Statistical Principles for the Biological Sciences, Fall 2015

Thursday October 8

Tuesday, August 24

Introduction, read p. 56-65 Appendix

and section 1.4.4 p. 72-73

Thursday, August 27,

-Conditional Probability: why is it useful?

-Introduction to discrete random variables,

Read pages 66-75 of the notes for next class

Tuesday, September 1st

-Elementary properties of

discrete random variables, Expected values and variances

-examples

For Thursday 3rd: no reading necessary, we will continue with Expected values

Thursday, September 3rd

-More on expected values

-Conditional probability distributions

-Conditional expectation

-Mark-recapture, sampling with replacement

-R program for the hierarchical binomial survival model.

Tuesday, September 8

-Mark-recapture, sampling with replacement

-The binomial distribution

-The likelihood function

Thursday, September 10

-Mark-recapture, sampling without replacement

-The hypergeometric distribution

– Comparison with sampling with replacement using means, variances and covariances

-Why adopting different probability models for the same experimental setting is important?

-Relationship between the binomial model and the hypergeometric model using conditional probability!!

Tuesday, September 15

 

-Introduction to the Poisson Process as a limit to the Binomial model

Thursday, September 17

– -Introduction to the Poisson Process as a limit to the Binomial model

 Tuesday September 22

Waiting times: introducing the exponential distribution using a Poisson process.

How do you write the likelihood function for a continuous probability model?  The MLE of the exponential rate parameter

 

 Thursday September 24

Waiting times until the kith event:  introducing the Gamma distribution using a Poisson process

-The Gamma function

– Connections between the Gamma model and the Poisson process

 

Tuesday September 29

-Heterogeneity in Ecology, pages 28-32 of the class notes:

-the negative binomial distribution

-the zero inflated poisson distribution

 Thursday October 1st

Note pages 32-41:

Probability Generating Functions and

-the geometric distribution

-the negative binomial distribution

-the log-series distribution

-Return HW to students!!!

 

Tuesday October 6

 

Note pages 32-41:

Probability Generating Functions and

-the geometric distribution

-the negative binomial distribution

-the log-series distribution

Thursday October 8

-The Multinomial distribution, part I

 Tuesday October 13

-The Multinomial distribution, part II

-Likelihood Ratio test

-Multinomial Goodness of fit test

Thursday October 15

-Fitting the Poisson process data to counts, comparing to Negative Binomial, Zero Inflated Poisson, and other models.