Bayesian Linear Models

.title[
# Bayesian Linear Models
]
.subtitle[
## 05 - Diagnostics
]
.author[
### Stefano Coretta
]
.institute[
### University of Edinburgh
]
.date[
### 2023/07/07
]

---

# MCMC chains diagnostics

---

```r
library(bayesplot)
as.array(rt_bm_4) %>% mcmc_trace("b_Intercept", np = nuts_params(rt_bm_4))
```

---

```r
as.array(rt_bm_4) %>%
  mcmc_trace("b_IsWordFALSE:PhonLev", np = nuts_params(rt_bm_4))
```

---

An example of bad MCMC chain mixing.

???

Picture from <https://www.rdatagen.net/post/diagnosing-and-dealing-with-estimation-issues-in-the-bayesian-meta-analysis/>.

---

** `\(\hat{R}\)` and Effective Sample Size**

```r
rt_bm_4
```

```
##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: RT ~ IsWord + PhonLev + IsWord:PhonLev 
##    Data: mald (Number of observations: 3000) 
##   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup draws = 4000
## 
## Population-Level Effects: 
##                     Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept             756.94     47.75   663.50   849.69 1.00     2008     2259
## IsWordFALSE           229.58     68.39    97.23   368.09 1.00     1590     1633
## PhonLev                31.75      6.65    18.93    44.62 1.00     1965     2330
## IsWordFALSE:PhonLev   -13.85      9.48   -32.78     4.28 1.00     1614     1700
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma   339.49      4.49   330.79   348.14 1.00     3106     2214
## 
## Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
```
]

---

# Posterior predictive checks

```r
pp_check(rt_bm_4, ndraws = 100)
```