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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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Can someone explain the concept of parameter didactically to me? [closed]

Let $\mathcal{P}$ denote a family of probability distributions on $\textbf{R}^{n}$. We then use a parametrization to describe $\mathcal{P}$, that is, a map $\theta\rightarrow\mathcal{P}_{\theta}$ from ...
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Estimation of covariance over a range of independent variable

I have a set of data that comprise 2 dependent variables (let's call them $x_1$ and $x_2$) evaluated at different temperatures, T. There is an assumption that for a range of T ($T_0<T<T_1$) ...
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23 views

Mixed parameterization of sample from normal distribution

I am studying exponential families and mixed parameterizations. Now, I am told that $$ \mathbf{\theta} = \begin{bmatrix}\mu\\ -\frac{1}{2\sigma^2}\end{bmatrix} $$ is the parameter in a variation-...
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22 views

How can I write an asymmetric-BEKK(1,1,1) model

To write a BEKK(1,1) model, I would write something like this, $$H_t=C^*C^{*'}+A_{11}\varepsilon_{t-1}\varepsilon_{t-1}'A_{11}'+ B_{11}H_{t-1}B_{11}' $$ How could I extend this to write the BEKK(1,...
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35 views

good terminology for the parameters of a lognormal distribution?

Is there any good short terminology for the two parameters of a lognormal distribution? I have been using mean-log for $\mu$ and volatility for $\sigma$, where the lognormal variable $X$ has $\ln(X)$ ...
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56 views

Understanding the definition of a location parameter

In some probability distributions, like normal or (non-standard) t distributions etc, there are location parameters such that a change to this parameter leads to the distribution moving rigidly to the ...
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47 views

Formula for cross-classified (a.k.a., crossed random factors) mixed effects model with interaction between two “second level” variables

I have a crossed-classified (Hox, 2010) mixed effects model—also known as crossed random factors (West, Welch, & Galecki, 2015), but I am struggling with how to write the formula for an ...
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12 views

Convert regression parameter standard error estimates to standard deviation estimates

Lets say I fit a linear model (in R), of y ~ x: x <- runif(100,0,5) y <- x*0.5 + rnorm(length(x)) summary(lm(y~x)) The summary output returned is: ...
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1answer
163 views

Some questions about exponential families

Regarding the book The Bayesian Choice I understand most of chapter three on exponential families, but there are two parts I have trouble understanding. The first is Consider$$f(x|\theta)=h(x)\...
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30 views

Choosing Gaussian PDF basis bandwidth depending on number of bases and range of data

Summary (details below!) I have a basis expansion of $m$ (univariate) Gaussian PDFs to model the density of a sample $X$. The means of these PDFs are spaced equidistantly through the domain of $X$ ...
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111 views

Testing whether the conditional correlations/covariances differ between two groups

I have two samples of variables $\{y_{1i},y_{2i},x_i,s_i\}$. Where $y_1$ and $y_2$ are binary variables, $x$ is a continuous variable and $s$ is a sample indicator, taking the value 0 in one sample ...
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50 views

How to find parameter $k$ from a negative binomial distribution in R?

I want to find the value of parameter $k$ from my data set. The data set is composed of several populations. Should I calculate the parameter $k$ for each subpopulation, or for the population at large?...
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1answer
41 views

Can every parameter $\Theta$ in Bayesian modelling be explained via De Finetti`s representation theorem

My question is the following: I recently got to know (and love) De Finetti`s representation theorem and I now started to read a Book an Bayesian statistics. However this book simply takes as the ...
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1answer
212 views

Correct understanding of De Finetti`s representation theorem

I am currently interestend in understanding De Finetti`s representation theorem. As I am only familiar with Frequentist thinking I have some problems to understand its meaning. I have already read the ...
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34 views

How to test for differences between model parameter estimates for different datasets?

