All Questions
Tagged with nonparametric bayesian
60
questions
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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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0
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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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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
11
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1
answer
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
votes
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
0
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2
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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
2
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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
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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
0
votes
2
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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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0
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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
votes
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 ...
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