# Questions tagged [parameterization]

For questions about how to parameterize some statistical model, or comparisons between different ways to parameterize.

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### Is it possible to reuse predictor fixed parameters in a nonlinear mixed effects model fit across mulitple nonlinear response parameters using nlme?

I have data where I want to fit a model given that I know the value at time zero of one stage is equal to the asymptotic value of the previous stage. In particular, I have kinetic growth curves ...
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### Complex parameterizations of real-valued distributions

Suppose we have some random variable $X$ that takes values in $\mathbb{R}^n$, parameterized by $\theta \in \Theta$ where the parameter space $\Theta$ is finite-dimensional. In almost all statistical ...
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### GLMs and their conditional expectation and variance

Let the density of the distribution of response $y_i | x_i$ in GLMs denote as: $$f(y; \theta, \phi) = \exp\left(\frac{y\theta - b(\theta)}{\phi} + c(y; \phi)\right)$$ Then conditional expectation and ...
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### Reparameterization of Poisson Distribution

In deep learning, especially generative models, sometimes we need to add some random noise to the input of model. To make the sampling of random noise learnable (or differentiable), we need to ...
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### Writing exponential family in canonical form

I have the following pdf with support $x>0$: $$f_{\mu}(x)=\frac{1}{\sqrt{2\pi x^3}}\textrm{exp}\left(-\frac{(x-\mu)^2}{2\mu^2x}\right)$$ This belongs to the exponential family, and I write this in ...
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### What are we modelling when a gamma distribution has non-integer shape parameter

I wish to receive a clear and concise answer as to what is being modeled for a gamma distribution with non-integer shape parameter, and a more detailed derivation of its distribution function for all ...
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### Estimating time varying parameters of ODE with the help of solution data

I am trying to extend a parameter estimation of ODE model from constant parameter estimation to time-varying parameter estimation. I have completed the constant parameter estimation (where parameter ...
258 views

### Weibull distribution parameterization

I have the following Weibull distribution: $f(x;\lambda,\beta) = (\lambda\beta)x^{(\beta-1)}e^{(-\lambda x^b)}$ where $\lambda$ is scale parameter and $\beta$ is shape parameter. I have an ...
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### Is the OLRE term meaningful in the negative binomial model? + Is overdispersion in the NB model an issue?

I'd like to ask three questions regarding the negative binomial (NB) regression / distribution. The NB model with NB2 parameterization ($var(Y_{NB2}) = \mu + \frac{\mu^2}{\theta}$) is sometimes ...
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### What does "parameterized by" mean?

Sometimes I have seen likelihood written as $L(\mu,\sigma |y)$ and sometimes as $L(y|\mu,\sigma)$. I have been told that in the first case it means that there is a pre-assumed model depicting the ...
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### Aren't ALL Parameters Eventually "Nuisance Parameters"?

I am an MBA student taking some courses in statistics. We attended a seminar on GLM Models for Count Data in which the presenter was introducing us to the concept of "Nuisance" Parameters. I ...
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### Differentiation on the conditional variables of a probability

I have been questioning how to calculate the partial derivatives of a conditional probability function with respect to its parameters. Assume $x$ is data and $\theta$ is a parameter(s). If I have a ...
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### Likelihood function-expectation

Given likelihood is a function of parameters, I cannot understand why the expectation of likelihood functions is not calculated with respect to the the parameter space but the sample space, as put ...
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### How many parameters on a Bayesian network

I'm taking Coursera's course on probabilistic graphical models, and I'm stuck on a question. The discussion forums there are dead, and I can't find any resource to help me, so I hope someone could ...
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### Interpretation of coefficients in GLM: coefficients associated to continuous covariates interpreted as MD's or OR's

I was having a discussion with someone regarding OR’s estimated trough a logistic regression and then he claims that OR’s for continuous variables can only be estimated trough a logistic regression. ...
1 vote
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### The effect of over-parameterization on local minima

While reading some papers about over-parameterization in deep learning models, I also read that "over-parametrization is a simple method to introduce additional dimensionality and help make the ...
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### Is there a sampling method to find multiple local minima for a multidimensional parameter space?

Firstly, I just want to declare that I'm not a statistician and I apologize for any obvious errors. Let's say I have a dataset with x and y values. Now, I have a model with 10 parameters/coefficients ...
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### Interpretation of drm parameter estimates and p-values for EXD.3 function in 'drc' package in R

I was wondering if someone could help me understand what the parameter estimates and p-values are saying in a three-parameter exponential decay function using the drm function in the 'drc' package in ...
1 vote
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### Multinomial likelihood function with data for only 2 of 3 outcomes

Can/should I use a binomial likelihood function if the data were generated from a multinomial process (3 possible outcomes) but data were only collected for two of the possible outcomes? In each trial ...
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### Need for reparameterization trick in RL (and others)?

This is a multi-fold question that has a number of closely related questions; that is why I will pose them all here, instead of separate questions. In RL you have a parameterized policy that dictates ...
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### T-distribution parameters with QRM package

I am fitting a t-distribution on some data I have using the fit.st function from the QRM package. The function returns 2 set of ...
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### Is the Jacobian term needed if the prior is on the transformation parameter?

Suppose I have a strictly positive parameter $\sigma$ and I need to estimate it using the random walk Metropolis-Hasting algorithm. I know that I can do a parameter transform, i.e., $\beta=log(\sigma)$...
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1 vote
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### M-estimator: There is no "of something" in the definition

I see that when talking about estimator, we have "of something", where "something" refers to a fixed parameter. For example, we say that the sample mean is an estimator of the ...
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### Why does the von Mises-Fisher distribution need two parameters?

The von Mises-Fisher distribution has two parameters: the mean $\mu \in \mathbb{R}^p$ and concentration $\kappa \geq 0$, where $\mu$ is constrained to have unit norm. Why not instead define the ...
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