Description of analysis I am considering grain yield response to available nitrogen with a linear-plateau piecewise regression model for two different field studies, denoted by the variable ...
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1answer
77 views

How to identify a Bayesian SEM parameter in R package blavaan

I have fit a Bayesian SEM using the R package blavaan. ...
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1answer
29 views

Why are mixed effect methods more effective when data are limited

In the study in here, it is said that mixed effects models are better in estimating parameters of a ODE system when there is only very small number of data to estimate the parameters. So, in a ...
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1answer
82 views

From OLS to semi-parametric GAM: parametric vs no-parametric

I am quite new to this kind of topic, but for my master thesis i built an multiple linear regression with OLS. Now I want to control for non-linear relationships using a semi-parametric GAM. My ...
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1answer
33 views

GLMMs, stable isotope distribution analysis

I am currently working with a set of samples of stable isotopic concentrations obtained from a group of individuals. I am trying to process this data through a glmm() from the package lme4 to ...
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How to Interpret Parameter Estimate Output from SPSS [duplicate]

Dear Community Members, Given the outputs of the SPSS analysis, how can the exp (B ) and Beta values be interpreted in terms of odd ratio ? and in relation to how the independent variable affects the ...
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43 views

Calibration of an individual-based model of an epidemic

I am currently developing an individual-based (or agent-based) mathematical model (IBM) of an epidemic. I want to calibrate the transmission parameters in my IBM to match empirical data (epidemic ...
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58 views

Fitting a reinforcement model to reaction time

I have a data set of reaction times in a simple reward/punishment task, in which the rate of feasible trials is probabilistical (around 2/3). After having a look at the reaction times, it seems ...
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Probability distribution over shapes (or: How to parameterize arbitrary polygons)

Has there been work on modeling variations of a 2D shape? E.g., say you want a distribution over 5-sided polygons, or over ellipses, or curved shapes? For simple shapes, like circles, rectangles, ...
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80 views

MCMC/Bayesian Inference Model Fitting: Parameters over-fitting to a sharply peaked data point. How can I fix this?

I am trying to fit three models to a data set: Method: Each measurement has some measurement uncertainty Generate X samples from a gaussian with mean of the measurement and std of the measurement ...
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Is there a standard name for a certain parameter for the beta distribution?

The beta distribution is $$ (\text{constant})\times x^{\alpha-1}(1-x)^{\beta-1} \, dx \quad\text{for } 0\le x\le 1. $$ Supposing $X$ to be so distributed, one has \begin{align} & \mu = \...
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Linear combination of two non-independent random variables

I would like to check if the slope coefficients retrieved from two separate regression models are significantly different. Both models have the same independent variables. The dependent variable (DV) ...
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1answer
62 views

Sampling parameters from exponential family

So suppose PDF $f_{X|\theta}(x_1,...,x_n;\theta_1,...,\theta_m)$ is from the exponential family. Is there any theory or general guidelines for sampling parameters from this PDF? This question is not ...
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37 views

use data of table in R [closed]

I have a table of data that I have already imported in R as variable Dataset and I want to apply the function fitdistr() to my ...
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Parametrization of a model with data-sheet's sensor information or with empirical data

When working with a 3D laser sensor (LiDAR), the volumetric point density versus distance $\rho_r$ can be theoretically worked out taking into account the physical properties of the laser (number of ...
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1answer
54 views

Anyone seen this parametrization of Weibull?

My lecturer uses a parametrization of Weibull that I can't find any where else so I'm wondering are they mistaken. Can anyone confirm if this is legitimate pdf of a Weibull? $$\lambda\theta y^{\...
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1answer
48 views

Parameters in a neural tensor network

I am reading the paper of "Reasoning With Neural Tensor Networks for Knowledge Base Completion". I read it many times but I couldn't understand the parameters that are used especially the parameter U. ...
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228 views

Generalized Normal Distribution

Is there a known distribution, $f(x|\theta_1,\theta_2,\theta_3,\theta_4)$, with the following properties: $E(X^n)=\theta_n$ for $n \in \{1, 2, 3, 4\}$. If $\theta_3=0$ and $\theta_4=3\theta_2^2$, ...
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Special cases of distributions under different parameterizations

Suppose you have two instances of a distribution that are parameterized differently, and for one of them a certain restriction on the parameter values of the pdf or CDF results (perhaps after some ...
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121 views

Are the Feller-Pareto and the generalized beta distributions really the same?

The Feller-Pareto distribution was originally is defined in terms of a transformed beta distribution. If $Y\sim \beta(\gamma_1, \gamma_2)$ then $W=\mu + \sigma\left(\left(1/Y\right) - 1\right)^\gamma=...
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48 views

How to calculate the probability of the parameters?

