Questions tagged [parameterization]

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

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3 views

How to find the best or optimal parameter value set for agent based or other kind of modeling?

I am doing agent based modeling (ABM) for infectious disease modeling, and the model has 50+ parameters which can any probability value between 0 and 1, or can be any float value from 0 to >0 (...
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41 views

Incidental parameter problem for fixed effects OLS regression with logarithmic dependent variable on a short panel

I have panel data over 7 years and 6000 observations in total, on which I am running an OLS regression with around 600 fixed effects dummies. The dependent variable is logarithmic. I have heard about ...
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14 views

Mixed parametrization for the multivariate Gaussian using submatrices of the covariance and inverse covariance matrices

I'm interested in specifying a zero-mean multivariate Gaussian distribution with a certain covariance structure over one subset of variables $A$, and a certain inverse covariance structure between the ...
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25 views

Total number of parameters in CNN [closed]

Considering a CNN of 3 convolutoonal layers, each with 5x5 filters, a stride of 2 and same padding. The lowest layer outputs 50 feature maps, the middle one 150 and the top one 500. The input are RBG ...
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Interpreting differences in categorical parameter estimates bayesian model

I've built a model using brms to describe ln-transformed gut length in fishes as predicted by diet, ln-transformed body length, the method used to measure the gut, and a couple of random variables (...
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Parameterization of gamma distribution in XGBoost 'reg:gamma'

I am looking into gamma regression using XGBoost in R. I am trying to understand the negative log-likelihood used in estimating the model. Github has the following ...
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1answer
34 views

What is the parametrization of 'survreg' in the 'survival' R package?

I am fitting AFT models using the command survreg from the R package survival. I want to do some further plots of the hazard ...
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9 views

Are populations related to random variables when discussing parameters?

The term "parameter" (as opposed to a statistic) is defined as a value used to describe a population, but it's also defined as a value used to describe the distribution of a random variable. ...
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8 views

What is the practical way to test for goodness-of-fit of alternative curves?

I have fitted (that is, I have found the best parameters) two curves (Holling type III and Gomperz) to the data (red dots) and obtained the following regression: How can I say which one is a better ...
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53 views

Parameters identifiability / estimation in Bayesian linear state-space models

Is it possible to tell if the parameters can be uniquely estimated in a Bayesian state-space models from the system equations (beyond redundant parameterisations). If so, how? For example, should it ...
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62 views

Identify bad models

Suppose, I have noisy data, which is linear by nature, but I do not know it. I want to fit the data but I do not know the good model so I try with two ''bad'' models. $y=(A_1+B_1)x+C_1$ $y=A_2x^2+...
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Number of parameters and neural networks

In basic statistics one often uses the rule-of-thumb that the number of parameters should not exceed the number of data points. There is obvious intuition behind it, grounded, e.g., in fitting data ...
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Modeling slope effects to measure individual consistency

I am trying to fit a model with some pretty sparse data; I cannot collect more data so please refrain from that suggestion. I do not have a large sample size, so I have issues with singularities for ...
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103 views

What exactly makes a model “overparameterized”?

I often read that training "overparameterized" networks works well in practice, and perhaps no one yet knows exactly why yet. However, when I look at the number of samples and parameters many NNs use, ...
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How to estimate epidemiologic parameters directly from epidemic data?

Is it possible to estimate the parameters needed for an epidemic modelling directly from life tables with numbers of incidence or do these need to be calculated experimentally? IN other words: the ...
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How to fit a time-delay variable to data in R?

I have two datasets that are known (or suspected) to be a similar shape, but with the second dataset delayed by time tau and scaled by a factor mu: F(t) C(t)=mu*F(t+tau) I have data for both C(t) ...
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Is a population parameter really a fixed quantity?

