Statistical inference

(a)| This question asks you to consider a Bayesian approach to inference about .1, the mortality rate in an exponential model for survival time. In order to take a Bayesian approach, we specify a prior distribution for A which is gamma distribution. I Show that the gamma distribution is a conjugate prior distribution for the exponential model, i.e. if we specify that 1"\"Gamma (a, ,3} a priori, then the posterior distribution is also Gamma, with parameters that depend on a, [3,113. o Provide expressions for the parameters of this Gamma posterior distribution, and for the mean and mode of the posterior distribution. 1. Briefly describe the steps involved in conducting phylogenetic inference using parsimony 2. Why is using parsimony with morphological data problematic? (Hint: imagine character - 'wings' of bats, humans, mice and butterflies. Based on parsimony, bats and butterfly will be put together. How is that a problem?) 3. The eyes of an octopus and human look very similar but they do not share a common ancestor. This is an example of a(n) a. Homoplasy b. Homology C. Synapomorphy d. Plesiomorphy e. Apomorphy 4. What does it mean for a trait to have an appropriate amount of variation for a use in a phylogenetic analysis? Use examples 5. Which statement(s) is/are true about Bayesian method? a. Bayesian searches for trees with highest posterior probability b. It is based on Bayes theorem C. Does not use models for tree inference d. Utilizes prior information/probability C. Same principle as maximum parsimonyDirections: Identify whether each statement describes inferential statistics or descriptive statistics. Circle the correct response. 33) The average age of the students in a statistics class over 22 years. A) descriptive statistics B) inferential statistics 34) The chances of winning the California Lottery are one chance in twenty-two million. A) descriptive statistics B) inferential statistics 35) There is a relationship between smoking cigarettes and getting emphysema. A) inferential statistics B) descriptive statistics 36) From past figures, it is predicted that 41% of the registered voters in South Carolina will vote in the next June primary. A) descriptive statistics B) inferential statistics 37) Based on previous clients, a marriage counselor concludes that the majority of marriages that begin with cohabitation before marriage will result in divorce. A) descriptive statistics B) inferential statistics45) B) random sampling Dj stratified sampling Identify whether the statement describes inferential statistics or descriptive statistics. 46) The average age of the students in a statistics class is 21 years. 46 A) descriptive statistics B) inferential statistics 47) Based on previous clients, a marriage counselor concludes that the majority of marriages that 47) begin with cohabitation before marriage will result in divorce. A) inferential statistics B) descriptive statistics