# Questions tagged [parameterization]

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

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### 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 ...
32 views

### 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: ...
13 views

### 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 ...
29 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 ...
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 $\mathcal{N}(... 0answers 113 views ### Why are decision trees (especially ID3) non-parametric? I was going through the definition of parametric and non-parametric models. So the parametric are the ones which have a fixed number of parameters that you are trying to learn and this number is ... 0answers 32 views ### State whether the model in question is parametric or non-parametric The number of eggs laid by an insect follows a Poisson distribution with an unknown mean$\lambda$. Once laid, each egg has an unknown chance,$p$, of hatching and the hatching of one egg is ... 1answer 73 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 $$\Pr(... 0answers 23 views ### Strategies for analyzing the functional relationship between two time series? Suppose we have time-dependent survey data about name recognition for a political campaign. We're interested in learning how campaign spending effects that name recognition. My interest is in ... 1answer 26 views ### Expected value without complete sample space The book way: Suppose, we have a bag with 8 balls numbered 1-8, we want to estimate the population parameter mean. we note down the entire sample space. (1,1)(1,2).. (8,8) calculate mean of each ... 0answers 22 views ### Hypothesis test practice question " Prof. J conducts a hypothesis test on whether the proportion of all students who bike to school (denoted as p) equals 30%. Specifically, Prof. J has H0: p=0.3 versus HA: p≠0.3. He obtains a P-value ... 1answer 53 views ### Flexible models and parameters I just started reading Introduction to Statistical Learning with R and I am currently trying to work through the exercises. One of the questions is "What are the advantages and disadvantages of a ... 2answers 5k views ### gamma parameter in xgboost I came across one comment in an xgboost tutorial. It says "Remember that gamma brings improvement when you want to use shallow (low max_depth) trees". My understanding is that higher gamma higher ... 0answers 8 views ### How do I create error bounds after parameter calibration? I have a power transform f I am applying to an Ornstein-Uhlenbeck stochastic process \{X(t), t\geq 0\}:$$dX(t) = \kappa (\mu - X(t)) dt + \sigma dW_{t}.$$From here, I was able to plug in my ... 0answers 46 views ### What to do when the meaning of a variable has changed over time? I have dataset of a company with 2014 data with 15 variables then 2018 data with same 15 variables.I want to combine both the datasets however the meaning of 1 variable has changed meaning that ... 1answer 107 views ### What’s the difference between k-theta and alpha-beta parameterization for gamma distribution? In my book “Mathematical statistics with Applications”, written by Wackerly, it’s stated that there are two methods for parameterization of gamma distribution. The first one is k-theta and the second :... 0answers 98 views ### Changing a conditional probability to a deterministic function Suppose that we have a conditional density function p(y|x;\theta^*), where \theta^* represents distribution parameters and are assumed to be deterministic. Is it possible that we write this ... 1answer 710 views ### Different notions of over-parameterization While reading a paper, I came across the statement This prediction function will be parameterized by a parameter vector \theta in a parameter space \Theta. Often, this prediction function ... 0answers 24 views ### Confused by “mean” and “median” of \alpha parameter in Lognormal Distribution I read a book and find the following content (Fig.1). It is about lognormal distribution. What confused me is in the red box. In Fig.1, \alpha is said "the mean of z on the log scale". Then I ... 1answer 40 views ### Is there a formal relation between weight regularization and compression? In my understanding, compression, strictly speaking, means that we diminish the amount of data required to describe something, such as a model. E.g. compressing an image file means to create a file ... 0answers 30 views ### Mixed parameterization of sample from normal distribution I am studying exponential families and mixed parameterizations. Now, I am told that$$ \mathbf{\theta} = \begin{bmatrix}\mu\\ -\frac{1}{2\sigma^2}\end{bmatrix} $$is the parameter in a variation-... 1answer 30 views ### How can I write an asymmetric-BEKK(1,1,1) model To write a BEKK(1,1) model, I would write something like this,$$H_t=C^*C^{*'}+A_{11}\varepsilon_{t-1}\varepsilon_{t-1}'A_{11}'+ B_{11}H_{t-1}B_{11}' $$How could I extend this to write the BEKK(1,... 