I am reading the Wikipedia article on posterior probability and I note the expression: $$P(\theta|X) = \frac{P(X|\theta)P(\theta)}{P(X)}$$ I understand that $\theta$ represents the parameters of the ...
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Parameter estimation of 3d model

Suppose we have cost data on some product line, let's say clothing. A simple model of the true cost of the clothing could look something like this: C$_{i,j,k}$ = c$_i \cdot \alpha_j \cdot \beta_k $, ...
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1answer
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How to select optimal observation number n from two marginal distributions?

I have two marginal distributions $(Y_1,Y_2)$ that follow distributions $N(\mu_1,50)$ and $N(\mu_2,100),$ respectively. I can allow for a total of 100 observations to estimate the parameter $\theta = \...
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111 views

Normalizing Flows, Real NVPs and Inverse Autoregressive Flows - Used for Probabilty Density Approximation or for Sampling?

Suppose we have a parametric family $g(x;\theta)$, where $\theta$ are the parameters. As far as I can tell, there are two ways we can use this family to model a probability distribution: Probability ...
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119 views

How to fit parameters of a stochastic model applied to agent modeling?

I have a network of agents, these are modeled roughly according to the paradigm of "Agent_Zero: Toward Neurocognitive Foundations for Generative Social Science". The main feature is that the equations ...
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1answer
169 views

Finding a closed-form solution of nonlinear function for parameter estimation

I've come across this problem of estimating parameters of nonlinear model using closed-form solution. I've read that logarithms can be used for certain forms, but they can't be applied to everything. ...
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191 views

Degrees of freedom of a hierarchical model

I have a nonlinear regression model that has two independent parameters, $a$ and $b$, and one dependent parameter, $c$, which is dependent on the independent parameters $\alpha$ and $\beta$ estimated ...
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How to map 2 vectors on the hyper plane to a similarity metric?

I am working on a face recognition application and one of the features I want to include is to compare if two pictures of $2$ people is the same. I have written code (Convoluted neural network) to ...
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How could one prove that b in the GB2 distribution is a scale parameter?

In the Generalized Beta distribution of the second kind (GB2), where a, p, and q are shape parameters and b is a scale parameter, the pdf is defined on $\mathbb{R}_+$ by: $$ GB2(y;a,b,p,q) = \frac{|a|...
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68 views

Basics of Akaike's Information Criterion in GIS/Hydrology

I have been asked to use the AIC to assess the relative fitness of various terrain wetness index (TWI) methods for predicting soil moisture in a specific study site. The TWI is calculated from a ...
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What set of parameters should I choose for Naive bayes and GBM models so that it creates minimal fitting error?

I understand that different set of parameters has to be chosen for each model so as to avoid under or over fitting. But is there is a 'safe set' of parameters which can be used for the widest range of ...
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Parameter estimation of exponential distribution depending on multiple factors/attributes

for a simulation I’ll need to simulate project delays. I’ve data on 20k projects with delays in quarters. Some of them were finished ahead of plan (i.e. neg. delays) others with a delay of 1-16 ...
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GARCH vs ARCH models - which is more parsimonious?

As I understand the inclusion of the GARCH term, $\sigma^2$, in a GARCH model allows for an infinite number of time series terms, $\epsilon^2$, to influence the conditional variance. Is this the case? ...
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159 views

Merits of reparameterizing the Gamma and inverse Gamma

Wikipedia states that the PDFs for the Gamma distribution is: $$ f(x|\alpha,\beta) = \frac{\beta^\alpha}{\Gamma(\alpha)}x^{\alpha-1}\exp(-\beta x) $$ However, in Rasmussen 2000, the pdf for the ...
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71 views

Optimize a regression forest (Better parameters and how to obtain them)

I'm currently working on sales forecasting. I'm using a Regression Forest to make my forecast. (with MLLib from Spark on Databricks) I'm trying to find what features are useful in my forecasting. ...
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Is this sensible: $P(y_{1}<Y\le y_{2}\mid Y\sim\mathcal{D}(\mu))$

I want to write: $$P(y_{1}<Y\le y_{2}\mid Y\sim\mathcal{D}(\mu))$$ to say: The probability of $Y$ being between $y_1$ and $y_2$ given that $Y$ is a random variable distributed according to ...