This might be a simple issue. I consistently come across internet sources that say that a population parameter is "fixed" and cannot change. However, if we define, for example, our parameter to be ...
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53 views

Small dataset and optimal parameters for XGboost

I am in the process of tuning the features for my xgboost such as ordinal (label) encoding and one-hot encoding. For example, run the model with column A one-hot ...
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5 views

Estimating Beta distribution parameter from Pert distribution ones

The Pert distribution is a modification of a Beta distribution defined by 3 parameters (a, b, c). Is it possible to specify the underlying Beta from those 3 parameters, transforming them into the ...
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23 views

Redundant Parameter in Random Effects

I am carrying out a mixed model binary logistic regression that predicts whether a student is popular (1 = nuclear popularity; 0 = non-nuclear popularity) from their popularity goals (whether they ...
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48 views

Can someone explain why neural networks are highly parameterized?

I understand that neural networks by definition, are a parametric model. If I am correct, Parametric methods make an assumption about the functional form, or shape, of f. For a neural network, what ...
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Boosting Algorithm: What would happen if you omit the lambda (Make it equal 1 or make it too large) in this algorithm?

Taken from The Introduction to Statistical Learning textbook. I read the excerpt about boosting and have a fine conceptual understanding of the matter. Although I am curious why the learning parameter ...
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How many parameters would the saturated model have if there were no constraints?

In a saturated log-linear model for three variables, the equation is $\lambda+\lambda^A+\lambda^B+\lambda^C+\lambda^{AB}+\lambda^{BC}+\lambda^{AC}+\lambda^{ABC}$ I understand that we have to impose ...
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Number of parameters in sigmoid vs. softmax cross entropy

Assume I have a data point $\mathbf{x} = [x_1, x_2, \ldots, x_D]^\top$ which I want to classify into one of two mutually exclusive categories $\mathcal{C}_0$ and $\mathcal{C}_1$. I can create a simple ...
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52 views

What are the scale and location parameters of the Student's t distribution?

I would like advice on how to correctly set the parameters (loc and scale) for the student T distribution that best fits my data of daily stock returns. I'm pulling random numbers from a student T ...
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“true parameters” in the example of election

A wiki post says In statistics, a confidence interval (CI) is a type of estimate computed from the statistics of the observed data. This proposes a range of plausible values for an unknown ...
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How to convert a likelihood function to a negative log likelihood and perform mle estimation in R

I have data in R constructed as follow. I have Likelihood function as follow. I was wondering how could I convert the likelihood function to neg log likelihood and then estimate the parameters in ...
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72 views

Biased estimator obtained by optimal experiment design

I am using a model-based approach to infer the parameters of a given system. Namely, I represent my system by a model $\mathcal{M}$ with parameters $\theta$. To estimate the true value of $\theta$, I ...
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24 views

Function of a parameter and re-parametrisation

Consider a parametric model with likelihood $f(\mathbf{y};\,\boldsymbol{\theta})$ where $\boldsymbol{\theta}$ is the parameter vector of length $p$ and $\mathbf{y}$ is the vector of observations. ...
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1answer
21 views

How to conclude the best parameter configuration of an optimisation algorithm?

Suppose that one is given an algorithm for solving a specific optimisation problem. This algorithm has various parameters (say, e.g., $p_1$, $p_2$ and $p_3$) that have to be fine-tuned to the ...
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51 views

How could one tune the parameter alpha of the sparse group lasso method (SGL) based on cross-validation?

The sparse-group lasso (SGL) method presented by Simon et al. as follow : $\min _{\beta} \frac{1}{2 n}\left\|y-\sum_{l=1}^{m} X^{(l)} \beta^{(l)}\right\|_{2}^{2}+(1-\alpha) \lambda \sum_{l=1}^{m} \...
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Estimation of errors after differentiation

I have a set of measured values (E, T, p), which I fitted with the following expression: E(T,p) = b1 + b2*T + b3*T*ln(T) + *b4**(p-1) + b5*p*ln(p) I also estimated variances for calculated parametes ...
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How to implement the estimation of parameters in negative binomial distribution in python?

Assuming the negative binomial distribution, How can I implement the estimation to parameters(r & p) especially by MLE? Which function or package should I use? scipy.stats, sympy?
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Why is it easier to estimate $P(X|Y)$ rather than $P(Y|X)$ in terms of number of parameters?