1answer 120 views ### good terminology for the parameters of a lognormal distribution? Is there any good short terminology for the two parameters of a lognormal distribution? I have been using mean-log for \mu and volatility for \sigma, where the lognormal variable X has \ln(X) ... 1answer 460 views ### Understanding the definition of a location parameter In some probability distributions, like normal or (non-standard) t distributions etc, there are location parameters such that a change to this parameter leads to the distribution moving rigidly to the ... 1answer 201 views ### Formula for cross-classified (a.k.a., crossed random factors) mixed effects model with interaction between two “second level” variables I have a crossed-classified (Hox, 2010) mixed effects model—also known as crossed random factors (West, Welch, & Galecki, 2015), but I am struggling with how to write the formula for an ... 1answer 175 views ### Some questions about exponential families Regarding the book The Bayesian Choice I understand most of chapter three on exponential families, but there are two parts I have trouble understanding. The first is Consider$$f(x|\theta)=h(x)\... 0answers 38 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$X$and ... 2answers 127 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 ... 0answers 158 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?... 1answer 60 views ### Can every parameter$\Theta$in Bayesian modelling be explained via De Finettis representation theorem My question is the following: I recently got to know (and love) De Finettis representation theorem and I now started to read a Book an Bayesian statistics. However this book simply takes as the ... 1answer 467 views ### Correct understanding of De Finettis representation theorem I am currently interestend in understanding De Finettis representation theorem. As I am only familiar with Frequentist thinking I have some problems to understand its meaning. I have already read the ... 1answer 141 views ### How to identify a Bayesian SEM parameter in R package blavaan I have fit a Bayesian SEM using the R package blavaan. ... 1answer 31 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 ... 1answer 107 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 ... 1answer 61 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 ... 0answers 206 views ### 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 ... 1answer 82 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 ... 0answers 113 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, ... 1answer 37 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$Xto be so distributed, one has \begin{align} & \mu = \... 0answers 71 views ### Linear combination of two non-independent random variables I would like to check if the slope coefficients retrieved from two separate regression models are significantly different. Both models have the same independent variables. The dependent variable (DV) ... 1answer 84 views ### Sampling parameters from exponential family So suppose PDFf_{X|\theta}(x_1,...,x_n;\theta_1,...,\theta_m)$is from the exponential family. Is there any theory or general guidelines for sampling parameters from this PDF? This question is not ... 1answer 40 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 ... 1answer 126 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? $$\lambda\theta y^{\... 1answer 63 views ### Parameters in a neural tensor network I am reading the paper of "Reasoning With Neural Tensor Networks for Knowledge Base Completion". I read it many times but I couldn't understand the parameters that are used especially the parameter U. ... 1answer 282 views ### Generalized Normal Distribution Is there a known distribution, f(x|\theta_1,\theta_2,\theta_3,\theta_4), with the following properties: E(X^n)=\theta_n for n \in \{1, 2, 3, 4\}. If \theta_3=0 and \theta_4=3\theta_2^2, ... 0answers 41 views ### Special cases of distributions under different parameterizations Suppose you have two instances of a distribution that are parameterized differently, and for one of them a certain restriction on the parameter values of the pdf or CDF results (perhaps after some ... 1answer 171 views ### Are the Feller-Pareto and the generalized beta distributions really the same? The Feller-Pareto distribution was originally is defined in terms of a transformed beta distribution. If Y\sim \beta(\gamma_1, \gamma_2) then W=\mu + \sigma\left(\left(1/Y\right) - 1\right)^\gamma=... 1answer 185 views ### How to calculate the probability of the parameters? I am reading the Wikipedia article on posterior probability and I note the expression:$$P(\theta|X) = \frac{P(X|\theta)P(\theta)}{P(X)}$$I understand that$\theta$represents the parameters of the ... 1answer 45 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 = \...
I am struggling to understand the following result from Casella and Berger about sufficiency and completeness for exponential families: Let $X_{1},X_{2},...,X_{n}$ be iid observations from an ...