# Questions tagged [bayesian]

Bayesian statistics is a statistical paradigm that contrasts with that of frequentist statistics. Bayesian methods rely on prior information do determine the degree of belief in the probability of a value.

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### If I use Gibbs sampling with a Bayesian model, what do I have to check is memoryless?

Right now I am trying to better understand how Bayesian modeling works with just the basics. I found through reading tutorials that some very basic Bayesian models like Bayesian Hierarchical Modeling ...
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### Is k-means with Mahalanobis a valid option for clustering?

I want more info into if k-means with Mahalanobis distance is a mathematically/methodologically correct option for datasets with different variance clusters. The steps are: Create aggregate datasets (...
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### How to update the posterior belief when we are observing a stream of correlated data from a fixed but unknown data source

I want to build a [probabilistic] model that aims to infer the true value of an unknown categorical variable, $y \in \{1,2,..., K\}$. We have a dataset $(X,y): \mathbb{R}^d\rightarrow \{1,2,..., K\}$ ...
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### Bayesian optimization for a Light GBM Model

I am able to successfully improve the performance of my XGBoost model through Bayesian optimization, but the best I can achieve through Bayesian optimization when using Light GBM (my preferred choice) ...
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### Bayes posteriograms

My main objective is to predict the posterior probability of an individual belonging to one of the classes, using Bayes theorem. The information I have is: value of the data point mean and stdev of ...
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### Algorithms behind "smartlinks" for online traffic distribution

Several traffic networks offer "smart links", where you can send online traffic, and the traffic will be sent to the most profitable segment. These networks include Monetizer, Glize etc. I.e. if you ...
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### Correct calculation of BIC (Bayesian Information Criterion) to determine K for K-Means

I am trying to calculate BIC in python. In python, there is no inbuilt library for computing BIC. I referenced the following link to compute variance and BIC further:- https://stats.stackexchange.com/...
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### How to integrate out hyperparameters of Gaussian process for Bayesian optimization?

I read this paper (https://arxiv.org/pdf/1206.2944.pdf) discussing about practical issues of Bayesian optimization and they mentioned that integrating out hyperparameters of Gaussian process using ...
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### Custom regularisation for logistics regression

My understanding of l2 regularisation: Weights of the model are assumed to have a prior guassian distribution centered around 0. Then MAP estimate over data adds an extra penalty in cost function. My ...
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### How to interpret long equations in Deep Learning papers

For eg. I've been studying a paper on Recommender systems using collaborative deep learning and I've just started learning. The paper revolves around the NN representation as shown below The ...
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### How to use pymc3 to sample the mean of a Pareto random variable?

I Have a variable which is Pareto-ly distributed 'x', with unknown alpha and m. I want to find out the distribution of its mean, so I use the following model: ...
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### Can we calculate Bayes Error rate, if we have a simulated data?

I am going through ISL(Python) and in section 2.2.3 ( Page No. 36), the author writes, "For our simulated data, the Bayes error is 0.133. It is greater than zero, because the classes overlap in ...
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### Global variant of Jeffreys Prior

The Jeffreys prior can be viewed as a way to ensure that "accidental similarities" between nearby models in some hypothesis space do not produce commensurate "accidental biases" in ...
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I have developed a model where the parameter is initially calibrated using common features (X1, X2, X3) from both source and target domains. Now, I want to incorporate additional specific features (X4 ...
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### Why posterior in EM algorithm tractable but in VAE not?

So I've read through this post, including the Bayesian Mixture of Gaussians supplied in the link in the last comment by oW_ there, to really see why the posterior is intractable. I just don't see yet ...
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### $p(f|X,Y) \propto p(Y|X,f)p(f)$

I'm reading a paper where it mentions Gaussian processes, the author defines a prior distribution over function space $p(f)$ and states the following about the posterior $p(f|X,Y) \propto p(Y|X,f)p(f)$...
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### Bayesian Linear regression for non-gaussian distribution

Which distribution should be considered for non-gaussian distribution while building Bayesian Linear regression. I am trying to build this model using Pymc3 library but since I have just started to ...
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### Parameter outside specified range using HGboost/Hyperopt library

I am trying to use the HGboost library which uses the Hyperopt library for doing hyperparameter optimization of an XGboost model. The script runs fine but the optimized parameter for "...
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### Prediction intervals for future timestamps - out-of-sample

I've created a model for out-of-sample forecasting that uses multistep recursive strategy to reduce my problem to regression, the predictions are sufficient but I was wondering if there is any ...
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### Using Bayesian statistics in time series forecasting

I would like to forecast demand count time series of taxi fleets at different locations on the map at different points in time. I.e. multivariate demand Time series forecasting. Given hierarchinal ...
I am using bayesopt to maximize a function that is everywhere less or equal to zero $(f(x) \leq 0)$. The score is essentially a negated Mean Absolute Error because the default behavior of bayesopt is ...