In the proposed methodology, reda counts (RNA sequencing) are analyzed using a negative binomial distribution model, as the observed variance significantly exceeds the mean. To evaluate the model’s performance in predicting read count parameters, a single-group scenario is considered. Noise reduction in read count prediction is the primary objective, and to achieve this, a synthetic dataset is created using the following code:

```
xreal = np.random.randint(1, 50, 10)
```

By incorporating plausible values for the parameters `alpha_noise`

, `beta_noise`

, `gamma_noise`

, and the dispersion `rj`

, the predicted read count is obtained:

```
alpha_noise = 0.7
beta_noise = 0.3
gamma_noise = 0.25
# dispersion
rj = 5
xpred = xreal * alpha_noise + xreal * beta_noise + xreal * gamma_noise
xExpirm = pm.NegativeBinomial.dist(mu=xpred, alpha=rj).eval()
```

To account for the absence of real counts prior to noise addition, xi parameters are incorporated into the model. Furthermore, a regularized coefficient is included to address potential differences in noise between parameters. Prior information for the noise parameters is as follows: `alpha_noise`

ranges from 0 to 1, `beta_noise`

varies between 0.5 and 0.25, and `gamma_noise`

has no specific knowledge, falling within the range of 0 to 1. Additionally, the dispersion parameter lacks substantial prior information.

After running the model, the predictions obtained are unsatisfactory. **Could anyone provide guidance or suggestions on potential errors or improvements that could be made to enhance the model’s performance?**

```
with pm.Model() as model:
alpha_noise = pm.Beta("alpha_noise", 3, 2)
beta_noise = pm.Beta("beta_noise", 3, 2)
gamma_noise = pm.Beta("gamma_noise", 3, 2)
# Prior for the unknown xi values
xi = pm.Uniform("xi", lower=0, upper=np.max(xExpirm), shape=len(xExpirm))
# Regularized coefficients
reg_param = 0.1 # You can adjust this parameter based on your knowledge about the problem
reg_alpha = pm.Laplace("reg_alpha", mu=alpha_noise, b=1 / reg_param)
reg_beta = pm.Laplace("reg_beta", mu=beta_noise, b=1 / reg_param)
reg_gamma = pm.Laplace("reg_gamma", mu=gamma_noise, b=1 / reg_param)
count_data_est = reg_alpha * xi + reg_beta * xi + reg_gamma * xi
r = pm.Exponential("r", 0.5)
obs_data = pm.NegativeBinomial("obs_data", mu=count_data_est, alpha=1/r, observed=xpred)
trace = pm.sample(15_000, tune=20_000,target_accept = 0.9)
```