$ categories.
I am interested in the ...
1
vote
0
answers
690
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Bayesian Wilcoxon test
I have a pre-post dataset with 2 observations per subject (propotion data -bounded between 0 and 1-).
I have analyzed the data with a classical dependent t-test under the NHST paradigm. However, as ...
- 157
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votes
2
answers
266
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Book Bayesian Nonparametrics [duplicate]
What is the best recommended book on Bayesian Non parametric approaches ? Specifically something which also tackles regression problems such as Gaussian processes.
1
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74
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Clustering and Dirichlet process' parameter
I am reading a paper in which they describe a bayesian model in which the prior $a_i$ is defined as a Dirichlet Process (DP). They say: "We use a DP to find the optimal $a_i$ via clustering".
Later on ...
- 11
8
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2
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665
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What is a mixture of finite mixtures?
A mixture of finite mixture models seem to be an interesting Bayesian (?) approach to solving clustering with an unknown $k$ number of components. It seems though, unlike the mixture model with a ...
- 3,056