# Questions tagged [likelihood]

Given a random variable $X$ which arise from a parameterized distribution $F(X;θ)$, the likelihood is defined as the probability of observed data as a function of $θ$: $\operatorname{L}(θ | x)=\operatorname{P}(X=x \mid θ)$

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### Analogue of landscape conjecture in likelihood theory or Bayes?

The so-called landscape conjecture in machine learning says that in high dimensions, most critical points of the loss surface are saddle points rather than poor local minima. Out of curiosity I was ...
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### Maximum likelihood in linear regression

My understanding is that when we do maximum likelihood we want to choose parameters $\theta$ such that the probability of observing the actual, fixed data is maximized. That's how I understood it ...
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### What exactly is likelihood? [duplicate]

My understanding about likelihood, given some reading, is that it is how likely we are to observe the actual data given a certain parameter or parameter values $\theta$. Like with the coin toss ...
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### pdf vs probability vs likelihood [duplicate]

How to compute the log likelihood? Let's take a simple example using a normal distribution and scipy to do the work. Assuming X is the data, and the normal distribution as the model (...
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### Interpretation of Maximum Likelihood Value

I have a question about Maximum Likelihood values, and how to interpret them. In order to explain the question, please see the Figure below. I will add explanation for how this figure has been created ...
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### Unbiased estimate of log-likelihood of Markov bridge

Note: I have cross-posted this question to MathSE. I have the following problem I am trying to solve. I have a parametric family of "transition" distributions $p_\theta(x_{i+1}\mid x_i)$ and ...
1 vote
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### Likelihood ratio as minimal sufficient statistics in infinite parameter space

I just read a question from here (Likelihood ratio minimal sufficient) and have some thoughts. Let me restate the question first: Consider a family of density functions $f(x|\theta)$ where the ...
1 vote
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### Likelihood of sum of log-normal and normal distribution [closed]

Given $y(x_t)=e^{f(x_t)}-\varepsilon _t$ with $\varepsilon _t\sim N(0,4e^{f(x_t)})$ and $f\sim GP(\mu,\sum)$. What is the likelihood $p(y|f)$? Is it $p(y|f)\sim N(e^{f(x_t)},4e^{f(x_t)})$? Thanks a ...
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### What is the correct way to refer to the Likelihood $L(\theta, \alpha | X)$ where $\theta$ and $\alpha$ are parameters?

I am currently studying some latent variable models. In many works, I found the following equation: $L( \theta, \boldsymbol\pi | x ) = \sum_{c=1}^{C} f(x| \theta, \alpha = \alpha_c) \cdot \pi_c$ where ...
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