Wyara Moura - Blog Posts

EM Question

inference

probability

EM

MLE

casella and berger

An alternative to the model in Example 7.2.17 (Casella and Berger, 2002) is the following: we observe \((Y_{i}, X_{i})\), \(i = 1, 2, \cdots, n\), where \(Y_{i} \sim…

Probit Model

bayesian statistics

probability

conditional probability

probit

Mostrar a equivalência dos seguintes modelos probitos e obter as distribuições condicionais completas para \(\beta\) e \(u_{i}\) assumindo uma priori normal para \(\beta\).

Characteristic Function (Question)

characteristic function

independence

probability

continuity theorem

resnick

Suppose \(X_{n}\) and \(Y_{n}\) are independent for each \(n\) and \[\begin{equation*} \begin{array}{lclllllll} X_{n} & \Rightarrow & X_{0}, \hspace{2ex} Y_{n} & \Rightarrow…

Linear Regression (Question)

linear regression

quadratic forms

estimator

Let \(\mathbf{X} = (X_{1}, X_{2}, \cdots, X_{n})^{\top}\) be a vector of independent and identically distributed random variables with \(\mathbb{E}(X_{i})=\mu\) e \(\mathbb{V…

Brook’s Lemma

brook's lemma

spatial statistics

probability

Suppose \(Y_{1}\) and \(Y_{2}\) are both binary variables, and that their joint distribution is defined through conditional logit models. That is,

`Jul 16, 2023`{=html}

Summer 2023

probability

tests

expected value

This summer, I attended ‘The Summer Program in Mathematics, UFMG 2023’ and I took the Introduction of Probability Theory course, below you can find the first test of the…

Central Limit Theorem (Question)

Application of the central limit theorem involving Poisson distribution.

probability

central limit theorem

poisson

Use the central limit theorem to verify that,

Newton-Raphson’s method for Weibull distribution

R

code

analysis

Let \(X_{i} \sim \mbox{Weibull}(\alpha, \beta)\) then,

Materials from Probability and Inference Courses

tests

latex

probability

inference

Some materials from the isolated courses that I took last year in the master program of statistics at UFMG. (All pdf materials are in portuguese.)