yada_sample_mcmc: Sample a likelihood function at a given temperature using an...

In MichaelHoltonPrice/yada: Yet Another Demographic Analysis package

Description

Given an input negative log-likelihood and temperature, do MCMC sampling of the parameter vector. Let eta be the value of the negative log-likelihood. The function that is sampled is exp(-eta/temp), where temp is the temperature; that is, the likelihood^(1/temp) is sampled. The proposal is made using an independent normal draw for each variable in the parameter vector, theta, with the standard deviation of the proposal distribution set by the scalar parameter prop_scale (the same scale is used for all variables).

The output is a list with starting and sampling information ,and includes the following named elements:

• theta0 The initial value of the parameter vector

• eta0 The initial value of the negative log-likelihood

• temp The temperature

• prop_scale The scale (standard deviation) for the normal proposal distribution

• theta_best The best parameter vector found (lowest negative log-likelihood)

• eta_best The best (lowest) negative log-likelihood encountered

• accept_vect A boolean vector indicating which samples were accepted

• eta_vect A vector of negative log-likelihood values (for kept samples)

• eta_vect A matrix of sampled parameter vectors, size num_samp by length(theta)

Usage

yada_sample_mcmc(neg_log_lik, theta0, num_samp, temp, prop_scale, ...)

Arguments

neg_log_lik	The function for the negative log-likelihood
theta0	The initial value of the parameter vector
num_samp	The number of samples to make
temp	The temperature
prop_scale	A scalar value for the standard deviation of the proposal distribution
...	Variables required by neg_log_lik

Value

A list containing starting and sampling information (see description)

MichaelHoltonPrice/yada documentation built on Sept. 19, 2021, 11:27 p.m.