# Tagged Questions

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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### Distribution for modelling return times with inflated zeros

I have data on people's return times which I wanted to fit a distribution to using maximum likelihood estimation. I was planning on using a Weibull or Gamma but there are a high number of return ...
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### Help in parameter estimation using MLE for time series data

I have training data $\mathbf{X}$ that consists of $N$ time series as examples where each time series $\{\mathbf{x}_i\}$ is of length $n$. The values of the elements of the times series are binary. ...
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### Fisher's information for multiple binomials

I am trying to quantify error of the MLE for the following model using Fisher's information: $Y_{j} \sim Binomial(n_{j}, p_{j})$ $logit(p_{j}) = \eta + \gamma_{j}$ where the $n_{j}$'s and $\gamma_{j}$'...
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### Sparsity as missing data + MLE

I just had this "funny" idea: what about a classifier that not only tries to learn weights for predicting y but actually works with "deleted" data (as in sparse ...
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### Help in unsupervised problem formuation for parameter estimation

In the supervised learning problem, the goal is, given a training set, to learn a function $h : X \mapsto Y$ so that $h (x)$ is a “good” predictor for the corresponding value of $y$. If $y$ takes ...
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### mle in R results in error: argument “probVector” is missing, with no default, even though probVector is properly initialized [migrated]

I am trying to call the R mle function as follows. ...
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### Is EM feasible when there is no closed form maximization of the expectation of log likelihood?

In every example I've seen of expectation maximization, the E step concludes with an expression of the expectation of log likelihood ( $Q(\theta | \theta^{(t)})$ ) for which a maximum w.r.t. $\theta$ ...
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### Finding a Scalable Approach to a modified coin-flip problem using MLE model

and thank you in advance for your help! I am interested in applying MLE to estimate parameters in a "modified" coin flip model, but have been having difficulties scaling the solution. The problem ...
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### Maximum likelihood estimation, how to derive the hessian

I am reading a paper and trying to understand how the authors estimated the standard errors of a set of parameter estimates $[\delta \ \ \phi \ \ \Sigma]$. Below is the loglikelihood function (sorry I ...
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### Setting up maximum likelihood estimation with multi-response data

I was trying to fit the parameters of a time-dependent system coupled of ODES related to a kinetic experiment with multi response data. Example: A->B+H A+H->C+H A->D dcA(t)/dt=-k1Ca(t)-k2Ca(t)*Ch(t)-...
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### Extract the different components of variance in a linear mixed model in R

Consider a mixed model as follows. ...
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### Variance of maximum likelihood estimator in R

In different sources there is an algorithm how to calculate the variance of MLE in R. To keep it short: construct the negative log likelihood function. minimize it via nlm or optim with hessian=TRUE ...
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### How can standard logistic regression model fractional response variable while denominator is available?

I have X and Y variables, as well as a cluster variable (State). X and State are derived from Database A, while Y and State are derived from Database B. X is a sentiment score ranging between -1 and ...
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### What is maximum likelihood PCA?

There are many papers on this topic, such as this one (pdf). However, I could not find out what exactly maximum likelihood PCA is, how it is applied and for which purpose. Can anyone explain it?
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### Layman explanation of Cramér–Rao bound [closed]

I am trying to understand Cramér–Rao bound, but I have a problem understanding the formula in Wikipedia. Can somebody tell me the intuitive way of it?
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### PyMC: Using maximum a posteriori on vector/matrix-valued variables

I am using PyMC to find a maximum a posteriori estimate for some data. The data is all vector-valued. I am trying to estimate my variable x based on a matrix-valued ...
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### AIC only applicable to maximum likelihood fit (not least squares)?

