# Questions tagged [maximum-likelihood]

a method of estimating parameters of a statistical model by choosing the parameter value that optimizes the probability of observing the given sample.

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### Why are the MLE and MMSE corrections for sample variances different?

I have a number of samples of sample size 2 and a number of sample of sample size 3. If my samples are all samples from populations with a shared population variances, I wish to estimate population ...
22 views

### Bayesian update vs optimization

Say I have a multivariate normal vector $$r \sim N(\mu , \Sigma ) \Rightarrow Pr \sim N(P\mu , P'\Sigma P )$$ and I observe that $$Pr = Q$$ Now I can use Bayes rule to calculate the ...
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### Why do we sometimes define likelihood as $p(\textbf{T}|\textbf{X},w)$ and sometimes as $p(\textbf{X}, \textbf{T}|w)$?

Let's suppose we have a dataset $\mathcal{D}=(\textbf{X}, \textbf{T})$ where $\textbf{X}$ are the samples and $\textbf{T}$ are the targets. We want to find $w$ such that the likelihood is maximized. ...
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### Hi all i try to solve the below equation but it is very difficult for me , Can anyone give me a hint or resources to solve this equation? [on hold]

This question is related to additive Gaussian noise with MSE and ML
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### Logistic regression does not seem to maximize model accuracy

I'm using gradient descent to train my logistic regression model for a classification task. However, I notice that the accuracy of my model (using a boundary threshold of 0.5 to classify each sample) ...
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### Estimate mean of Poisson from binary data

If you assume that counts in sample units would be distributed according to a Poisson distribution, but the data that you have are observations of only presence (count would be 1 or more) or absence (...
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### Consistency of the MLE

I have a sample of size n from the following distribution: $$\frac{\alpha x^{\alpha-1}}{\beta^\alpha}$$ for $0<x<\beta$ and $\alpha > 0$. I found that the MLEs are $$\hat{\beta}=x_{(n)}$$ ...
361 views

### Fisher information for MLE with constraint

Supposing I have a probability distribution $f(x|\vec\theta)$, where $x$ is a random variable and $\vec\theta$ is a vector of distribution parameters. I also know that parameters $\vec\theta$ should ...
14 views

### Can the GAN objective function be written as related to a log-likelihood of some “classical” statistical model?

Can the objective function that GAN (Generative Adversarial Network) models optimize be written as a lower bound of the log-likelihood of some "classical" statistical model? I am reading through the ...
18k views

### MLE vs MAP estimation, when to use which?

MLE = Maximum Likelihood Estimation MAP = Maximum a posteriori MLE is intuitive/naive in that it starts only with the probability of observation given the parameter (i.e. the likelihood function) ...
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### Relation between MAP, EM, and MLE

I am a beginner in machine learning. I can do programming fine but the theory confuses me a lot of the times. What is the relation between Maximum Likelihood Estimation (MLE), Maximum A posteriori (...
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### Asymtotic distribution of the MLE of a Uniform

A property of the Maximum Likelihood Estimator is, that it asymptotically follows a normal distribution if the solution is unique. In case of a continuous Uniform distribution the Maximum Likelihood ...
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59 views

### How to find manually the value of the likelihood function?

I have a statistic homework and this is my question: Outcome (binary)=f(age, number of books) And that I have four observations in my dataset: Observation 1: Outcome=1, age=0.5, number of books=5 ...
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### Negative Variance from inverse Hessian [on hold]

In python, I'm using the inverse Hessian as an estimator of error for parameter estimation which works fine for most trials. For some small number of the trials I get negative variances on the ...
60 views

### Maximum Likelihood - Normal Errors - When is the Jacobian needed?

I am considering the following non-linear model $$h(z) - \lambda_0 - \lambda_1 z - \lambda_2x = v$$ where $v \sim \mathcal N(0,\sigma^2)$ unobserved error and where $\lambda_j$ are unknown ...
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### logistic mcmc start [closed]

I am doing logistic regression with MCMC . What is a good start for MCMC ?
39 views

### uniform distribution MLE with U($\theta$,$\theta+1$)

If my data $X_1, X_2,....,X_{10}$ has distribution of $U(\theta, \theta+1)$, and $X_{(10)} = 2$, would the MLE for $\theta$ actually be any $\theta$ in it's parameter space? I'm assuming this is ...
40 views