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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 ...
wdkrnls's user avatar
  • 297
2 votes
0 answers
24 views

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 ...
Randy Savage's user avatar
6 votes
2 answers
216 views

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 ...
Marlon Brando's user avatar
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0 answers
27 views

Overcoming posterior correlation for a model with random effects (for a Gibbs sampler)

I am trying to infer parameters for a model of case numbers of different infectious diseases in different locations over time. The model is $$ \log \left(1 + y_{ijt}\right)\sim\mathsf{Normal}\left(\mu ...
Till Hoffmann's user avatar
-1 votes
1 answer
48 views

Maximum-LIkelihood Estimation with NLL using parameters in Logscale

Consider the following toy problem: I have a $\mathcal{C}^\infty$ function $f(t,\Theta):[0,t_{\max}] \times (0, \infty)^n \to \mathbb{R}$. I choose some "correct/ground-truth" parameter ...
Paul Joh's user avatar
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0 answers
6 views

Running ARIMA-SEATS with different weekdays

Is it possible to run the Census Bureau's ARIMA X-13 SEATS with, say Sunday-Thursday as working days, or Sunday-Friday, for that matter? I'm running in R with the 'seasonal' package, if that matters.
BlackNinja's user avatar
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141 views

What's the difference and relationship between theta, theta star and theta hat?

I understand that $\theta$ is the true distribution parameter (great explanation here). I also know that $\hat\theta$ is an estimator of the true $\theta$ (so for example, MLE is an example of $\hat\...
HeyJude's user avatar
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1 answer
45 views

parameterize, estimate & interprete interaction terms between two factors in a Cox Proportional Hazard model

Overview I was trying to fit a cox proportional hazard model to look at interactions between two time-constant covariates, both of which are factors. I parameterized the model in two different but ...
Xuan's user avatar
  • 3
1 vote
0 answers
76 views

Determining the Identifiability of Models

I am completing exercises in the book Mathematical Statistics: Basic Ideas and Selected Topics regarding proving or disproving that a model is identifiable. The problem I am struggling with considers $...
YessuhYessuhYessuh's user avatar
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0 answers
16 views

About Estimating Parameters from Unpaired Datasets

I possess three datasets: $x$, $y$ and $z$. It's hypothesized that a relationship exists between these variables, represented by the equation $z=a*x+b*y$. My goal is to estimate the values of $a$ and $...
JING's user avatar
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Defining parameters so that they obey multiple constraints

I'd like to define parameters $\beta_i$ for $i=1,\ldots,I$ for a problem so that they automatically obey some constraints. The constraints are: $\sum_{i=1,\ldots,I} w_i \beta_i = c_1$ and $\sum_{i=1,\...
Björn's user avatar
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3 votes
1 answer
317 views

Is there an exponential family such that its natural parameter mapping is non-invertible or has non-convex range?

On the Wikipedia article for exponential families the density of a distribution on a measure space $(X, \xi)$ from an exponential family is written as $$f_{\theta} \colon X \to \mathbb{R}_{\ge 0}, \...
ViktorStein's user avatar
4 votes
1 answer
365 views

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 ...
Lorin60's user avatar
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1 answer
36 views

Understanding a parameter in a bayesian Poisson model ($\beta$)

I would like to know the meaning or signification of the parameter $\beta$ in this Bayesian model. I have a Poisson model : $ s_{i} \mid \lambda_{i} \sim Poisson(\lambda_{i}t_{i})$ Where $\lambda_i\...
xenuti's user avatar
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2 votes
0 answers
32 views

Bayesian reparametrization are they equivalent?

Suppose that we are in a Bayesian context, we we have the following matrix $n,$ $K\times K,$ as parameter, and we assume that $$n_{ij}\sim Pois(w*w_{ij})$$ where $w\sim Gamma(N+1,1)$ and $w_{ij}$ is ...
Fiodor1234's user avatar
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3 votes
1 answer
404 views

How to extract the correct parameters for the lognormal distribution when using the survreg() function in survival analysis?

I am testing simulation of the lognormal distribution against the lung dataset, as an example of right-censored data, from the ...
Village.Idyot's user avatar
1 vote
1 answer
94 views

Options for transforming the variance-covariance matrix generated by the survreg() function to the original scale of the Weibull distribution?

I'm working with the survreg() function of the R survival package, and I understand that the default scale parameter for the ...
Village.Idyot's user avatar
0 votes
0 answers
61 views

Estimation of Distribution using multiple ECDFs

Every day, I keep track of the processing times for each input to my CPU and create empirical cumulative distribution functions (ECDFs) based on this data. Let's assume I have 100 observations per day ...
smv's user avatar
  • 53
0 votes
1 answer
133 views

Parameterizing a Gaussian distribution

I am reading this blog post where the author talks about diffusion models. Let's keep diffusion out of the conversation for now. The author showcased that we can parameterize a Gaussian distribution ...
enterML's user avatar
  • 378
2 votes
2 answers
631 views

Parameterization of inverse gamma prior in Bayesian methods

For a prior of $\sigma^2 \sim IG(0.01, 0.01)$, often recommended as an uninformative prior for the variance parameter in MCMC approaches and other Bayesian methods, which parameterization does this ...
bob's user avatar
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0 answers
19 views

How to detect an unknown number of segments, each to be fitted with an unknown parametric curve/surface equation?