In chapter 3 of the book by Mitchell ("Generative and discriminative classifiers: Naive Bayes and logistic regression") he states that "accurately estimating P(X|Y) typically requires many more ...
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Starting values for an nls model in R [duplicate]

I'm trying to fit an exponential model using nls, but I don't know how to select the starting values for the parameters. I know this question has been answered multiple times, but I spent some days ...
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Fitting SIR model with 2019-nCoV data doesn't conververge

I am trying to calculate the basic reproduction number $R_0$ of the new 2019-nCoV virus by fitting a SIR model to the current data. My code is based on https://arxiv.org/pdf/1605.01931.pdf, p. 11ff: <...
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parameterize distribution of subsets

Suppose there is a set $S=\{1, 2, 3, ..., n\}$, then I need a distribution of its subsets with fixed size k, which can be denoted as $A=\{x_1, x_2, ..., x_k\}$ where $x_1$ to $x_k$ are from 1 to n. ...
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211 views

What is the definition of a scalar parameter?

I'm having trouble understanding what explicity is a scalar parameter. I understand what a location parameter and scale parameter represent but what exactly is the definition of a scalar parameter? ...
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Reparameterize b(K,pi) in terms of theta

Question: $X_1, ... , X_n$ follows a binomial distribution with parameters K and 0 < $\pi\ <1.$ Use properties of Regular Exponential Class of distributions to show that the sample total $T = \...
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Delimit the area in that parameter space that contains 95.4% confidence

Given the equation $y = fc + fe\times \sin(2\pi(x-t_0)/12)$ Considering the two parameters of amplitude fc and fe simultaneously, delimit (using the χ2 variation method) the area in that parameter ...
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85 views

How to parameterize a bivariate Normal distribution output for a neural network?

For a neural net where the output is a Gaussian distribution, the output is usually parameterized as $(\mu=O_1, \sigma^2=e^{O_2})$. That is to say, the neural net will output the mean, and also output ...
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35 views

Robustness of a model to learnt parameters

There is a recent push to study how sensitive a model is to small changes in its input. This has also been studied from an adversarial point of view: e.g what is the smallest input perturbation that ...
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89 views

Why can't algorithms avoid overfitting themselves?

So, I understand overfitting (bonus question: precise statistical definition of overfitting?). You don't want to match the noise in your sample. What I don't understand is why this requires a ...
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Why are these 2 ARIMA formulations equivalent?

In the "Understanding constants in R" section of his book, Hyndman & Athanasopoulos textbook "Forecasting: Principles and Practice" claims that the following AR processes equations are equivalent: ...
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Alternative to plug-in estimation for log-tranformed linear model

I want to estimate a relationship of the form: $$y=ax^b\times\epsilon$$ If I log this model i get: $$\log(y)=\log(a)+b\log(x)+ \log(\epsilon)$$ If I then proceed and estimate this model using a ...
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Estimate distribution of aleatoric variable using Bayesian inference

Given a model as follows: $$y = cx + e$$ where y is the model output, x is the model input, c is an unknown variable and e is a Gaussian model error with zero mean: $$e \sim N(0,\sigma)$$ Data is ...
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Is this parametrization identifiable?

So I have this problem which I'm unsure of my answer. Any tip on how to treat it differently is more than welcome. X and Y are independent $\mathcal{N}(\mathcal{\mu_1},\sigma^2)$ and $\mathcal{N}(...
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Why are decision trees (especially ID3) non-parametric?

I was going through the definition of parametric and non-parametric models. So the parametric are the ones which have a fixed number of parameters that you are trying to learn and this number is ...
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State whether the model in question is parametric or non-parametric

The number of eggs laid by an insect follows a Poisson distribution with an unknown mean $\lambda$. Once laid, each egg has an unknown chance, $p$, of hatching and the hatching of one egg is ...
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The meaning of a parameterization of the logarithmic distribution

In calculus one learns that $$ p + \frac{p^2} 2 + \frac{p^3} 3 + \frac{p^4} 4 + \cdots = -\log(1-p). \tag 1 $$ Thus a discrete probability distribution on the set $\{1,2,3,\ldots\}$ is given by $$ \Pr(...

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