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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 ...
pierround's user avatar
3 votes
2 answers
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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 (...
Stefanos Stamatiadis's user avatar
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1 answer
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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 $(X,y): \mathbb{R}^d\rightarrow \{1,2,..., K\}$ ...
Mo-'s user avatar
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Probability distributions for Directed Cyclic Graphs

Given a directed cyclic graph where vertex A is 'infected', and there are different infection probabilities between each node, what is the best approach towards computing the conditional probability $...
Jonas Hjulstad's user avatar
2 votes
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Firebase AB testing algorithm

We have run an AB test at firebase which has the following results: I was also building my own Bayesian AB-test suite and was wondering how they came to these conclusions. What I was doing was ...
Boris Mulder's user avatar
2 votes
1 answer
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What are the tradeoffs between Bayesian Deep Learning and Deep Gaussain Processes?

I understand the differences between Deep Gaussian Processes(DGPs) and Bayesian Deep Learning(BDL): DGPs are essentially feed-forward neural networks where each node is a Gaussian Processes, which BDL ...
MattyIce's user avatar
2 votes
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109 views

PyMC3: how to efficiently regress on many variables?

I am sorry ahead of time if this seems like a basic question, but I had difficulty finding resources online addressing this. In PyMC3, when building a basic model of a few variables, it is easy to ...
Coolio2654's user avatar
2 votes
2 answers
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When to model a problem by using the Bayes' theorem?

I have a labeled training dataset where each observation has a sentence either in English or in French as its predictors and its label (target value) is whether this sentence is English or French. The ...
Outcast's user avatar
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Bayesian linear regression / categorical variable / Laplace prior

I'm trying to do feature selection in the bayesian framework with a Laplace prior with the following code in Python; Code: ...
glouis's user avatar
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2 votes
0 answers
61 views

information leakage when using empirical Bayesian to generate a predictor

Consider the following problem: I want to predict the next bat of a set of baseball player. I have a training data set, where it contains the historical bat records (0-1 encoded, which is our target ...
KevinKim's user avatar
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Implement gaussian mixture model with stochastic variational inference

I am trying to implement Gaussian Mixture model with stochastic variational inference, following this paper. This is the pgm of Gaussian Mixture. According to the paper, the full algorithm of ...
user5779223's user avatar
1 vote
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Which statistical approach is best for diverse conversion rates in a controlled experiment?

Our software startup builds chat bots for ecommerce websites. The chatbot talks to customers that open the chat bot, and has the goal of closing the sale with the store’s main product. We have about ...
Rage's user avatar
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Occam's factor and the VC dimension

I was watching this lecture by Prof. Dr. Philipp Hennig (Probabilistic ML) and when he reached this formula which is the type two maximum log likelihood I had the following question: The Occam's ...
HAMDI ABDERRAHMENE's user avatar
1 vote
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80 views

Model uncertainty quantification

I'm reading a paper about model uncertainty quantification. Specifically, it says epistemic uncertainty is a kind of uncertainty due to lack of knowledge about a particular region in the input space. ...
piero's user avatar
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bayesian neural network and the flipout estimator

i was reading the flipout paper and i stumbled over this passage. I will summarize the main point here: In bayesian neural networks the weights are random variables sampled from a distribution. W is ...
Alucard's user avatar
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Probability for Nth Place in Race from Bradley-Terry Model Inputs and Outputs

I have created a motorcycle race prediction model that is given pairs of racers and outputs the probability of each rider beating the other in each pairwise comparison. That info is then processed ...
bdwilson24's user avatar
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How to guide exploration in reinforcement leanring/model predictive control/dual control problem

Consider the following optimization/control problem: We aim to maximize the cumulative reward R during the horizon H by every day allocating a portion of total budget B to our two different investment ...
stewardbranson's user avatar
1 vote
1 answer
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Problem understanding the forward algorithm for HMMs

I found a recursive version of the forward algorithm on wikipedia, however I don't understand the notation given in the pseudocode: What means $$x_{t-1}$$ under the summation sign? What do I need to ...
teoML's user avatar
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What methods I could use to analyze the contingency table?

I am data science beginner, and I have a question about methods that I could use to analyze the following data. It is a simple case, I am trying to check the influence of cohabitation before marriage ...
Karpi's user avatar
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0 answers
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Why and how Variational Inference underestimates variance?