Let's say I have a set of points (possibly noisy) in an N-dimensional space that represent an arbitrary number of curved segments, each segment having an arbitrary type of curve. See the 2D sample ...
Anson Kao's user avatar
  • 101
1 vote
1 answer
63 views

Excercise 6.1 and its solution in Bishop's PRML, Question 1

The problem comes from Exercise 6.1 of "Pattern Recognition and Machine Learning" by Christopher M. Bishop: Consider the dual formulation of the least squares linear regression problem ...
zzzhhh's user avatar
  • 333
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0 answers
39 views

How do I impose restrictions $ 0\leq \alpha \leq \beta <1$?

I want to restrict values s.t. I get $\theta = (\alpha, \beta) =g(\theta_1, \theta_2)$ with the following restrictions. $ 0\leq \alpha \leq \beta <1 $ I know the correct answer should be $\beta = (...
user773674's user avatar
2 votes
1 answer
249 views

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 ...
pecer10012's user avatar
3 votes
1 answer
194 views

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 ...
Cai's user avatar
  • 83
0 votes
0 answers
80 views

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 ...
Formal_that's user avatar
2 votes
1 answer
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 ...
forecaster's user avatar
  • 8,445
3 votes
1 answer
142 views

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 ...
Eva Šragová's user avatar
7 votes
2 answers
1k views

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 ...
Kirsten's user avatar
  • 803
11 votes
1 answer
1k views

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 ...
stats_noob's user avatar
2 votes
0 answers
41 views

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 ...
Yutaka Tsuzuki's user avatar
1 vote
0 answers
67 views

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 ...
Wenxu's user avatar
  • 11
2 votes
3 answers
290 views

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 ...
João Areias's user avatar
2 votes
1 answer
234 views

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. ...
Nicolas Molano's user avatar
1 vote
1 answer
303 views

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 ...
AGM's user avatar
  • 11
0 votes
0 answers
25 views

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 ...
Agnibha Banerjee's user avatar
2 votes
1 answer
663 views

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 ...
tedwin183's user avatar
1 vote
0 answers
69 views

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 ...
Alex's user avatar
  • 11
0 votes
1 answer
389 views

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 ...
Schach21's user avatar
  • 145
1 vote
1 answer
108 views

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 ...
Mayeul sgc's user avatar
2 votes
1 answer
314 views

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., $\beta=log(\sigma)$...
Ding Li's user avatar
  • 453
1 vote
0 answers
86 views

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 ...
TrungDung's user avatar
  • 852
6 votes
3 answers
2k views

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 ...
Rylan Schaeffer's user avatar
0 votes
1 answer
72 views

More stable reparametrization of a parameter on $(-1,1)$?

Suppose that a distribution contains a parameter $\theta \in (-1,1)$. I want to reparametrize this model in terms of $\beta = h(\theta) \in (-\infty,\infty)$. I am considering: $$h(\theta) = \mbox{...
Calip's user avatar
  • 1
0 votes
0 answers
26 views

Understanding "In Bayesian inference, the difference between data and a parameter is that one is observed (data) and one isn't (parameter)" [duplicate]

In his statistical rethinking course, Richard Mclreath states "In Bayesian inference, the difference between data and a parameter is that one is observed (data) and one isn't (parameter)" I ...
Mir Henglin's user avatar
2 votes
1 answer
411 views

Anova models: different parametrizations give different results

In class our teacher explained that there are different parametrization which can be used to make the design matrix called CornerPoint parametrization: the first coefficient represents the mean value ...
Tortar's user avatar
  • 356
2 votes
1 answer
95 views

Guide to self-starter estimators (parameter initialization) for "simple" functions

Background I have a collection of functions with trainable parameters that I am implementing as Keras model classes, which enables immediate use of a variety of objective functions, optimizers, and ...
Galen's user avatar
  • 9,361
2 votes
1 answer
160 views

Bootstrap instances of a statistic for MLE?

Let's say that I have real-valued random variables, $\{X_1. \cdots, X_n \}$, and some statistic $T(X_1, \cdots, X_n)$ for which I hypothesize might have a distribution $f(T(X_1, \cdots, X_n); \vec{\...
Galen's user avatar
  • 9,361
2 votes
0 answers
60 views

Vanishing partial derivative of least squares w.r.t. Verhulst growth parameter

The Verhulst growth model can be given as $$P(t) = \frac{k}{1+ \left( \frac{k-P_0}{P_0} \right)\exp(-rt)}$$ where $P(t)$ is the population size at time $t$, $k$ is the carrying capacity, $P_0$ is the ...
Galen's user avatar
  • 9,361
1 vote
1 answer
112 views

Function fit to skewed data and non-zero beginning of the function

I would like to find a function that would represent the best fit to represent this type of biological data. More precisely, I would like to estimate expected daily egg production by an insect, based ...
MIH's user avatar
  • 205

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