Questions tagged [parameterization]

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

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17 views

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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18 views

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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18 views

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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49 views

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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Strategies for analyzing the functional relationship between two time series?

Suppose we have time-dependent survey data about name recognition for a political campaign. We're interested in learning how campaign spending effects that name recognition. My interest is in ...
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25 views

Expected value without complete sample space

The book way: Suppose, we have a bag with 8 balls numbered 1-8, we want to estimate the population parameter mean. we note down the entire sample space. (1,1)(1,2).. (8,8) calculate mean of each ...
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Hypothesis test practice question

" Prof. J conducts a hypothesis test on whether the proportion of all students who bike to school (denoted as p) equals 30%. Specifically, Prof. J has H0: p=0.3 versus HA: p≠0.3. He obtains a P-value ...
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Flexible models and parameters

I just started reading Introduction to Statistical Learning with R and I am currently trying to work through the exercises. One of the questions is "What are the advantages and disadvantages of a ...
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188 views

gamma parameter in xgboost

I came across one comment in an xgboost tutorial. It says "Remember that gamma brings improvement when you want to use shallow (low max_depth) trees". My understanding is that higher gamma higher ...
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11 views

Speed of transition parameter constraints

Given a logistic smooth transition regression \begin{equation} y_{t}=x_{t}^{\prime }\beta _{1}(1-{g}(z_{t};\gamma ,\delta ))+x_{t}^{\prime }\beta _{2}{g}(z_{t};\gamma ,\delta )+\varepsilon _{t}% \text{...
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How do I create error bounds after parameter calibration?

I have a power transform $f$ I am applying to an Ornstein-Uhlenbeck stochastic process $\{X(t), t\geq 0\}$: $$dX(t) = \kappa (\mu - X(t)) dt + \sigma dW_{t}.$$ From here, I was able to plug in my ...
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What to do when the meaning of a variable has changed over time?

I have dataset of a company with 2014 data with 15 variables then 2018 data with same 15 variables.I want to combine both the datasets however the meaning of 1 variable has changed meaning that ...
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What’s the difference between k-theta and alpha-beta parameterization for gamma distribution?

In my book “Mathematical statistics with Applications”, written by Wackerly, it’s stated that there are two methods for parameterization of gamma distribution. The first one is k-theta and the second :...
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42 views

Changing a conditional probability to a deterministic function

Suppose that we have a conditional density function $p(y|x;\theta^*)$, where $\theta^*$ represents distribution parameters and are assumed to be deterministic. Is it possible that we write this ...
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1answer
30 views

Different notions of over-parameterization

While reading a paper, I came across the statement This prediction function will be parameterized by a parameter vector $\theta$ in a parameter space $\Theta$. Often, this prediction function ...
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Confused by “mean” and “median” of $\alpha$ parameter in Lognormal Distribution

I read a book and find the following content (Fig.1). It is about lognormal distribution. What confused me is in the red box. In Fig.1, $\alpha$ is said "the mean of $z$ on the log scale". Then I ...
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22 views

Is there a formal relation between weight regularization and compression?

In my understanding, compression, strictly speaking, means that we diminish the amount of data required to describe something, such as a model. E.g. compressing an image file means to create a file ...
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22 views

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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25 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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23 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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73 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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154 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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1answer
71 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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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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167 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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32 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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115 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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101 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
45 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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306 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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1answer
93 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
84 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
44 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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1answer
54 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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89 views

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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1answer
29 views

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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47 views

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
69 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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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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78 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
51 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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249 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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37 views

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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1answer
141 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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1answer
63 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
43 views

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 = \...