When I read about AIC I see that it is calculated for maximum likelihood model estimation. For example, R function arima0 estimated by ...
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### Conditional distribution (on N) of arrival times in a nonhomogenous poisson process

Conditional on $N(t)$, given some $\lambda(t)$ characterizing some Nonhomogenous poisson point process, the distribution of an arrival time $t_i$ is $\lambda(t_i)/\int_{A}\lambda\left(t\right)dt$ ...
22 views

### MLE of exponential distribution

Let $Y\sim Exp(1)$ and $T=\mu+Y,\ \mu\in \mathbb{R}$. Let $t_1,\dots,t_n$ be a simple random sample from $T$ with $\mu$ unknown parameter. How can I find MLE for $\mu$? I know that the likelihood ...
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### Find MLE on custom density function

Let $y_1,\dots,y_n$ be i.i.d. random variables from $$p_{Y_i}(y_i;\alpha,\beta)=exp\{y_i(\alpha+\beta x_i)-ln(1-e^{\alpha+\beta y_i})\},\ y_i=0,1$$ $\alpha, \beta$ are unknown real parameters ...
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### Maximization of a special log-likelihood function

I'm clear on how you found the likelihood function by multiply the pdf of all observations and then do the log to help when you derive. But here I don't understand the (2). Is it in a tobit censored ...
33 views

### Residual standard error difference between optim and glm

I try to reproduce with optim the results from a simple linear regression fitted with glm or even ...
26 views

### Are Maximum Likelihood Estimators asymptotically unbiased?

I can follow the proofs in which the asymptotic normal-distribution of a maximum likelihood estimator $\tilde{\theta}_n$ is derived. however, does this already imply that the maximum likelihood ...
51 views

### Maximize response for input params clusters from a blackbox function

I have a blackbox function which takes finite number of integers V1, V2, Vn parameters and based on time series variable produce a scalar response. I would like to ...
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### Maximum Likelihood Methods and derivate

I have an exercise about ML, I have some ideas but I can't go through. Here is what I need to answer and what I think I should do. Consider the following econometric model: $$y = \max(y∗, 0) \tag 2$$...
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### Confused about logistic regression equality

Problem: Prove that: \begin{align} \Delta E(in) &= -\frac{1}{N} \sum_{n=1}^N \frac{y_n x_n}{1 + e^{(y_n w^t x_n)}} \\[10pt] &=\frac{1}{N} * \sum_{n=1}^N - y_n x_n \theta (-y_n w^T ...
127 views

### 95% confidence intervals on prediction of censored binomial model estimated using mle2 / maximum-likelihood

I am working on a problem in which I have multiple pairs of currently living males i that each have a presumed paternal ancestor ...
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### factor analysis using Maximum likelihood or Principle axis factor to extract factors for 6 point likert type questions?

We have a questionnaire, which have many questions on 6-point likert scale. So these variables are ordinal, not normally distributed. In performing factor analysis, there are two major methods in ...
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### MLE of heteroscedastic model

I'm doing some practice questions for an upcoming exam and am unsure whether I've understood the problem correctly. Can anyone confirm what I've done or point out where I've gone wrong? My final ...
32 views

### Learning just a decoder (autoencoder without encoder)

I am trying to do something quite unusual: learning a latent representation of some data just by optimizing a decoder. Basically, a probabilistic model of a neural network autoencoder without the ...
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### Expectation of infinite sum of random wishart matrices

I have problem figuring out how to find the expectation for an infinite sum of random matrices. More explicitly, my problem is: Let $\mathbf{S}_i$ be the maximum likelihood estimator of the sample ...
11 views

### Maximum likelihood of gaussian with right censoring

I'm trying to fit the mean $\mu$ of right-censored gaussian data ($n$ samples) in a toy example (let's assume $\sigma^2=1$ is known), and the censoring happens always at the same value $s$. As far as ...
40 views

### Find Bayesian estimator with random sample from poisson and prior distribution from exponential distribution

Let $X_{1}$ .....$X_n$ be a random sample from Poisson distribution, prior distribution with parameter $\pi(\lambda) = \beta e^{-\beta\lambda}$. Find Bayesian estimator I couldn't take integration ...
58 views

### Properties of conditional maximum likelihood estimators

I am trying to find a source that describes the properties of conditional likelihood estimates like those obtained from conditional logistic regression?
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### mle for the binomial distributed data

For example i have folowing dataset of number of boys in families that have 5 kids: 0 boy - 34(number of such families) 1 boy - 128 families 2 boys - 233 families 3 boys - 267 families 4 boys - 144 ...