Linked Questions

2
votes
2answers
5k views

Sum of squared difference and Gaussian noise model

I have been reading that when the underlying error is distributed normally, then minimising the sum of squared difference between the observed data and the model is the appropriate cost function to do ...
11
votes
1answer
7k views

Is Bayesian Ridge Regression another name of Bayesian Linear Regression?

I searched about Bayesian Ridge Regression on Internet but most of the result I got is about Bayesian Linear Regression. I wonder if it's both the same things because the formula look quite similar
8
votes
1answer
1k views

What exactly is a hyperparameter?

Title says it all. I have seen both "the hyperparameter of the Dirichlet distribution" and "the parameter of the Dirichlet distribution" What are the differences?
5
votes
1answer
941 views

Questions on Bayesian Softmax Regression [closed]

My question is about how to actually do this both rigorously and practically. Allow me to elaborate. Suppose that we have data $(x_1,y_1),...,(x_N,y_N) \in \mathbb{R}^p \times \{0,...,k-1 \}$. I'd ...
4
votes
1answer
3k views

Posterior vs conditional probability

When talking about events, there is the following formula called Bayes' rule, where $A$ and $B$ are random events: $$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$$ Now let's say that for now only $A$ happened. I ...
3
votes
1answer
1k views

What is the real-life benefit and application of Bayesian regression [closed]

Question What is the real-life example of the benefit and application of the benefit of Bayesian regression? Having read the items and it looks having the range of inference (possible values and ...
3
votes
1answer
2k views

Estimation of Bayesian Ridge Regression

According to scikit-learn, by using a probabilistic model : $p(y|X,\omega,\alpha) = \mathcal{N}(y|X\omega,\alpha)$ with $\omega$ given by a spherical Gaussian: $p(\omega|\lambda) = \mathcal{N}(\...
2
votes
1answer
330 views

Implementing Bayesian Linear Regression using PyMC3

I am learning a Bayesian Approach towards implementing Linear Regression. The motivation is that Bayesian Approach gives you a range on predictions which might be useful when investing money in ...
2
votes
1answer
184 views

Intuition on simple linear regression signal plus noise model

I'm currently studying linear regression on this book "F.M. Dekking - A Modern Introduction to Probability and Statistics: Understanding Why and How" where the signal+noise model is presented: $Y_i =...
1
vote
1answer
535 views

Bayesian smoothing using Dirichlet prior : why not MAP?

I am reading about smoothing methods for language model ( I am working on unigram model). If you are not familiar with unigram model, it is closely related to multinomial distribution (with the ...
1
vote
1answer
64 views

Extra information at prediction time when using a Bayesian logistic regression vs. normal

I have a binary classification problem (i.e. is observation positive or negative) and I'm interested in what information I can obtain about observations in my test set. I don't care about the model ...
0
votes
1answer
20 views

Using prior knowledge about correlated variable in ridge regression

I am wondering what methods are available for incorporating prior knowledge of some variable that is correlated with the unknown regression coefficients in a ridge regression. I have a sparse matrix ...
0
votes
1answer
113 views

Is possible to perform a linear regression using log-normal priors?

I am trying to do a Bayesian linear regression. Since my data cannot be negative a gave them a log-Normal distribution, but I am not sure if the priors should be positive also. If I write my model ...
0
votes
1answer
18 views

Placing constraints on linear model coefficients

I have this bit of data : ...
0
votes
1answer
44 views

what is the posterior in the case of regression

I am having trouble "mapping" the variables in the Bayes equation onto the case of regression. As notation, say $$ P(\theta|D) = \frac{P(D|\theta) P(\theta)}{ P(D) } $$ I have come to think of $\...

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