# Questions tagged [parameterization]

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

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### Fitting variable-dependent normal distribution to data

Given a sample, one can usually find the best fitting normal distribution by matching the mean and variance. What's the correct way to fit a normal distribution to data when the parameters aren't ...
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### Does it make sense to worry about stability of parameters?

I'm working on a problem where I'm using grid search on logistic regression and I'm checking two parameters, penalty and C. I ...
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1 vote
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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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### Which data do you use when finding parameters for your model after cross-validation?

Let's say I have a dataset (X, Y) for which I want to find the best fitting polynomial model (say degree = 1 through 10) using k-fold CV. Let's say after doing k-fold CV on degrees 1 through 10, I ...
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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### Likelihood in Bayesian inference: p(x|theta, I) = p(x| I)?

In page 164 of the book “Probability theory: the logic of science” the author says that: $$p(D|\theta I) = \prod_{i=1}^{n} p(x_i|\theta I) = \theta^r(1-\theta)^{n-r}$$ $\theta$, in this equation, ...
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### Can I still use parametrical test if Shapiro-wilk test saying that my data is not normally distributed?

My data are mostly 0 and 1 so therefore I can't pass normality test. Can I still use parametric tests like repeated measures anova to test for significance? If the answer is yes, how can I justify ...
18 views

### How do I calculate the probability according to a geometric distribution given the value of X, its mean and its variance? In R

I want to predict a time series of intermittent demand items. For this, I want to use a geometric distribution for the demand sizes. How do I get the probability that X = k - according to a geometric ...
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### Parameter estimation of a model with exponential almon lag structure

Suppose I have the following model: $$y_t = \beta_0\sum_{i=0}^p w(\delta;i)x_{t-i}$$ Where $\displaystyle w(\delta;i)=\frac{\exp(\delta_1 i+ \delta_2 i^2)}{\sum_{i=0}^p \exp(\delta_1 i+ \delta_2 i^2)}$...
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### How to perform Chow Test on balanced panel data with multiple breakpoints simultaneously?

I'm currently working with a balanced panel data dataset. I have 27 individuals over a 7 year period. My objective is to perform a Chow Test to determine if ANY of the estimated parameters change from ...
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### Standard error in parametrization

I calibrated the parameters of the GARCH model. Now I would like to calibrate the standard errors in MATLAB of the parameters but I don't know how to do it, can someone explain me how?
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### Amortized inference in convolutional variational autoencoders

VAEs are an efficient way of performing variational inference at scale. I read that VAEs employ the strategy of amortized variational inference. They approximate the intractable posteriors p(zjx) by ...
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### Parameter simplification of ARIMA model

I am constructing an ARIMA model on a cryptocurrency price time series. Using the autocorrelation and partial autocorrelation plots I came to the parameters of (p,d,q)=(3,1,2). The resulting RMSE was ...
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### Effect of scaling data on ARMA coefficients [duplicate]

For numerical stability, I thought it might be a good idea to scale my data before feeding them into an ARMA GARCH model. I have gone through a few older posts and understand the affect scaling ...
• 159
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### Bayesian parameter optimization of a Voight matrix

I have constructed a finite element model of a musical instrument. The physical properties of the wood were very difficult to obtain and as they are anisotropic they need all 3 dimensions. I am ...
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1 vote
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### What is exactly the structure included in a parameter space?

According to Wikipedia, a space in mathematics is: a set (sometimes called a universe) with some added structure. In statistical literature, I usually find references to a parameter space in the ...
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1 vote
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### ARMA GARCH fitting

I've made a few posts regarding a manual ARMA GARCH implementation and I have made some great progress. However, I am still shy of a working program as I am obtaining some rather large forecasts. I've ...
• 159
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### Issues Manually Implementing ARMA GARCH

I have been working on manually implementing an ARMA GARCH (1,1) model but have been running into a few issues, namely a very large forecasted variance. I am hoping by outlining my process someone can ...
• 159
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### Fitting ARMA GARCH

I am interested in fitting an ARMA GARCH model by hand (that is without the use of a package such as rugarch), but am unclear on how the parameters are estimated. I have read that one should use MLE, ...
• 159
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### How to fit ARMA-GARCH parameters for any distributions

To better understand the ARMA-GARCH model I am working on implementing it while avoiding as many packages as I can. For data I am working on returns and for simplicity I am starting with ARMA (1,1) ...
• 159
67 views

### Change of metric for probability density vs for probability

When one changes the variable in a probability density function, one must account for the jacobian to ensure the elementary probability is constant (eg Derivation of change of variables of a ...
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### What are parametric conditions?

My dissertation supervisor asked me to explain further the following question for a GARCH model: "what are the alpha's and the beta's and what are their parametric conditions, and what do the ...