All Questions
Tagged with nonparametric bayesian
26
questions with no upvoted or accepted answers
4
votes
0
answers
44
views
German tank variant: estimate resolution of camera given cropped photo sizes
Make whatever assumptions you like, but I like the flavor of nonparametric techniques.
I have a list of the $x_i$ by $y_i$ resolutions of a number of photos, all cropped from photos taken at the same ...
- 2,121
4
votes
0
answers
408
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Is this how a Bayesian bootstrap works?
I am a bit new to the whole nonparametric and Bayesian idea, so tell me if this is correct: to estimate, say, the mean of a dataset's population we do the following:
We define a function $f(x)$ that ...
- 2,121
3
votes
0
answers
323
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Bayesian approach to trend detection in non-parametric data
I have a series of data points, and I want to see how much evidence there is that the points are getting bigger over time. The data themselves are counts, but for various reasons I don't want to build ...
- 81
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
votes
0
answers
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
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
votes
0
answers
73
views
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
2
votes
0
answers
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
2
votes
0
answers
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
1
vote
0
answers
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
1
vote
0
answers
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
vote
0
answers
31
views
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
vote
0
answers
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
1
vote
0
answers
64
views
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
views
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