# Least Squares fitting is equivalent to homoskedastic Normal likelihood fitting

In this module, students will learn how the Least Squares fit statistic can be expressed as a likelihood.

Visits: 2233

# Model validation methods

In this module, students will become familiar with the importance of, and methods for, model validation.

Visits: 3493

# Population standardized regression methods

In this module, students will become familiar with population standardized regression methods when working with data that is expressed as per-capita rates

Visits: 4986

# Logistic (Binomial) regression

In this module, students will become familiar with logistic (Binomial) regression for data that either consists of 1’s and 0’s (“yes” and “no”), or fractions that represent the number of successes out of n trials.  We focus on the R glm() method for logistic linear regression. Continue reading

Visits: 21683

# Poisson regression

In this module, students will become familiar with Poisson regression for count data.  We focus on the R glm() method for linear regression, and then describe the R optim() method that can be used for non-linear models. Continue reading

Visits: 10518

# Students t- and z-tests of sample means, and ANOVA to compare multiple means

In this module we will discuss how to conduct one-sample and two-sample Students t-tests of sample means when the variance of the sample is unknown, testing the equality of the means of several samples, and z-test of sample means when the variance is known.

Contents:

Visits: 8266

Visits: 1252

# Introduction to hypothesis testing

[In this course we will be learning how to formulate figure-of-merit statistics that can help to answer research questions like “Is quantity A significantly greater/less than quantity B?”, or “Does quantity X appear to be significantly related to quantity Y?”.  As we are about to discuss, statistics that can be used to answer these types of questions do so using the underlying probability distribution to the statistic.  Every statistic used for hypothesis testing has an underlying probability distribution.]

Visits: 898

# Bringing together disparate sources of data

In this module, we will discuss how to “mesh” two or more data sets together in order to answer a research question.

Visits: 1925

# Sunspot activity and influenza pandemics: a statistical assessment of the purported association

The R code associated with the analysis presented in the paper Sunspot activity and influenza pandemics: a statistical assessment of the purported association is in sunspot_analysis.R

The file reads in the data files summary_pandemic_data.txt, and sunspot_wolf_and_group_1700_to_2014.txt

The R script produces the following plot, shown in the paper,

Visits: 893

# Incorporating prior belief of parameter estimates into model fits to data

For our models, we often obtain estimates of some of the parameters from prior studies in the literature.  For example, for most diseases, the incubation and infectious periods are usually estimated from observational studies.  For animal populations, the birth rates are also usually estimated from observational studies.

However, these parameter estimates in the literature are not a fixed exact value, and have uncertainties associated with them.  Those uncertainties, when properly taken into account in our fits using the graphical Monte Carlo method, will feed into the uncertainties on the parameters we are trying to fit for. In this module, we will discuss how to incorporate this “prior-belief” of known parameters and their uncertainties into our graphical Monte Carlo fits.

Visits: 2090

# A (sometimes) better method for estimation of confidence intervals compared to the fmin+1/2 method: the weighted mean method

In this past module, we talked about the “fmin+1/2” method that can be used to easily estimate one standard deviation confidence intervals on parameter estimates when using the graphical Monte Carlo method to fit our model parameters to data by minimizing a negative log likelihood goodness of fit statistic.  In this module, we will discuss an alternate method to the fmin+1/2 method for estimating parameter uncertainties, the works for many cases, and also provides an estimate of the covariance matrix of the parameter estimates (something that is very difficult to do with the fmin+1/2 method).

Visits: 3078

Visits: 1533

# temp

[CP_CALCULATED_FIELDS][CP_CALCULATED_FIELDS_VAR name=””]

Visits: 841

Visits: 765

# another test

JavaScript program to calculate multiplication and division of two numbers

1st Number : 2nd Number:

The Result is :

Visits: 1075

Contact Details

Visits: 1378

# Example of applying Least Squares, Poisson likelihood, and Negative Binomial likelihood fitting methods to count data

[This module compares the results of fitting a model to data when Least Squares,  Poisson and Negative Binomial likelihood statistics are optimized]

Visits: 3650

# Monte Carlo methods for assessing uncertainty in model estimates due to uncertainties in parameters

[This module presents Monte Carlo stochastic methods that can be used to assess uncertainty in model estimates due to uncertainty in one or more parameters]

Visits: 1740

# Combining stochastic modelling methods: MCMC and SDE’s

[In past modules, we have discussed Markov Chain Monte Carlo methods and Stochastic Differential Equations with Gaussian noise for stochastic modelling of compartmental models. In this module, we will describe how combing the two has the potential to simultaneously optimize computational efficiency and accuracy]