I referred to the Quora link here as well, but could not understand clearly. Can anyone please help me understand why and how variational inference underestimates the variance of the true posterior ...
Curious's user avatar
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Confusion regarding which distribution Monte Carlo considers for sampling

Considering Bayesian posterior inference, which distribution does Monte Carlo sampling take samples from: posterior or prior? Posterior is intractable because the denominator (evidence) is an ...
Curious's user avatar
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1 answer
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Confused on Naive Bayes classifier

In the last part of Andrew Ng's lectures about Gaussian Discriminant Analysis and Naive Bayes Classifier, I am confused as to how Andrew Ng derived $(2^n) - 1$ features for Naive Bayes Classifier. ...
Alpha code 's user avatar
1 vote
0 answers
14 views

Bayesian Linear Regression using the Kernel Trick vs Constructing features using Kernels as Prototypes

How different is it to do Bayesian linear regression using the GP approach (kernel trick) versus constructing features using kernels to prototypes? As far as I know, this very basic question is ...
Robert's user avatar
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1 vote
1 answer
239 views

Update of mean and variance of weights

I'm trying to understand the Bayes by Backprop algorithm from the paper Weight Uncertainty in Neural Networks, the idea is to make a NN in which each weight has it's own probability distribution. I ...
Cosapocha's user avatar
1 vote
1 answer
46 views

Combining multiple probabilities from a classifier. Propagating probabilities

Let's say I have trained a classifier that classifies images of animals into 10 different classes. And let's say that I have 20 different images of a particular animal and because I know the ...
AstroAllie's user avatar
1 vote
1 answer
242 views

Visualize n-dimensional bayesian optimization results

I am working on a 6-dimensional bayesian optimization problem using (skopt's gp_minimize). After the optimizer ran for j iterations I would like to somehow visualize the "progress/result" of ...
FR_MPI's user avatar
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1 vote
0 answers
11 views

Tracking time-series latency using conjugate priors

I need to do a project using Bayesian statistics for a class and I am trying to apply it to my work. I help manage a time series database with 40,000+ different time series that we collect. The time ...
Jeff Tilton's user avatar
1 vote
1 answer
87 views

Poisson model with overdisperssion

I'm working with a dataset $X$ (of length $N$) of count data, which looks like: I developed a statistical model which can be improved, so I'm asking for any suggestions, for instance, differnet ...
ignatius's user avatar
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1 vote
0 answers
46 views

Custom Loss Function for Mixing Sparse and Dense Features for a Prediction Problem

I have a largely uncorrelated feature space of about 40 dichotomous features, using which I'm trying to predict a continuous target variable. Now, some of these features are very sparse (Active less ...
Recyclops's user avatar
1 vote
0 answers
58 views

Specifying priors in rstanarm for hierarchical model

We are given the model $$ \begin{align*} y_{ij} & \sim \mathsf{Normal}(\alpha_j + \beta x_i, \sigma^2)\\ \alpha_j & \sim \mathsf{Normal}(\gamma_0 + \gamma_1 u_j, \tau^2) \end{align*} $$ with ...
Trevor Mason's user avatar
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0 answers
40 views

GMM with Dirichlet prior

I'm learning about the variational inference - mean field approximation on from this online course DeepBayes2019 page 30 The probabilistic model is written as follows: $p(X, Z \mid \pi, \mu, \lambda) =...
glouis's user avatar
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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) ...
xxyy's user avatar
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1 vote
0 answers
45 views

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 ...
user3116297's user avatar
1 vote
0 answers
36 views

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 ...
j Rodr's user avatar
  • 11
1 vote
0 answers
780 views

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/...
Batman22's user avatar
  • 111
1 vote
0 answers
171 views

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 ...
user3326682's user avatar
1 vote
1 answer
299 views

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 ...
claudius's user avatar
  • 153
1 vote
0 answers
36 views

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 ...
m2rik's user avatar
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1 vote
0 answers
263 views

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: ...
Guy's user avatar
  • 11
0 votes
0 answers
9 views

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 ...
Prashant Kumar's user avatar
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0 answers
7 views

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 ...
TLDR's user avatar
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0 answers
6 views

Updating Model Parameter in Domain Adaptation with Additional Features

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 ...
Adham Enaya's user avatar
0 votes
0 answers
17 views

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 ...
Anon's user avatar
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0 answers
19 views

$p(f|X,Y) \propto p(Y|X,f)p(f)$

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 $p(f|X,Y) \propto p(Y|X,f)p(f)$...
piero's user avatar
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0 answers
28 views

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 ...
Archaeolexicologist's user avatar
0 votes
0 answers
19 views

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 "...
AWGIS's user avatar
  • 101
0 votes
1 answer
91 views

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 ...
kkkk0's user avatar
  • 1
0 votes
0 answers
37 views

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 ...
Jose_Peeterson's user avatar
0 votes
2 answers
46 views

Is there no reason to ever use naive bayesian learning?

I found this slide in the university course on machine learning I am currently taking. The reasons seem sound but I have not found this confirmed anywhere everywhere I read that for certain types of ...
user154502's user avatar
0 votes
0 answers
7 views

How to interpet the bolded lines in bayesopt

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 ...
Enk9456's user avatar
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